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0 HcmV?d00001 diff --git a/tests/testthat.R b/tests/testthat.R deleted file mode 100644 index fc5e0cb..0000000 --- a/tests/testthat.R +++ /dev/null @@ -1,4 +0,0 @@ -library(testthat) -library(ESGtoolkit) - -test_check("ESGtoolkit") diff --git a/vignettes/ESG2toolkit_Intro_012020-concordance.tex b/vignettes/ESG2toolkit_Intro_012020-concordance.tex deleted file mode 100644 index 01d0bc8..0000000 --- a/vignettes/ESG2toolkit_Intro_012020-concordance.tex +++ /dev/null @@ -1,4 +0,0 @@ -\Sconcordance{concordance:ESG2toolkit_Intro_012020.tex:ESG2toolkit_Intro_012020.Rnw:% -1 267 1 49 0 4 1 4 0 16 1 4 0 18 1 4 0 14 1 4 0 8 1 23 0 9 1 11 0 22 1 % -4 0 6 1 11 0 23 1 4 0 24 1 4 0 24 1 6 0 12 1 4 0 10 1 6 0 19 1 15 0 7 1 % -6 0 8 1 4 0 12 1 6 0 44 1 18 0 21 1} diff --git a/vignettes/ESG2toolkit_Intro_012020.Rnw b/vignettes/ESG2toolkit_Intro_012020.Rnw deleted file mode 100644 index 80abb42..0000000 --- a/vignettes/ESG2toolkit_Intro_012020.Rnw +++ /dev/null @@ -1,568 +0,0 @@ -%\VignetteEngine{knitr::knitr} -%\VignetteIndexEntry{ESGtoolkit} -\documentclass[a4paper]{article} -\usepackage[british]{babel} -\usepackage[sc]{mathpazo} % Use the Palatino font -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage[colorlinks,linkcolor=red, citecolor=blue, urlcolor=red]{hyperref} -\usepackage{xcolor} -\usepackage{url} -\usepackage{float} -\usepackage{amssymb,amsfonts,amsmath} -\usepackage{graphicx} -\usepackage{latexsym} -\usepackage[authoryear]{natbib} -\usepackage{fancyhdr} % Headers and footers -\pagestyle{fancy} % All pages have headers and footers -\fancyhead{} % Blank out the default header -\fancyhead[C]{\code{ESGtoolkit}, tools for stochastic simulation $\bullet$ January 2020} % -\date{} -\newcommand{\CC}{\ensuremath{\mathbb{C}} } -\newcommand{\NN}{\ensuremath{\mathbb{N}} } -\newcommand{\RR}{\ensuremath{\mathbb{R}} } -\newcommand{\QQ}{\ensuremath{\mathbb{Q}} } -\newcommand{\EE}{\ensuremath{\mathbb{E}} } -\newcommand{\PP}{\ensuremath{\mathbb{P}} } -\newcommand{\noi}{\noindent} -\newcommand{\II}{\mbox{\large 1\hskip -0,353em 1}} -\newcommand{\dps}{\displaystyle} -\newcommand{\ms}{\medskip} -\newcommand{\itb}{\ms\item[$\bullet$]} -\newcommand{\itm}{\ms\item} -\newcommand{\pkg}[1]{{\normalfont\fontseries{b}\selectfont #1}} -\newcommand{\proglang}[1]{\textsf{#1}} -\newcommand{\code}[1]{\mbox{\texttt{#1}}} -\newcommand{\MN}{\mathcal{N}} -\newcommand{\MM}{\mathcal{M}} -\newcommand{\FF}{\mathcal{F}} -\newcommand{\GG}{\mathcal{G}} -\newcommand{\HH}{\mathcal{H}} -\newcommand{\LL}{\mathcal{L}} -\newcommand{\AT}{\mathcal{A}} - - -\begin{document} - -\title{\bf{\code{ESGtoolkit}, a tool for stochastic simulation (\code{v0.2.0})}} % Article title -\author{ -Thierry Moudiki\\ % Your name -%\url{http://thierrymoudiki.wordpress.com}\\ % Your institution -\today{} -%\href{mailto:thierry.moudiki@gmail.com}{thierry.moudiki@gmail.com} % Your email address -} -\maketitle - -\tableofcontents - -\newpage - -\section{Overview} - -\subsection{Context} - -Initially, I developped this package for insurance. In 2014. \textbf{If you're not working in insurance, \code{ESGtoolkit} is still relevant for stochastic simulation} in Finance, Economics, or Physics (...). In that case, you can start directly by reading \ref{sec:simdiff}. Oh, in this section, read at least this paragraph: \ref{para}. - -\medskip - -An \textit{Economic Scenario Generator} (ESG) is a tool for projection of plausible future paths of insurers' financial assets. It helps in pricing its products, and assessing its current and future solvency. Two types of ESGs are generally needed: a \textit{real-world} ESG, and a a \textit{market consistent} ESG. - - -\medskip - -The aim of a real-world ESG is to produce projections of risk factors, whose patterns are coherent with the past distribution of those risk factors. Real-world scenarios are mainly used for the valuation of solvency requirements. - -\medskip - -A market consistent ESG shall produce projections of risk factors that are coherent with market prices observed at the valuation date. Market consistent scenarios are mainly used for the best estimate valuation of technical reserves. - - -\medskip - -Hence, in real-world simulations the historical probability is used and in market consistent simulations, the projection of risk factors is made in a risk-neutral probability. A risk-neutral probability measure is a measure under which the discounted prices of assets are martingales. - -\medskip - -A simple example of transitioning from a simulation under the historical probability to a simulation under a risk-neutral probability can be made by using the Black-Scholes model, a geometric Brownian motion. In a real-world simulation, we can assume that an asset evolves according to the following Stochastic Differential Equation (SDE) (with a drift $\mu$, a volatility $\sigma$, and $\left( W(t) \right)_{t \geq 0}$ being a standard brownian motion): - -\begin{equation} -dS(t) = \mu S(t) dt + \sigma S(t) dW(t) -\end{equation} - -\medskip - -Let $r$ be a constant risk-free rate. $e^{-rt}S(t)$, the discounted price of $S(t)$, will be a martingale if -\begin{equation} -d(e^{-rt}S(t)) -\end{equation} - -is driftless. Applying Ito's formula to $e^{-rt}S(t)$, we have : - -\begin{eqnarray} -d(e^{-rt}S(t)) &=& -r e^{-rt} S(t) dt + e^{-rt} dS(t) - \frac{1}{2}.0 \\ - &=& -r e^{-rt} S(t) dt + e^{-rt} \mu S(t) dt + e^{-rt} S(t) \sigma dW(t) \\ - &=& e^{-rt} S(t) \left[ (\mu - r) dt + \sigma dW(t) \right] -\end{eqnarray} - -Thus, the drift vanishes iff $\mu = r$. That is, if our asset with price $S(t)$ at time $t$ rewards the risk-free rate $r$. Under this martingale probability measure, asset price dynamics over time can be re-written as: - -\begin{equation} -dS(t) = r S(t) dt + \sigma S(t) dW^*(t) -\end{equation} -Where $\left(W^*(t)\right)_{t \geq 0}$ is a standard brownian motion under the chosen risk-neutral measure. - -\medskip - -As we'll see in section \ref{sec:simdiff}, \code{ESGtoolkit} does not directly provide multiple asset models but instead, some building blocks for constructing a variety of these. Two main functions are therefore provided for his purpose: \code{simshocks}, \code{simdiff}. Other tools for statistical testing and visualization are presented as well. - -\paragraph{As a reminder:} -\label{para} -There are no perfect models, and the more sophisticated doesn't necessarily mean the most judicious. To avoid possible disasters, it's important to know precisely the strengths and weaknesses of a model before using it. - -\subsection{\code{simdiff}} -\label{sec:simdiff} - -Let $(W(t))_{t \geq 0}$ be a standard brownian motion. \code{simdiff} makes simulations of a diffusion process $(X(t))_{t \geq 0}$, which evolves through time according to the following equation: - -\begin{equation} -\label{eq:genericsde} -\textcolor{blue}{dX(t) = \mu(t, X(t)) dt + \sigma(t, X(t))} \textcolor{red}{dW(t)} + \textcolor{green}{\gamma(t, X(t-), J)dN(t)} -\end{equation} - -\medskip - -Actually, (Eq. \ref{eq:genericsde}) is a generic formulation of all \code{simdiff} models. {\bf Not all parts of this expression are required all the times}, but $\textcolor{blue}{\sigma(t, X(t))} \textcolor{red}{dW(t)}$, describing our process' volatility. Let's describe the other parts. - -\medskip - -$\textcolor{green}{\gamma(t, X(t-), J) dN(t)}$ is optional. It contains jumps of the process, that occur according to a homogeneous Poisson process $(N(t))_{t \geq 0}$ with intensity $\lambda$. The time elasped between two jumping times follows an exponential $\epsilon(\lambda)$ distribution; and the number of jumps of the process on $[0, t[$ follows a Poisson distribution $\mathcal{P}(\lambda t)$. The magnitude of the jumps is controlled by $J$. - -\medskip - -Now, for the \textcolor{blue}{blue part} of (Eq. \ref{eq:genericsde}), we could have: - -\begin{itemize} - -\item An Orsnstein-Uhlenbeck process; for \code{simdiff} used with parameter \newline \code{model = "OU"}, and parameters \code{theta1}, \code{theta2} and \code{theta3} provided (if \code{theta1} or \code{theta2} are not necessary for building the model, they are to be provided and set to \code{0}): -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& (\theta_1 - \theta_2 X(t))\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_3\\ -\end{eqnarray*} - -\item A Cox-Ingersoll-Ross process; for \code{simdiff} used with parameter \newline \code{model = "CIR"}, and parameters \code{theta1}, \code{theta2}, \code{theta3} provided (if \code{theta1} or \code{theta2} are not necessary for building the model, they are to be provided and set to \code{0}) : - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& (\theta_1 - \theta_2 X(t))\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_3 \sqrt{X(t)}\\ -\end{eqnarray*} - -\item A Geometric Brownian motion, or \textit{augmented} versions; for \code{simdiff} used with parameter \code{model = "GBM"}, and parameters \code{theta1}, \code{theta2}, \code{theta3} provided. For the sake of clarity, the argument \code{model} is set to \code{"GBM"}, but not only the Geometric Brownian motion with constant parameters is available. We could have : - -A Geometric Brownian Motion - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1 X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2 X(t)\\ -\end{eqnarray*} - -A modified Geometric Brownian Motion, with time-varying drift and constant volatility - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1(t) X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2 X(t)\\ -\end{eqnarray*} - -A modified Geometric Brownian Motion, with time-varying volatility and constant drift - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1 X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2(t) X(t)\\ -\end{eqnarray*} -\end{itemize} - -It's technically possible to have both $\theta_1$ and $\theta_2$ varying with time (both provided as multivariate time series). But it's not advisable to do this, unless you know exactly why you're doing it. - -\medskip - -Jumps are available only for \code{model = "GBM"}. The jumps arising from the Poisson process have a common magnitude $J = 1+Z$, whose distribution $\nu$ is either lognormal or double-exponential. Between two jumps, the process behaves like a Geometric Brownian motion, and at jumping times, it increases by $Z$\%. For lognormal jumps (Merton model), the distribution $\nu$ of $J$ is: -\begin{equation} -log(J) = log(1+Z) \sim \MN(log(1+\mu_Z) - \frac{\sigma_Z^2}{2}, \sigma_Z^2) -\end{equation} - -For double exponential jumps (Kou's model), the distribution $\nu$ of $J$ is: - -\begin{equation} -log(J) = log(1+Z) \sim \nu(dy) = p\frac{1}{\eta_u} e^{- \frac{1}{\eta_u}} \II_{y > 0} + (1-p)\frac{1}{\eta_d} e^{\frac{1}{\eta_d}} \II_{y < 0} -\end{equation} - -Hence for taking jumps into account when \code{model = "GBM"}, optional parameters are to be provided to \code{simdiff}, namely: - - -\begin{itemize} -\item \code{lambda}: intensity of the Poisson process -\item \code{mu\underline{ }z}: average jump magnitude (only for {\bf lognormal} jumps) -\item \code{sigma\underline{ }z}: standard deviation of the jump magnitude (only for {\bf lognormal} jumps) -\item \code{p}: probability of positive jumps (only for {\bf double exponential} jumps) -\item \code{eta\underline{ }up}: the mean of positive jumps (only for {\bf double exponential} jumps) -\item \code{eta\underline{ }down}: the mean of negative jumps (only for {\bf double exponential} jumps) -\end{itemize} - -\medskip - -\code{simdiff}'s core loops are written in C++ \textit{via} \href{http://cran.r-project.org/web/packages/Rcpp/index.html}{Rcpp} because: speed. Currently, for an Ornstein-Uhlenbeck process with \code{model = "OU"}, a Cox-Ingersoll-Ross process with \code{model = "CIR"}, or a geometric brownian motion with \code{model = "GBM"}, an exact simulation is used, which means there's no discretization of $(X(t))_{t \geq 0}$ on a time grid. You can also choose an \code{horizon} of projection and a sampling \code{frequency} (annual, semi-annual, quarterly $\ldots$). \code{simdiff}'s output is a time series object created by base \proglang{R} function \code{ts()}. And since this output is a \code{ts()} object, it means you can use \proglang{R} functions such as \code{window.ts} or \code{frequency} on it. - -\medskip - -For a customized simulation of $\textcolor{red}{\epsilon} \sim \MN(0, 1)$ embedded in (Eq. \ref{eq:genericsde}) \textit{via} $\textcolor{red}{dW(t) = \epsilon dt}$, you can fill \code{simdiff}'s parameter \code{eps} with an output of function \code{simshocks}. \code{simshocks} is described in the next section, \ref{sec:simshocks}, and an example of such a procedure is described in \ref{sec:examples}. - - -\subsection{\code{simshocks}} -\label{sec:simshocks} - -\code{simshocks} is the complementary function to \code{simdiff}, with which you can simulate $\epsilon \sim \MN(0, 1)$ (that we call shocks), embedded into diffusion (Eq. \ref{eq:genericsde}) as: - -\begin{equation} -\textcolor{red}{dW(t) = \epsilon dt} -\end{equation} - -\medskip - -As \code{simdiff}, \code{simshocks} is written in C++ \textit{via} \code{Rcpp}. And when it comes to the simulation of multi-factors models, or the simulation of risk factors with flexible dependence structure, \code{simshocks} calls the underlying function \code{CDVinesim}, from package \href{http://cran.r-project.org/web/packages/CDVine/index.html}{CDVine}. \code{CDVineSim} makes simulations of canonical ({\bf C-vine}) and {\bf D-vine copulas}. - -\medskip - -Simply put, a copula is a function which gives a multidimensional distribution to given margins. If $(X_1, \ldots, X_d)^T$ is a random vector with margins of cumulative distribution functions $F_1, \ldots, F_d$, there exists a copula function $C$, such that the d-dimensional cumulative distribution function of $(X_1, \ldots, X_d)^T$ is : - -\begin{equation} -F(x_1, \ldots, x_d) = C(F_1(x_1), \ldots, F_d(x_d)) -\end{equation} - - -If the marginal distributions $F_1, \ldots, F_d$ are continuous, then $C$ is unique. On the other hand, if $C$ is a copula, and $F_1, \ldots, F_d$ are 1-dimensional cumulative distribution functions, the previous equation defines a joint cumulative distribution function for $(X_1, \ldots, X_d)^T$, with margins $F_1, \ldots, F_d$. - -\medskip - -Contrary to the multivariate Gaussian or Student-t copulas, vine copulas accurately model the dependence in high dimensions. They use the density functions of bivariate copulas (called pair-copula) to iteratively build a multivariate density function, which leads to a great flexibility in modeling the dependence. - -\medskip - -\code{simshocks} applies inverse standard gaussian cumulative distribution function to the uniform margins of \code{CDVinesim} to obtains gaussian shocks, with various dependence structures between them. - -\medskip - -\code{CDVineSim} can be used first, to choose the copula, and make an inference on it. Sometimes, the choice of the relevant copula is also made with expert knowledge. - -\medskip - -\section{Examples} -\label{sec:examples} - -Section \ref{sec:installation} is about \code{ESGtoolkit}'s installation. Section \ref{sec:exampleshocks} is related to \ref{sec:simshocks}. That is, to generating correlated $\epsilon$'s from $\textcolor{red}{dW(t) = \epsilon dt}$ in (Eq. \ref{eq:genericsde}). Then, section \ref{sec:examplesimulation} presents a complete example of simulation of a Stochastic Volatility Jump Diffusion (SVJD) model. This SVJD model uses \ref{sec:simshocks}. - -\subsection{Installation} -\label{sec:installation} - -\begin{itemize} -\item From Github: - -<>= -library(devtools) -devtools::install_github("thierrymoudiki/ESGtoolkit") -@ - -\item From CRAN: - -TBD - -\end{itemize} - - -\subsection{Generating dependent shocks $\epsilon$ with \code{simshocks}} -\label{sec:exampleshocks} - -To use \code{simshocks}, you need the specify the number of simulations of $\epsilon$ that you need, \code{n}, the type of dependence, \code{family}, and additional parameters depending on the copula that you want to use. For a simulation of a Gaussian copula, \code{family} is \code{1} : - -<>= -library(ESGtoolkit) -@ - -<>= -# Number of simulations -nb <- 1000 - -# Number of risk factors -d <- 2 - -# Number of possible combinations of the risk factors (here : 1) -dd <- d*(d-1)/2 - -# Family : Gaussian copula -fam1 <- rep(1, dd) - -# Correlation coefficients between the risk factors (d*(d-1)/2) -par0_1 <- 0.1 -par0_2 <- -0.9 -@ - - -A correlation coefficient is provided to \code{simshocks} through its argument \code{par}: - -<>= -set.seed(2) - -# Simulation of shocks for the d risk factors -s0_par1 <- simshocks(n = nb, horizon = 4, -family = fam1, par = par0_1) - -s0_par2 <- simshocks(n = nb, horizon = 4, -family = fam1, par = par0_2) -@ - -You can make a correlation test on \code{simshocks} outputs with \code{esgcortest}, to assess whether correlation estimate between shocks is significantly close to the correlation you specified or not. If \code{esgcortest}'s confidence interval contains the true value at a given confidence level, the null hypothesis is not to be rejected at this level. - - -<>= -# Correlation test -esgcortest(s0_par1) -@ - -These confidence intervals on the estimated correlations can also be visualized with \code{esgplotbands}: - -<>= -test <- esgcortest(s0_par2) -par(mfrow=c(1, 2)) -esgplotbands(esgcortest(s0_par1)) -esgplotbands(test) -@ - -Now with other types of dependences, namely rotated versions of the Clayton copula : - -<>= -# Family : Rotated Clayton (180 degrees) -fam2 <- 13 -par0_3 <- 2 - -# Family : Rotated Clayton (90 degrees) -fam3 <- 23 -par0_4 <- -2 - -# number of simulations -nb <- 200 - -# Simulation of shocks for the d risk factors -s0_par3 <- simshocks(n = nb, horizon = 4, -family = fam2, par = par0_3) - -s0_par4 <- simshocks(n = nb, horizon = 4, -family = fam3, par = par0_4) -@ - -There's a nice function from the package, \code{esgplotshocks}, that helps you in visualizing dependence between shocks (inspired by \href{http://rforpublichealth.blogspot.fr/2014/02/ggplot2-cheatsheet-for-visualizing.html}{this blog post}) : - -<>= -esgplotshocks(s0_par3, s0_par4) -@ - -\newpage - -\subsection{Example with \code{simdiff} and \code{simshocks} : Option pricing under the Bates model (SVJD) for equity} -\label{sec:examplesimulation} - -SVJD stands for Stochastic Volatility with Jump Diffusion. In this model, the volatility of our asset's price evolves as a CIR process. The price itself is a Geometric Brownian motion between jumps, arising from a Poisson process. Here, we consider jumps with lognormal magnitude. - -\medskip - -{\bf The model} - -\begin{eqnarray*} -\label{eq:batesmodel} -dS(t) &=& (r - \lambda \mu_Z) S(t) dt + \sqrt{v(t)} S(t) dW(t)^{(1)} + (J - 1) dN(t)\\ -dv(t) &=& \kappa(\theta - v(t)) dt + \sigma \sqrt{v(t)} dW(t)^{(2)}\\ -dW(t)^{(1)} dW(t)^{(2)} &=& \rho dt -\end{eqnarray*} - -We use the package \code{fOptions} to compute options' prices from market implied volatility : -<>= -library(fOptions) -@ - -The parameters of Bates model are : -<<>= -# Spot variance -V0 <- 0.1372 -# mean-reversion speed -kappa <- 9.5110/100 -# long-term variance -theta <- 0.0285 -# volatility of volatility -volvol <- 0.8010/100 -# Correlation between stoch. vol and prices -rho <- -0.5483 -# Intensity of the Poisson process -lambda <- 0.3635 -# mean and vol of the merton jumps diffusion -mu_J <- -0.2459 -sigma_J <- 0.2547/100 -m <- exp(mu_J + 0.5*(sigma_J^2)) - 1 -# Initial stock price -S0 <- 4468.17 -# Initial short rate -r0 <- 0.0357 -@ - -Now we make \code{300} simulations of shocks and diffusions, on a weekly basis, from today, up to year 1. The shocks are simulated by using a variance reduction technique : antithetic variates (argument \code{method}). - -<<>= -n <- 300 -horizon <- 1 -freq <- "weekly" - -# Simulation of shocks, with antithetic variates -shocks <- simshocks(n = n, horizon = horizon, - frequency = freq, - method = "anti", - family = 1, par = rho) - -# Vol simulation -sim_vol <- simdiff(n = n, horizon = horizon, - frequency = freq, model = "CIR", x0 = V0, - theta1 = kappa*theta, theta2 = kappa, - theta3 = volvol, - eps = shocks[[1]]) - -# Plotting the volatility (only for a low number of simulations) -esgplotts(sim_vol) -@ - -To finish, the simulation of asset price $S$ takes {\bf exactly the same parameters} \code{n, horizon, frequency} as \code{simshocks} and \code{simdiff}, and diffusion's volatility is embedded through \code{theta2}. - -<<>= -# prices simulation -sim_price <- simdiff(n = n, horizon = horizon, - frequency = freq, model = "GBM", x0 = S0, - theta1 = r0 - lambda*m, theta2 = sim_vol, - lambda = lambda, mu_z = mu_J, - sigma_z = sigma_J, - eps = shocks[[2]]) -@ - -In the figure below, we can clearly see asset prices jumping with \code{matplot}. \code{esgplotbands}, which depicts asset paths by percentiles, will be more useful for thousands of simulations : - -<<>= -par(mfrow=c(2, 1)) -matplot(time(sim_price), sim_price, type = 'l', - main = "with matplot") -esgplotbands(sim_price, main = "with esgplotbands", xlab = "time", - ylab = "values") -@ - -Now, we would like to study the convergence of estimated discounted prices to the initial asset price : - -\begin{equation} -\frac{1}{N}\sum_{i = 1}^N e^{-rT} S_T^{(i)} \longrightarrow \EE[e^{-rT}S_T] = S_0 -\end{equation} - -where $N$ is the number of simulations, $r$ is the constant risk free rate, and $T$ is a maturity of 2 weeks. - -<<>= -# Discounted Monte Carlo price -print(as.numeric(esgmcprices(r0, sim_price, 2/52))) - -# Inital price -print(S0) - -# pct. difference -print(as.numeric((esgmcprices(r0, sim_price, 2/52)/S0 - 1)*100)) -@ - -One would also want to see how fast is the convergence towards $S0$ : -<<>= -# convergence of the discounted price -esgmccv(r0, sim_price, 2/52, - main = "Convergence towards the initial \n asset price") -@ - -\code{esgmcprices} and \code{esgmccv} give information about the mean, but a statistical test gives more information. - -<<>= -martingaletest_sim_price <- esgmartingaletest(r = r0, - X = sim_price, - p0 = S0) -@ - -\code{esgmartingaletest} computes for each $T$, a Student's t-test of -$$H_0 : \EE[e^{-rT}S_T - S_0] = 0$$ -versus the alternative hypothesis that the mean is not $0$, at a given confidence level (default is $95\%$). - -\medskip - -\code{esgmartingaletest} also provides p-values, and confidence intervals for the mean value (print \code{martingaletest\underline{ }sim\underline{ }price}!). If all the confidence intervals contain $0$, then the null hypothesis is not rejected at the given level, let's say $95\%$. Which means that there are less than $5$ chances out of $100$ to be wrong by saying that the true mean of the distribution is $0$. \code{esgplotbands} is a companion function to \code{esgmartingaletest}, that gives a visualization of confidence intervals and average discounted prices. - -<<>= -esgplotbands(martingaletest_sim_price) -@ - -\newpage - -Another interesting exercise is to price a \href{https://en.wikipedia.org/wiki/Call_option}{Call Option} under the Bates model described at the beginning of this section: - -<<>= -# Option pricing - -# Strike -K <- 3400 -Kts <- ts(matrix(K, nrow(sim_price), ncol(sim_price)), - start = start(sim_price), - deltat = deltat(sim_price), - end = end(sim_price)) - -# Implied volatility -sigma_imp <- 0.6625 - -#Maturity -maturity <- 2/52 - -# payoff at maturity -payoff_ <- (sim_price - Kts)*(sim_price > Kts) -payoff <- window(payoff_, - start = deltat(sim_price), - deltat = deltat(sim_price), - names = paste0("Series ", 1:n)) - -# True price -c0 <- GBSOption("c", S = S0, X = K, Time = maturity, r = r0, - b = 0, sigma = sigma_imp) -print(c0@price) - -# Monte Carlo price -print(as.numeric(esgmcprices(r = r0, X = payoff, maturity))) - -# pct. difference -print(as.numeric((esgmcprices(r = r0, X = payoff, - maturity = maturity)/c0@price - 1)*100)) - -# Convergence towards the option price -esgmccv(r = r0, X = payoff, maturity = maturity, - main = "Convergence towards the call \n option price") -@ - -\newpage - -\nocite{bates1996jumps} -\nocite{black1973pricing} -\nocite{brechmann2012risk} -\nocite{brechmann2013modeling} -\nocite{brigo2006interest} -\nocite{cox1985theory} -\nocite{eddelbuettel2011rcpp} -\nocite{glasserman2004monte} -\nocite{iacus2008simulation} -\nocite{kou2002jump} -\nocite{merton1976option} -\nocite{uhlenbeck1930theory} -\nocite{vasicek1977equilibrium} -\nocite{wickham2009ggplot2} -\bibliographystyle{jss} -\bibliography{mabiblio} - -\end{document} \ No newline at end of file diff --git a/vignettes/ESG2toolkit_Intro_012020.bbl b/vignettes/ESG2toolkit_Intro_012020.bbl deleted file mode 100644 index f81bd4f..0000000 --- a/vignettes/ESG2toolkit_Intro_012020.bbl +++ /dev/null @@ -1,88 +0,0 @@ -\begin{thebibliography}{14} -\newcommand{\enquote}[1]{``#1''} -\providecommand{\natexlab}[1]{#1} -\providecommand{\url}[1]{\texttt{#1}} -\providecommand{\urlprefix}{URL } -\expandafter\ifx\csname urlstyle\endcsname\relax - \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else - \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup - \urlstyle{rm}\Url}\fi -\providecommand{\eprint}[2][]{\url{#2}} - -\bibitem[{Bates(1996)}]{bates1996jumps} -Bates DS (1996). -\newblock \enquote{Jumps and stochastic volatility: Exchange rate processes - implicit in deutsche mark options.} -\newblock \emph{Review of financial studies}, \textbf{9}(1), 69--107. - -\bibitem[{Black and Scholes(1973)}]{black1973pricing} -Black F, Scholes M (1973). -\newblock \enquote{The pricing of options and corporate liabilities.} -\newblock \emph{The journal of political economy}, pp. 637--654. - -\bibitem[{Brechmann and Czado(2012)}]{brechmann2012risk} -Brechmann EC, Czado C (2012). -\newblock \enquote{Risk management with high-dimensional vine copulas: An - analysis of the Euro Stoxx 50.} - -\bibitem[{Brechmann and Schepsmeier(2013)}]{brechmann2013modeling} -Brechmann EC, Schepsmeier U (2013). -\newblock \enquote{Modeling dependence with C-and D-vine copulas: The R-package - CDVine.} -\newblock \emph{Journal of Statistical Software}, \textbf{5}(3), 1--27. - -\bibitem[{Brigo and Mercurio(2006)}]{brigo2006interest} -Brigo D, Mercurio F (2006). -\newblock \emph{Interest rate models-theory and practice: with smile, inflation - and credit}. -\newblock Springer. - -\bibitem[{Cox \emph{et~al.}(1985)Cox, Ingersoll~Jr, and Ross}]{cox1985theory} -Cox JC, Ingersoll~Jr JE, Ross SA (1985). -\newblock \enquote{A theory of the term structure of interest rates.} -\newblock \emph{Econometrica: Journal of the Econometric Society}, pp. - 385--407. - -\bibitem[{Eddelbuettel and Fran{\c{c}}ois(2011)}]{eddelbuettel2011rcpp} -Eddelbuettel D, Fran{\c{c}}ois R (2011). -\newblock \enquote{Rcpp: Seamless R and C++ integration.} -\newblock \emph{Journal of Statistical Software}, \textbf{40}(8), 1--18. - -\bibitem[{Glasserman(2004)}]{glasserman2004monte} -Glasserman P (2004). -\newblock \emph{Monte Carlo methods in financial engineering}, volume~53. -\newblock Springer. - -\bibitem[{Iacus(2008)}]{iacus2008simulation} -Iacus SM (2008). -\newblock \emph{Simulation and inference for stochastic differential equations: - with R examples}. -\newblock Springer. - -\bibitem[{Kou(2002)}]{kou2002jump} -Kou SG (2002). -\newblock \enquote{A jump-diffusion model for option pricing.} -\newblock \emph{Management science}, \textbf{48}(8), 1086--1101. - -\bibitem[{Merton(1976)}]{merton1976option} -Merton RC (1976). -\newblock \enquote{Option pricing when underlying stock returns are - discontinuous.} -\newblock \emph{Journal of financial economics}, \textbf{3}(1), 125--144. - -\bibitem[{Uhlenbeck and Ornstein(1930)}]{uhlenbeck1930theory} -Uhlenbeck GE, Ornstein LS (1930). -\newblock \enquote{On the theory of the Brownian motion.} -\newblock \emph{Physical review}, \textbf{36}(5), 823. - -\bibitem[{Vasicek(1977)}]{vasicek1977equilibrium} -Vasicek O (1977). -\newblock \enquote{An equilibrium characterization of the term structure.} -\newblock \emph{Journal of financial economics}, \textbf{5}(2), 177--188. - -\bibitem[{Wickham(2009)}]{wickham2009ggplot2} -Wickham H (2009). -\newblock \emph{ggplot2: elegant graphics for data analysis}. -\newblock Springer. - 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% - \ifdim\Gin@nat@width>\linewidth - \linewidth - \else - \Gin@nat@width - \fi -} -\makeatother - -\definecolor{fgcolor}{rgb}{0.345, 0.345, 0.345} -\newcommand{\hlnum}[1]{\textcolor[rgb]{0.686,0.059,0.569}{#1}}% -\newcommand{\hlstr}[1]{\textcolor[rgb]{0.192,0.494,0.8}{#1}}% -\newcommand{\hlcom}[1]{\textcolor[rgb]{0.678,0.584,0.686}{\textit{#1}}}% -\newcommand{\hlopt}[1]{\textcolor[rgb]{0,0,0}{#1}}% -\newcommand{\hlstd}[1]{\textcolor[rgb]{0.345,0.345,0.345}{#1}}% -\newcommand{\hlkwa}[1]{\textcolor[rgb]{0.161,0.373,0.58}{\textbf{#1}}}% -\newcommand{\hlkwb}[1]{\textcolor[rgb]{0.69,0.353,0.396}{#1}}% -\newcommand{\hlkwc}[1]{\textcolor[rgb]{0.333,0.667,0.333}{#1}}% -\newcommand{\hlkwd}[1]{\textcolor[rgb]{0.737,0.353,0.396}{\textbf{#1}}}% -\let\hlipl\hlkwb - -\usepackage{framed} -\makeatletter -\newenvironment{kframe}{% - \def\at@end@of@kframe{}% - \ifinner\ifhmode% - \def\at@end@of@kframe{\end{minipage}}% - \begin{minipage}{\columnwidth}% - \fi\fi% - \def\FrameCommand##1{\hskip\@totalleftmargin \hskip-\fboxsep - \colorbox{shadecolor}{##1}\hskip-\fboxsep - % There is no \\@totalrightmargin, so: - \hskip-\linewidth \hskip-\@totalleftmargin \hskip\columnwidth}% - \MakeFramed {\advance\hsize-\width - \@totalleftmargin\z@ \linewidth\hsize - \@setminipage}}% - {\par\unskip\endMakeFramed% - \at@end@of@kframe} -\makeatother - -\definecolor{shadecolor}{rgb}{.97, .97, .97} -\definecolor{messagecolor}{rgb}{0, 0, 0} -\definecolor{warningcolor}{rgb}{1, 0, 1} -\definecolor{errorcolor}{rgb}{1, 0, 0} -\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX - -\usepackage{alltt} -\usepackage[british]{babel} -\usepackage[sc]{mathpazo} % Use the Palatino font -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage[colorlinks,linkcolor=red, citecolor=blue, urlcolor=red]{hyperref} -\usepackage{xcolor} -\usepackage{url} -\usepackage{float} -\usepackage{amssymb,amsfonts,amsmath} -\usepackage{graphicx} -\usepackage{latexsym} -\usepackage[authoryear]{natbib} -\usepackage{fancyhdr} % Headers and footers -\pagestyle{fancy} % All pages have headers and footers -\fancyhead{} % Blank out the default header -\fancyhead[C]{\code{ESGtoolkit}, tools for stochastic simulation $\bullet$ January 2020} % -\date{} -\newcommand{\CC}{\ensuremath{\mathbb{C}} } -\newcommand{\NN}{\ensuremath{\mathbb{N}} } -\newcommand{\RR}{\ensuremath{\mathbb{R}} } -\newcommand{\QQ}{\ensuremath{\mathbb{Q}} } -\newcommand{\EE}{\ensuremath{\mathbb{E}} } -\newcommand{\PP}{\ensuremath{\mathbb{P}} } -\newcommand{\noi}{\noindent} -\newcommand{\II}{\mbox{\large 1\hskip -0,353em 1}} -\newcommand{\dps}{\displaystyle} -\newcommand{\ms}{\medskip} -\newcommand{\itb}{\ms\item[$\bullet$]} -\newcommand{\itm}{\ms\item} -\newcommand{\pkg}[1]{{\normalfont\fontseries{b}\selectfont #1}} -\newcommand{\proglang}[1]{\textsf{#1}} -\newcommand{\code}[1]{\mbox{\texttt{#1}}} -\newcommand{\MN}{\mathcal{N}} -\newcommand{\MM}{\mathcal{M}} -\newcommand{\FF}{\mathcal{F}} -\newcommand{\GG}{\mathcal{G}} -\newcommand{\HH}{\mathcal{H}} -\newcommand{\LL}{\mathcal{L}} -\newcommand{\AT}{\mathcal{A}} -\IfFileExists{upquote.sty}{\usepackage{upquote}}{} -\begin{document} - -\title{\bf{\code{ESGtoolkit}, a tool for stochastic simulation (\code{v0.2.0})}} % Article title -\author{ -Thierry Moudiki\\ % Your name -%\url{http://thierrymoudiki.wordpress.com}\\ % Your institution -\today{} -%\href{mailto:thierry.moudiki@gmail.com}{thierry.moudiki@gmail.com} % Your email address -} -\maketitle - -\tableofcontents - -\newpage - -\section{Overview} - -\subsection{Context} - -Initially, I developped this package for insurance. In 2014. \textbf{If you're not working in insurance, \code{ESGtoolkit} is still relevant for stochastic simulation} in Finance, Economics, or Physics (...). In that case, you can start directly by reading \ref{sec:simdiff}. Oh, in this section, read at least this paragraph: \ref{para}. - -\medskip - -An \textit{Economic Scenario Generator} (ESG) is a tool for projection of plausible future paths of insurers' financial assets. It helps in pricing its products, and assessing its current and future solvency. Two types of ESGs are generally needed: a \textit{real-world} ESG, and a a \textit{market consistent} ESG. - - -\medskip - -The aim of a real-world ESG is to produce projections of risk factors, whose patterns are coherent with the past distribution of those risk factors. Real-world scenarios are mainly used for the valuation of solvency requirements. - -\medskip - -A market consistent ESG shall produce projections of risk factors that are coherent with market prices observed at the valuation date. Market consistent scenarios are mainly used for the best estimate valuation of technical reserves. - - -\medskip - -Hence, in real-world simulations the historical probability is used and in market consistent simulations, the projection of risk factors is made in a risk-neutral probability. A risk-neutral probability measure is a measure under which the discounted prices of assets are martingales. - -\medskip - -A simple example of transitioning from a simulation under the historical probability to a simulation under a risk-neutral probability can be made by using the Black-Scholes model, a geometric Brownian motion. In a real-world simulation, we can assume that an asset evolves according to the following Stochastic Differential Equation (SDE) (with a drift $\mu$, a volatility $\sigma$, and $\left( W(t) \right)_{t \geq 0}$ being a standard brownian motion): - -\begin{equation} -dS(t) = \mu S(t) dt + \sigma S(t) dW(t) -\end{equation} - -\medskip - -Let $r$ be a constant risk-free rate. $e^{-rt}S(t)$, the discounted price of $S(t)$, will be a martingale if -\begin{equation} -d(e^{-rt}S(t)) -\end{equation} - -is driftless. Applying Ito's formula to $e^{-rt}S(t)$, we have : - -\begin{eqnarray} -d(e^{-rt}S(t)) &=& -r e^{-rt} S(t) dt + e^{-rt} dS(t) - \frac{1}{2}.0 \\ - &=& -r e^{-rt} S(t) dt + e^{-rt} \mu S(t) dt + e^{-rt} S(t) \sigma dW(t) \\ - &=& e^{-rt} S(t) \left[ (\mu - r) dt + \sigma dW(t) \right] -\end{eqnarray} - -Thus, the drift vanishes iff $\mu = r$. That is, if our asset with price $S(t)$ at time $t$ rewards the risk-free rate $r$. Under this martingale probability measure, asset price dynamics over time can be re-written as: - -\begin{equation} -dS(t) = r S(t) dt + \sigma S(t) dW^*(t) -\end{equation} -Where $\left(W^*(t)\right)_{t \geq 0}$ is a standard brownian motion under the chosen risk-neutral measure. - -\medskip - -As we'll see in section \ref{sec:simdiff}, \code{ESGtoolkit} does not directly provide multiple asset models but instead, some building blocks for constructing a variety of these. Two main functions are therefore provided for his purpose: \code{simshocks}, \code{simdiff}. Other tools for statistical testing and visualization are presented as well. - -\paragraph{As a reminder:} -\label{para} -There are no perfect models, and the more sophisticated doesn't necessarily mean the most judicious. To avoid possible disasters, it's important to know precisely the strengths and weaknesses of a model before using it. - -\subsection{\code{simdiff}} -\label{sec:simdiff} - -Let $(W(t))_{t \geq 0}$ be a standard brownian motion. \code{simdiff} makes simulations of a diffusion process $(X(t))_{t \geq 0}$, which evolves through time according to the following equation: - -\begin{equation} -\label{eq:genericsde} -\textcolor{blue}{dX(t) = \mu(t, X(t)) dt + \sigma(t, X(t))} \textcolor{red}{dW(t)} + \textcolor{green}{\gamma(t, X(t-), J)dN(t)} -\end{equation} - -\medskip - -Actually, (Eq. \ref{eq:genericsde}) is a generic formulation of all \code{simdiff} models. {\bf Not all parts of this expression are required all the times}, but $\textcolor{blue}{\sigma(t, X(t))} \textcolor{red}{dW(t)}$, describing our process' volatility. Let's describe the other parts. - -\medskip - -$\textcolor{green}{\gamma(t, X(t-), J) dN(t)}$ is optional. It contains jumps of the process, that occur according to a homogeneous Poisson process $(N(t))_{t \geq 0}$ with intensity $\lambda$. The time elasped between two jumping times follows an exponential $\epsilon(\lambda)$ distribution; and the number of jumps of the process on $[0, t[$ follows a Poisson distribution $\mathcal{P}(\lambda t)$. The magnitude of the jumps is controlled by $J$. - -\medskip - -Now, for the \textcolor{blue}{blue part} of (Eq. \ref{eq:genericsde}), we could have: - -\begin{itemize} - -\item An Orsnstein-Uhlenbeck process; for \code{simdiff} used with parameter \newline \code{model = "OU"}, and parameters \code{theta1}, \code{theta2} and \code{theta3} provided (if \code{theta1} or \code{theta2} are not necessary for building the model, they are to be provided and set to \code{0}): -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& (\theta_1 - \theta_2 X(t))\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_3\\ -\end{eqnarray*} - -\item A Cox-Ingersoll-Ross process; for \code{simdiff} used with parameter \newline \code{model = "CIR"}, and parameters \code{theta1}, \code{theta2}, \code{theta3} provided (if \code{theta1} or \code{theta2} are not necessary for building the model, they are to be provided and set to \code{0}) : - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& (\theta_1 - \theta_2 X(t))\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_3 \sqrt{X(t)}\\ -\end{eqnarray*} - -\item A Geometric Brownian motion, or \textit{augmented} versions; for \code{simdiff} used with parameter \code{model = "GBM"}, and parameters \code{theta1}, \code{theta2}, \code{theta3} provided. For the sake of clarity, the argument \code{model} is set to \code{"GBM"}, but not only the Geometric Brownian motion with constant parameters is available. We could have : - -A Geometric Brownian Motion - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1 X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2 X(t)\\ -\end{eqnarray*} - -A modified Geometric Brownian Motion, with time-varying drift and constant volatility - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1(t) X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2 X(t)\\ -\end{eqnarray*} - -A modified Geometric Brownian Motion, with time-varying volatility and constant drift - -\begin{eqnarray*} -\textcolor{blue}{\mu(t, X(t))} &=& \theta_1 X(t)\\ -\textcolor{blue}{\sigma(t, X(t))} &=& \theta_2(t) X(t)\\ -\end{eqnarray*} -\end{itemize} - -It's technically possible to have both $\theta_1$ and $\theta_2$ varying with time (both provided as multivariate time series). But it's not advisable to do this, unless you know exactly why you're doing it. - -\medskip - -Jumps are available only for \code{model = "GBM"}. The jumps arising from the Poisson process have a common magnitude $J = 1+Z$, whose distribution $\nu$ is either lognormal or double-exponential. Between two jumps, the process behaves like a Geometric Brownian motion, and at jumping times, it increases by $Z$\%. For lognormal jumps (Merton model), the distribution $\nu$ of $J$ is: -\begin{equation} -log(J) = log(1+Z) \sim \MN(log(1+\mu_Z) - \frac{\sigma_Z^2}{2}, \sigma_Z^2) -\end{equation} - -For double exponential jumps (Kou's model), the distribution $\nu$ of $J$ is: - -\begin{equation} -log(J) = log(1+Z) \sim \nu(dy) = p\frac{1}{\eta_u} e^{- \frac{1}{\eta_u}} \II_{y > 0} + (1-p)\frac{1}{\eta_d} e^{\frac{1}{\eta_d}} \II_{y < 0} -\end{equation} - -Hence for taking jumps into account when \code{model = "GBM"}, optional parameters are to be provided to \code{simdiff}, namely: - - -\begin{itemize} -\item \code{lambda}: intensity of the Poisson process -\item \code{mu\underline{ }z}: average jump magnitude (only for {\bf lognormal} jumps) -\item \code{sigma\underline{ }z}: standard deviation of the jump magnitude (only for {\bf lognormal} jumps) -\item \code{p}: probability of positive jumps (only for {\bf double exponential} jumps) -\item \code{eta\underline{ }up}: the mean of positive jumps (only for {\bf double exponential} jumps) -\item \code{eta\underline{ }down}: the mean of negative jumps (only for {\bf double exponential} jumps) -\end{itemize} - -\medskip - -\code{simdiff}'s core loops are written in C++ \textit{via} \href{http://cran.r-project.org/web/packages/Rcpp/index.html}{Rcpp} because: speed. Currently, for an Ornstein-Uhlenbeck process with \code{model = "OU"}, a Cox-Ingersoll-Ross process with \code{model = "CIR"}, or a geometric brownian motion with \code{model = "GBM"}, an exact simulation is used, which means there's no discretization of $(X(t))_{t \geq 0}$ on a time grid. You can also choose an \code{horizon} of projection and a sampling \code{frequency} (annual, semi-annual, quarterly $\ldots$). \code{simdiff}'s output is a time series object created by base \proglang{R} function \code{ts()}. And since this output is a \code{ts()} object, it means you can use \proglang{R} functions such as \code{window.ts} or \code{frequency} on it. - -\medskip - -For a customized simulation of $\textcolor{red}{\epsilon} \sim \MN(0, 1)$ embedded in (Eq. \ref{eq:genericsde}) \textit{via} $\textcolor{red}{dW(t) = \epsilon dt}$, you can fill \code{simdiff}'s parameter \code{eps} with an output of function \code{simshocks}. \code{simshocks} is described in the next section, \ref{sec:simshocks}, and an example of such a procedure is described in \ref{sec:examples}. - - -\subsection{\code{simshocks}} -\label{sec:simshocks} - -\code{simshocks} is the complementary function to \code{simdiff}, with which you can simulate $\epsilon \sim \MN(0, 1)$ (that we call shocks), embedded into diffusion (Eq. \ref{eq:genericsde}) as: - -\begin{equation} -\textcolor{red}{dW(t) = \epsilon dt} -\end{equation} - -\medskip - -As \code{simdiff}, \code{simshocks} is written in C++ \textit{via} \code{Rcpp}. And when it comes to the simulation of multi-factors models, or the simulation of risk factors with flexible dependence structure, \code{simshocks} calls the underlying function \code{CDVinesim}, from package \href{http://cran.r-project.org/web/packages/CDVine/index.html}{CDVine}. \code{CDVineSim} makes simulations of canonical ({\bf C-vine}) and {\bf D-vine copulas}. - -\medskip - -Simply put, a copula is a function which gives a multidimensional distribution to given margins. If $(X_1, \ldots, X_d)^T$ is a random vector with margins of cumulative distribution functions $F_1, \ldots, F_d$, there exists a copula function $C$, such that the d-dimensional cumulative distribution function of $(X_1, \ldots, X_d)^T$ is : - -\begin{equation} -F(x_1, \ldots, x_d) = C(F_1(x_1), \ldots, F_d(x_d)) -\end{equation} - - -If the marginal distributions $F_1, \ldots, F_d$ are continuous, then $C$ is unique. On the other hand, if $C$ is a copula, and $F_1, \ldots, F_d$ are 1-dimensional cumulative distribution functions, the previous equation defines a joint cumulative distribution function for $(X_1, \ldots, X_d)^T$, with margins $F_1, \ldots, F_d$. - -\medskip - -Contrary to the multivariate Gaussian or Student-t copulas, vine copulas accurately model the dependence in high dimensions. They use the density functions of bivariate copulas (called pair-copula) to iteratively build a multivariate density function, which leads to a great flexibility in modeling the dependence. - -\medskip - -\code{simshocks} applies inverse standard gaussian cumulative distribution function to the uniform margins of \code{CDVinesim} to obtains gaussian shocks, with various dependence structures between them. - -\medskip - -\code{CDVineSim} can be used first, to choose the copula, and make an inference on it. Sometimes, the choice of the relevant copula is also made with expert knowledge. - -\medskip - -\section{Examples} -\label{sec:examples} - -Section \ref{sec:installation} is about \code{ESGtoolkit}'s installation. Section \ref{sec:exampleshocks} is related to \ref{sec:simshocks}. That is, to generating correlated $\epsilon$'s from $\textcolor{red}{dW(t) = \epsilon dt}$ in (Eq. \ref{eq:genericsde}). Then, section \ref{sec:examplesimulation} presents a complete example of simulation of a Stochastic Volatility Jump Diffusion (SVJD) model. This SVJD model uses \ref{sec:simshocks}. - -\subsection{Installation} -\label{sec:installation} - -\begin{itemize} -\item From Github: - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{library}\hlstd{(devtools)} -\hlstd{devtools}\hlopt{::}\hlkwd{install_github}\hlstd{(}\hlstr{"thierrymoudiki/ESGtoolkit"}\hlstd{)} -\end{alltt} -\end{kframe} -\end{knitrout} - -\item From CRAN: - -TBD - -\end{itemize} - - -\subsection{Generating dependent shocks $\epsilon$ with \code{simshocks}} -\label{sec:exampleshocks} - -To use \code{simshocks}, you need the specify the number of simulations of $\epsilon$ that you need, \code{n}, the type of dependence, \code{family}, and additional parameters depending on the copula that you want to use. For a simulation of a Gaussian copula, \code{family} is \code{1} : - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{library}\hlstd{(ESGtoolkit)} -\end{alltt} -\end{kframe} -\end{knitrout} - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Number of simulations} -\hlstd{nb} \hlkwb{<-} \hlnum{1000} - -\hlcom{# Number of risk factors} -\hlstd{d} \hlkwb{<-} \hlnum{2} - -\hlcom{# Number of possible combinations of the risk factors (here : 1)} -\hlstd{dd} \hlkwb{<-} \hlstd{d}\hlopt{*}\hlstd{(d}\hlopt{-}\hlnum{1}\hlstd{)}\hlopt{/}\hlnum{2} - -\hlcom{# Family : Gaussian copula } -\hlstd{fam1} \hlkwb{<-} \hlkwd{rep}\hlstd{(}\hlnum{1}\hlstd{, dd)} - -\hlcom{# Correlation coefficients between the risk factors (d*(d-1)/2)} -\hlstd{par0_1} \hlkwb{<-} \hlnum{0.1} -\hlstd{par0_2} \hlkwb{<-} \hlopt{-}\hlnum{0.9} -\end{alltt} -\end{kframe} -\end{knitrout} - - -A correlation coefficient is provided to \code{simshocks} through its argument \code{par}: - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{set.seed}\hlstd{(}\hlnum{2}\hlstd{)} - -\hlcom{# Simulation of shocks for the d risk factors} -\hlstd{s0_par1} \hlkwb{<-} \hlkwd{simshocks}\hlstd{(}\hlkwc{n} \hlstd{= nb,} \hlkwc{horizon} \hlstd{=} \hlnum{4}\hlstd{,} -\hlkwc{family} \hlstd{= fam1,} \hlkwc{par} \hlstd{= par0_1)} - -\hlstd{s0_par2} \hlkwb{<-} \hlkwd{simshocks}\hlstd{(}\hlkwc{n} \hlstd{= nb,} \hlkwc{horizon} \hlstd{=} \hlnum{4}\hlstd{,} -\hlkwc{family} \hlstd{= fam1,} \hlkwc{par} \hlstd{= par0_2)} -\end{alltt} -\end{kframe} -\end{knitrout} - -You can make a correlation test on \code{simshocks} outputs with \code{esgcortest}, to assess whether correlation estimate between shocks is significantly close to the correlation you specified or not. If \code{esgcortest}'s confidence interval contains the true value at a given confidence level, the null hypothesis is not to be rejected at this level. - - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Correlation test} -\hlkwd{esgcortest}\hlstd{(s0_par1)} -\end{alltt} -\begin{verbatim} -## $cor.estimate -## Time Series: -## Start = 1 -## End = 4 -## Frequency = 1 -## [1] 0.02168139 0.13205902 0.10534299 0.06487379 -## -## $conf.int -## Time Series: -## Start = 1 -## End = 4 -## Frequency = 1 -## Series 1 Series 2 -## 1 -0.040365943 0.08356216 -## 2 0.070644283 0.19247635 -## 3 0.043634863 0.16625037 -## 4 0.002892336 0.12635869 -\end{verbatim} -\end{kframe} -\end{knitrout} - -These confidence intervals on the estimated correlations can also be visualized with \code{esgplotbands}: - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{test} \hlkwb{<-} \hlkwd{esgcortest}\hlstd{(s0_par2)} -\hlkwd{par}\hlstd{(}\hlkwc{mfrow}\hlstd{=}\hlkwd{c}\hlstd{(}\hlnum{1}\hlstd{,} \hlnum{2}\hlstd{))} -\hlkwd{esgplotbands}\hlstd{(}\hlkwd{esgcortest}\hlstd{(s0_par1))} -\hlkwd{esgplotbands}\hlstd{(test)} -\end{alltt} -\end{kframe} - -{\centering \includegraphics[width=\maxwidth]{figure/example_simshocks_3-1} - -} - - - -\end{knitrout} - -Now with other types of dependences, namely rotated versions of the Clayton copula : - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Family : Rotated Clayton (180 degrees)} -\hlstd{fam2} \hlkwb{<-} \hlnum{13} -\hlstd{par0_3} \hlkwb{<-} \hlnum{2} - -\hlcom{# Family : Rotated Clayton (90 degrees)} -\hlstd{fam3} \hlkwb{<-} \hlnum{23} -\hlstd{par0_4} \hlkwb{<-} \hlopt{-}\hlnum{2} - -\hlcom{# number of simulations} -\hlstd{nb} \hlkwb{<-} \hlnum{200} - -\hlcom{# Simulation of shocks for the d risk factors} -\hlstd{s0_par3} \hlkwb{<-} \hlkwd{simshocks}\hlstd{(}\hlkwc{n} \hlstd{= nb,} \hlkwc{horizon} \hlstd{=} \hlnum{4}\hlstd{,} -\hlkwc{family} \hlstd{= fam2,} \hlkwc{par} \hlstd{= par0_3)} - -\hlstd{s0_par4} \hlkwb{<-} \hlkwd{simshocks}\hlstd{(}\hlkwc{n} \hlstd{= nb,} \hlkwc{horizon} \hlstd{=} \hlnum{4}\hlstd{,} -\hlkwc{family} \hlstd{= fam3,} \hlkwc{par} \hlstd{= par0_4)} -\end{alltt} -\end{kframe} -\end{knitrout} - -There's a nice function from the package, \code{esgplotshocks}, that helps you in visualizing dependence between shocks (inspired by \href{http://rforpublichealth.blogspot.fr/2014/02/ggplot2-cheatsheet-for-visualizing.html}{this blog post}) : - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{esgplotshocks}\hlstd{(s0_par3, s0_par4)} -\end{alltt} -\end{kframe} - -{\centering \includegraphics[width=\maxwidth]{figure/example_simshocks_5-1} - -} - - - -\end{knitrout} - -\newpage - -\subsection{Example with \code{simdiff} and \code{simshocks} : Option pricing under the Bates model (SVJD) for equity} -\label{sec:examplesimulation} - -SVJD stands for Stochastic Volatility with Jump Diffusion. In this model, the volatility of our asset's price evolves as a CIR process. The price itself is a Geometric Brownian motion between jumps, arising from a Poisson process. Here, we consider jumps with lognormal magnitude. - -\medskip - -{\bf The model} - -\begin{eqnarray*} -\label{eq:batesmodel} -dS(t) &=& (r - \lambda \mu_Z) S(t) dt + \sqrt{v(t)} S(t) dW(t)^{(1)} + (J - 1) dN(t)\\ -dv(t) &=& \kappa(\theta - v(t)) dt + \sigma \sqrt{v(t)} dW(t)^{(2)}\\ -dW(t)^{(1)} dW(t)^{(2)} &=& \rho dt -\end{eqnarray*} - -We use the package \code{fOptions} to compute options' prices from market implied volatility : -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{library}\hlstd{(fOptions)} -\end{alltt} -\end{kframe} -\end{knitrout} - -The parameters of Bates model are : -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Spot variance} -\hlstd{V0} \hlkwb{<-} \hlnum{0.1372} -\hlcom{# mean-reversion speed} -\hlstd{kappa} \hlkwb{<-} \hlnum{9.5110}\hlopt{/}\hlnum{100} -\hlcom{# long-term variance} -\hlstd{theta} \hlkwb{<-} \hlnum{0.0285} -\hlcom{# volatility of volatility} -\hlstd{volvol} \hlkwb{<-} \hlnum{0.8010}\hlopt{/}\hlnum{100} -\hlcom{# Correlation between stoch. vol and prices} -\hlstd{rho} \hlkwb{<-} \hlopt{-}\hlnum{0.5483} -\hlcom{# Intensity of the Poisson process} -\hlstd{lambda} \hlkwb{<-} \hlnum{0.3635} -\hlcom{# mean and vol of the merton jumps diffusion} -\hlstd{mu_J} \hlkwb{<-} \hlopt{-}\hlnum{0.2459} -\hlstd{sigma_J} \hlkwb{<-} \hlnum{0.2547}\hlopt{/}\hlnum{100} -\hlstd{m} \hlkwb{<-} \hlkwd{exp}\hlstd{(mu_J} \hlopt{+} \hlnum{0.5}\hlopt{*}\hlstd{(sigma_J}\hlopt{^}\hlnum{2}\hlstd{))} \hlopt{-} \hlnum{1} -\hlcom{# Initial stock price} -\hlstd{S0} \hlkwb{<-} \hlnum{4468.17} -\hlcom{# Initial short rate} -\hlstd{r0} \hlkwb{<-} \hlnum{0.0357} -\end{alltt} -\end{kframe} -\end{knitrout} - -Now we make \code{300} simulations of shocks and diffusions, on a weekly basis, from today, up to year 1. The shocks are simulated by using a variance reduction technique : antithetic variates (argument \code{method}). - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{n} \hlkwb{<-} \hlnum{300} -\hlstd{horizon} \hlkwb{<-} \hlnum{1} -\hlstd{freq} \hlkwb{<-} \hlstr{"weekly"} - -\hlcom{# Simulation of shocks, with antithetic variates} -\hlstd{shocks} \hlkwb{<-} \hlkwd{simshocks}\hlstd{(}\hlkwc{n} \hlstd{= n,} \hlkwc{horizon} \hlstd{= horizon,} - \hlkwc{frequency} \hlstd{= freq,} - \hlkwc{method} \hlstd{=} \hlstr{"anti"}\hlstd{,} - \hlkwc{family} \hlstd{=} \hlnum{1}\hlstd{,} \hlkwc{par} \hlstd{= rho)} - -\hlcom{# Vol simulation} -\hlstd{sim_vol} \hlkwb{<-} \hlkwd{simdiff}\hlstd{(}\hlkwc{n} \hlstd{= n,} \hlkwc{horizon} \hlstd{= horizon,} - \hlkwc{frequency} \hlstd{= freq,} \hlkwc{model} \hlstd{=} \hlstr{"CIR"}\hlstd{,} \hlkwc{x0} \hlstd{= V0,} - \hlkwc{theta1} \hlstd{= kappa}\hlopt{*}\hlstd{theta,} \hlkwc{theta2} \hlstd{= kappa,} - \hlkwc{theta3} \hlstd{= volvol,} - \hlkwc{eps} \hlstd{= shocks[[}\hlnum{1}\hlstd{]])} - -\hlcom{# Plotting the volatility (only for a low number of simulations)} -\hlkwd{esgplotts}\hlstd{(sim_vol)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/_example_SVJD_2-1} - -\end{knitrout} - -To finish, the simulation of asset price $S$ takes {\bf exactly the same parameters} \code{n, horizon, frequency} as \code{simshocks} and \code{simdiff}, and diffusion's volatility is embedded through \code{theta2}. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# prices simulation} -\hlstd{sim_price} \hlkwb{<-} \hlkwd{simdiff}\hlstd{(}\hlkwc{n} \hlstd{= n,} \hlkwc{horizon} \hlstd{= horizon,} - \hlkwc{frequency} \hlstd{= freq,} \hlkwc{model} \hlstd{=} \hlstr{"GBM"}\hlstd{,} \hlkwc{x0} \hlstd{= S0,} - \hlkwc{theta1} \hlstd{= r0} \hlopt{-} \hlstd{lambda}\hlopt{*}\hlstd{m,} \hlkwc{theta2} \hlstd{= sim_vol,} - \hlkwc{lambda} \hlstd{= lambda,} \hlkwc{mu_z} \hlstd{= mu_J,} - \hlkwc{sigma_z} \hlstd{= sigma_J,} - \hlkwc{eps} \hlstd{= shocks[[}\hlnum{2}\hlstd{]])} -\end{alltt} -\end{kframe} -\end{knitrout} - -In the figure below, we can clearly see asset prices jumping with \code{matplot}. \code{esgplotbands}, which depicts asset paths by percentiles, will be more useful for thousands of simulations : - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{par}\hlstd{(}\hlkwc{mfrow}\hlstd{=}\hlkwd{c}\hlstd{(}\hlnum{2}\hlstd{,} \hlnum{1}\hlstd{))} -\hlkwd{matplot}\hlstd{(}\hlkwd{time}\hlstd{(sim_price), sim_price,} \hlkwc{type} \hlstd{=} \hlstr{'l'}\hlstd{,} - \hlkwc{main} \hlstd{=} \hlstr{"with matplot"}\hlstd{)} -\hlkwd{esgplotbands}\hlstd{(sim_price,} \hlkwc{main} \hlstd{=} \hlstr{"with esgplotbands"}\hlstd{,} \hlkwc{xlab} \hlstd{=} \hlstr{"time"}\hlstd{,} - \hlkwc{ylab} \hlstd{=} \hlstr{"values"}\hlstd{)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/_example_SVJD_4-1} - -\end{knitrout} - -Now, we would like to study the convergence of estimated discounted prices to the initial asset price : - -\begin{equation} -\frac{1}{N}\sum_{i = 1}^N e^{-rT} S_T^{(i)} \longrightarrow \EE[e^{-rT}S_T] = S_0 -\end{equation} - -where $N$ is the number of simulations, $r$ is the constant risk free rate, and $T$ is a maturity of 2 weeks. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Discounted Monte Carlo price} -\hlkwd{print}\hlstd{(}\hlkwd{as.numeric}\hlstd{(}\hlkwd{esgmcprices}\hlstd{(r0, sim_price,} \hlnum{2}\hlopt{/}\hlnum{52}\hlstd{)))} -\end{alltt} -\begin{verbatim} -## [1] 4477.961 -\end{verbatim} -\begin{alltt} -\hlcom{# Inital price} -\hlkwd{print}\hlstd{(S0)} -\end{alltt} -\begin{verbatim} -## [1] 4468.17 -\end{verbatim} -\begin{alltt} -\hlcom{# pct. difference} -\hlkwd{print}\hlstd{(}\hlkwd{as.numeric}\hlstd{((}\hlkwd{esgmcprices}\hlstd{(r0, sim_price,} \hlnum{2}\hlopt{/}\hlnum{52}\hlstd{)}\hlopt{/}\hlstd{S0} \hlopt{-} \hlnum{1}\hlstd{)}\hlopt{*}\hlnum{100}\hlstd{))} -\end{alltt} -\begin{verbatim} -## [1] 0.219129 -\end{verbatim} -\end{kframe} -\end{knitrout} - -One would also want to see how fast is the convergence towards $S0$ : -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# convergence of the discounted price} -\hlkwd{esgmccv}\hlstd{(r0, sim_price,} \hlnum{2}\hlopt{/}\hlnum{52}\hlstd{,} - \hlkwc{main} \hlstd{=} \hlstr{"Convergence towards the initial \textbackslash{}n asset price"}\hlstd{)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/_example_SVJD_cvS0-1} - -\end{knitrout} - -\code{esgmcprices} and \code{esgmccv} give information about the mean, but a statistical test gives more information. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{martingaletest_sim_price} \hlkwb{<-} \hlkwd{esgmartingaletest}\hlstd{(}\hlkwc{r} \hlstd{= r0,} - \hlkwc{X} \hlstd{= sim_price,} - \hlkwc{p0} \hlstd{= S0)} -\end{alltt} -\end{kframe} -\end{knitrout} - -\code{esgmartingaletest} computes for each $T$, a Student's t-test of -$$H_0 : \EE[e^{-rT}S_T - S_0] = 0$$ -versus the alternative hypothesis that the mean is not $0$, at a given confidence level (default is $95\%$). - -\medskip - -\code{esgmartingaletest} also provides p-values, and confidence intervals for the mean value (print \code{martingaletest\underline{ }sim\underline{ }price}!). If all the confidence intervals contain $0$, then the null hypothesis is not rejected at the given level, let's say $95\%$. Which means that there are less than $5$ chances out of $100$ to be wrong by saying that the true mean of the distribution is $0$. \code{esgplotbands} is a companion function to \code{esgmartingaletest}, that gives a visualization of confidence intervals and average discounted prices. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{esgplotbands}\hlstd{(martingaletest_sim_price)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/_example_SVJD_martingale_2-1} - -\end{knitrout} - -\newpage - -Another interesting exercise is to price a \href{https://en.wikipedia.org/wiki/Call_option}{Call Option} under the Bates model described at the beginning of this section: - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlcom{# Option pricing} - -\hlcom{# Strike} -\hlstd{K} \hlkwb{<-} \hlnum{3400} -\hlstd{Kts} \hlkwb{<-} \hlkwd{ts}\hlstd{(}\hlkwd{matrix}\hlstd{(K,} \hlkwd{nrow}\hlstd{(sim_price),} \hlkwd{ncol}\hlstd{(sim_price)),} - \hlkwc{start} \hlstd{=} \hlkwd{start}\hlstd{(sim_price),} - \hlkwc{deltat} \hlstd{=} \hlkwd{deltat}\hlstd{(sim_price),} - \hlkwc{end} \hlstd{=} \hlkwd{end}\hlstd{(sim_price))} - -\hlcom{# Implied volatility} -\hlstd{sigma_imp} \hlkwb{<-} \hlnum{0.6625} - -\hlcom{#Maturity} -\hlstd{maturity} \hlkwb{<-} \hlnum{2}\hlopt{/}\hlnum{52} - -\hlcom{# payoff at maturity} -\hlstd{payoff_} \hlkwb{<-} \hlstd{(sim_price} \hlopt{-} \hlstd{Kts)}\hlopt{*}\hlstd{(sim_price} \hlopt{>} \hlstd{Kts)} -\hlstd{payoff} \hlkwb{<-} \hlkwd{window}\hlstd{(payoff_,} - \hlkwc{start} \hlstd{=} \hlkwd{deltat}\hlstd{(sim_price),} - \hlkwc{deltat} \hlstd{=} \hlkwd{deltat}\hlstd{(sim_price),} - \hlkwc{names} \hlstd{=} \hlkwd{paste0}\hlstd{(}\hlstr{"Series "}\hlstd{,} \hlnum{1}\hlopt{:}\hlstd{n))} - -\hlcom{# True price} -\hlstd{c0} \hlkwb{<-} \hlkwd{GBSOption}\hlstd{(}\hlstr{"c"}\hlstd{,} \hlkwc{S} \hlstd{= S0,} \hlkwc{X} \hlstd{= K,} \hlkwc{Time} \hlstd{= maturity,} \hlkwc{r} \hlstd{= r0,} - \hlkwc{b} \hlstd{=} \hlnum{0}\hlstd{,} \hlkwc{sigma} \hlstd{= sigma_imp)} -\hlkwd{print}\hlstd{(c0}\hlopt{@}\hlkwc{price}\hlstd{)} -\end{alltt} -\begin{verbatim} -## [1] 1069.945 -\end{verbatim} -\begin{alltt} -\hlcom{# Monte Carlo price} -\hlkwd{print}\hlstd{(}\hlkwd{as.numeric}\hlstd{(}\hlkwd{esgmcprices}\hlstd{(}\hlkwc{r} \hlstd{= r0,} \hlkwc{X} \hlstd{= payoff, maturity)))} -\end{alltt} -\begin{verbatim} -## [1] 1082.626 -\end{verbatim} -\begin{alltt} -\hlcom{# pct. difference} -\hlkwd{print}\hlstd{(}\hlkwd{as.numeric}\hlstd{((}\hlkwd{esgmcprices}\hlstd{(}\hlkwc{r} \hlstd{= r0,} \hlkwc{X} \hlstd{= payoff,} - \hlkwc{maturity} \hlstd{= maturity)}\hlopt{/}\hlstd{c0}\hlopt{@}\hlkwc{price} \hlopt{-} \hlnum{1}\hlstd{)}\hlopt{*}\hlnum{100}\hlstd{))} -\end{alltt} -\begin{verbatim} -## [1] 1.185204 -\end{verbatim} -\begin{alltt} -\hlcom{# Convergence towards the option price} -\hlkwd{esgmccv}\hlstd{(}\hlkwc{r} \hlstd{= r0,} \hlkwc{X} \hlstd{= payoff,} \hlkwc{maturity} \hlstd{= maturity,} - \hlkwc{main} \hlstd{=} \hlstr{"Convergence towards the call \textbackslash{}n option price"}\hlstd{)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/_example_pricing-1} - -\end{knitrout} - -\newpage - -\nocite{bates1996jumps} -\nocite{black1973pricing} -\nocite{brechmann2012risk} -\nocite{brechmann2013modeling} -\nocite{brigo2006interest} -\nocite{cox1985theory} -\nocite{eddelbuettel2011rcpp} -\nocite{glasserman2004monte} -\nocite{iacus2008simulation} -\nocite{kou2002jump} -\nocite{merton1976option} -\nocite{uhlenbeck1930theory} -\nocite{vasicek1977equilibrium} -\nocite{wickham2009ggplot2} -\bibliographystyle{jss} -\bibliography{mabiblio} - -\end{document} diff --git a/vignettes/ESG2toolkit_Intro_012020.toc b/vignettes/ESG2toolkit_Intro_012020.toc deleted file mode 100644 index 4c5866e..0000000 --- a/vignettes/ESG2toolkit_Intro_012020.toc +++ /dev/null @@ -1,10 +0,0 @@ -\select@language {british} -\contentsline {section}{\numberline {1}Overview}{2}{section.1} -\contentsline {subsection}{\numberline {1.1}Context}{2}{subsection.1.1} -\contentsline {paragraph}{As a reminder:}{3}{section*.2} -\contentsline {subsection}{\numberline {1.2}\unhbox \voidb@x \hbox {\texttt {simdiff}}}{3}{subsection.1.2} -\contentsline {subsection}{\numberline {1.3}\unhbox \voidb@x \hbox {\texttt {simshocks}}}{5}{subsection.1.3} -\contentsline {section}{\numberline {2}Examples}{6}{section.2} -\contentsline {subsection}{\numberline {2.1}Installation}{6}{subsection.2.1} -\contentsline {subsection}{\numberline {2.2}Generating dependent shocks $\epsilon $ with \unhbox \voidb@x \hbox {\texttt {simshocks}}}{6}{subsection.2.2} -\contentsline {subsection}{\numberline {2.3}Example with \unhbox \voidb@x \hbox {\texttt {simdiff}} and \unhbox \voidb@x \hbox {\texttt {simshocks}} : Option pricing under the Bates model (SVJD) for equity}{10}{subsection.2.3} diff 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a/vignettes/mabiblio.bib b/vignettes/mabiblio.bib deleted file mode 100644 index 5192242..0000000 --- a/vignettes/mabiblio.bib +++ /dev/null @@ -1,436 +0,0 @@ -% This file was created with JabRef 2.9.2. -% Encoding: Cp1252 - -@ARTICLE{annaert2012estimating, - author = {Annaert, Jan and Claes, Anouk and De Ceuster, Marc and Zhang, Hairui}, - title = {Estimating the Yield Curve Using the {N}elson-{S}iegel Model: A Ridge - Regression Approach}, - journal = {International Review of Economics \& Finance, Forthcoming}, - year = {2012} -} - -@TECHREPORT{bandh2008, - author = {Barrie and Hibbert}, - title = {A framework for estimating and extrapolating the termstructure of - interestrates}, - institution = {Barrie and Hibbert}, - year = {2008} -} - -@article{bates1996jumps, - title={Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options}, - author={Bates, David S}, - journal={Review of financial studies}, - volume={9}, - number={1}, - pages={69--107}, - year={1996}, - publisher={Soc Financial Studies} -} - -@TECHREPORT{benaim2008arbitrage, - author = {Benaim, Shalom and Dodgson, Matthew and Kainth, Dherminder}, - title = {An arbitrage-free method for smile extrapolation}, - institution = {Working Paper, QuaRC, Royal Bank of Scotland}, - year = {2008} -} - -@article{black1973pricing, - title={The pricing of options and corporate liabilities}, - author={Black, Fischer and Scholes, Myron}, - journal={The journal of political economy}, - pages={637--654}, - year={1973}, - publisher={JSTOR} -} - -@ARTICLE{bolder1999yield, - author = {Bolder, David and Str{\'e}liski, David}, - title = {Yield curve modelling at the Bank of Canada}, - journal = {Available at SSRN 1082845}, - year = {1999} -} - -@article{brechmann2012risk, - title={Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50}, - author={Brechmann, Eike Christian and Czado, Claudia}, - year = {2012} -} - -@article{brechmann2013modeling, - title={Modeling dependence with C-and D-vine copulas: The R-package CDVine}, - author={Brechmann, Eike Christian and Schepsmeier, Ulf}, - journal ={Journal of Statistical Software}, - year = {2013}, - volume={5}, - number={3}, - pages={1--27} -} - -@BOOK{brigo2006interest, - title = {Interest rate models-theory and practice: with smile, inflation and - credit}, - publisher = {Springer}, - year = {2006}, - author = {Brigo, Damiano and Mercurio, Fabio} -} - -@TECHREPORT{qis5calibpaper2010, - author = {CEIOPS}, - title = {Solvency II Calibration paper}, - institution = {CEIOPS}, - year = {2010} -} - -@TECHREPORT{qis5riskfree2010, - author = {CEIOPS}, - title = {QIS 5 Risk-free interest rates Extrapolation method}, - institution = {CEIOPS}, - year = {2010} -} - -@article{cox1985theory, - title={A theory of the term structure of interest rates}, - author={Cox, John C and Ingersoll Jr, Jonathan E and Ross, Stephen A}, - journal={Econometrica: Journal of the Econometric Society}, - pages={385--407}, - year={1985}, - publisher={JSTOR} -} - -@TECHREPORT{croforum2010, - author = {{CRO Forum}}, - title = {CRO Forum Best Practice paper - Extrapolation of Market Data}, - institution = {CRO Forum}, - year = {2010} -} - -@TECHREPORT{cfocroforum2010, - author = {{CRO Forum and CFO Forum}}, - title = {{QIS 5} Technical Specification Risk-free interest rates}, - institution = {CFO Forum and CRO Forum}, - year = {2010} -} - -@ARTICLE{curves2005technical, - author = {Curves, Zero-Coupon Yield}, - title = {Technical Documentation}, - journal = {BIS papers}, - year = {2005}, - volume = {25} -} - -@OTHER{delcouruse2012, - author = {Delcour, Ir Gil and Schoutens, W}, - institution = {Katholieke Universiteit Leuven}, - title = {On the use of risk-free rates in the discounting of insurance cash - flows}, - year = {2012} -} - -@TECHREPORT{delcouruse2011, - author = {Delcour, Ir Gil and Schoutens, W}, - title = {On the use of risk-free rates in the discounting of insurance cash - flows}, - year = {2011}, - note = {Master Thesis from the {K}atholieke {U}niversiteit {L}euven}, - institute = {{K}atholieke {U}niversiteit {L}euven} -} - -@BOOK{denuit2007actuariat, - title = {Actuariat des assurances de personnes: mod{\'e}lisation, tarification - et provisionnement}, - publisher = {Economica Paris}, - year = {2007}, - author = {Denuit, Michel and Robert, Christian P} -} - -@article{eddelbuettel2011rcpp, - title={Rcpp: Seamless R and C++ integration}, - author={Eddelbuettel, Dirk and Fran{\c{c}}ois, Romain}, - journal={Journal of Statistical Software}, - volume={40}, - number={8}, - pages={1--18}, - year={2011} -} - -@BOOK{filipovic2009term, - title = {Term-structure models: A graduate course}, - publisher = {Springer}, - year = {2009}, - author = {Filipovi{\'c}, Damir} -} - -@MISC{finanstilsynet2010, - author = {FINANSTILSYNET}, - title = {A Technical Note on the {S}mith-{W}ilson Method}, - year = {2010} -} - -@ARTICLE{geman1995changes, - author = {Geman, Helyette and El Karoui, Nicole and Rochet, Jean-Charles}, - title = {Changes of numeraire, changes of probability measure and option pricing}, - journal = {Journal of applied Probability}, - year = {1995}, - pages = {443--458}, - publisher = {JSTOR} -} - -@ARTICLE{gilli2010calibrating, - author = {Gilli, Manfred and Gro{\ss}e, Stefan and Schumann, Enrico}, - title = {Calibrating the nelson-siegel-svensson model}, - journal = {Available at SSRN 1676747}, - year = {2010} -} - -@book{glasserman2004monte, - title={Monte Carlo methods in financial engineering}, - author={Glasserman, Paul}, - volume={53}, - year={2004}, - publisher={Springer} -} - -@ARTICLE{hagan2006interpolation, - author = {Hagan, Patrick S and West, Graeme}, - title = {Interpolation methods for curve construction}, - journal = {Applied Mathematical Finance}, - year = {2006}, - volume = {13}, - pages = {89--129}, - number = {2}, - publisher = {Taylor \& Francis} -} - -@ARTICLE{harrison1983stochastic, - author = {Harrison, J Michael and Pliska, Stanley R}, - title = {A stochastic calculus model of continuous trading: complete markets}, - journal = {Stochastic processes and their applications}, - year = {1983}, - volume = {15}, - pages = {313--316}, - number = {3}, - publisher = {Elsevier} -} - -@ARTICLE{harrison1981martingales, - author = {Harrison, J Michael and Pliska, Stanley R}, - title = {Martingales and stochastic integrals in the theory of continuous - trading}, - journal = {Stochastic processes and their applications}, - year = {1981}, - volume = {11}, - pages = {215--260}, - number = {3}, - publisher = {Elsevier} -} - -@TECHREPORT{hibbert2013, - author = {Hibbert, John}, - title = {Yield curve extrapolation:work in progress}, - institution = {Moody's Analytics}, - year = {2013} -} - -@ARTICLE{hull1994numerical, - author = {Hull, John C and White, Alan D}, - title = {Numerical procedures for implementing term structure models II: Two-factor - models}, - journal = {The Journal of Derivatives}, - year = {1994}, - volume = {2}, - pages = {37--48}, - number = {2}, - publisher = {Institutional Investor Journals} -} - -@BOOK{iacus2008simulation, - title = {Simulation and inference for stochastic differential equations: with - R examples}, - publisher = {Springer}, - year = {2008}, - author = {Iacus, Stefano Maria} -} - -@ARTICLE{jarrow2003pricing, - author = {Jarrow, Robert and Yildirim, Yildiray}, - title = {Pricing treasury inflation protected securities and related derivatives - using an HJM model}, - journal = {Journal of Financial and Quantitative Analysis}, - year = {2003}, - volume = {38}, - pages = {337--358}, - number = {2}, - publisher = {Cambridge Univ Press} -} - -@article{kou2002jump, - title={A jump-diffusion model for option pricing}, - author={Kou, Steven G}, - journal={Management science}, - volume={48}, - number={8}, - pages={1086--1101}, - year={2002}, - publisher={INFORMS} -} - -@ARTICLE{leung2011inflation, - author = {Leung, Kwai Sun and Wu, Lixin}, - title = {Inflation derivatives: From market model to foreign currency analogy}, - journal = {Submitted for publication}, - year = {2011} -} - -@ARTICLE{litterman1991common, - author = {Litterman, Robert B and Scheinkman, Jose}, - title = {Common factors affecting bond returns}, - journal = {The Journal of Fixed Income}, - year = {1991}, - volume = {1}, - pages = {54--61}, - number = {1}, - publisher = {Institutional Investor Journals} -} - -@TECHREPORT{NBERw10418, - author = {Francis A. Longstaff and Sanjay Mithal and Eric Neis}, - title = {Corporate Yield Spreads: Default Risk or Liquidity? New Evidence - from the Credit-Default Swap Market}, - institution = {National Bureau of Economic Research}, - year = {2004}, - type = {Working Paper}, - number = {10418}, - month = {April}, - abstract = {We use the information in credit-default swaps to obtain direct measures - of the size of the default and nondefault components in corporate - spreads. We find that the majority of the corporate spread is due - to default risk. This result holds for all rating categories and - is robust to the definition of the riskless curve. We also find that - the nondefault component is time varying and strongly related to - measures of bond-specific illiquidity as well as to macroeconomic - measures of bond-market liquidity.}, - series = {Working Paper Series}, - url = {http://www.nber.org/papers/w10418} -} - -@ARTICLE{mercurio2005pricing, - author = {Mercurio, Fabio}, - title = {Pricing Inflation-indexed derivatives}, - journal = {Quantitative Finance}, - year = {2005}, - volume = {5}, - pages = {289--302}, - number = {3}, - publisher = {Taylor \& Francis} -} - -@article{merton1976option, - title={Option pricing when underlying stock returns are discontinuous}, - author={Merton, Robert C}, - journal={Journal of financial economics}, - volume={3}, - number={1}, - pages={125--144}, - year={1976}, - publisher={Elsevier} -} - -@MANUAL{Moudiki2013Ra, - title = {mcGlobaloptim: Global optimization using Monte Carlo and Quasi Monte - Carlo simulation}, - author = {Thierry Moudiki}, - year = {2013}, - note = {R package version 0.1 available at \url{http://goo.gl/qnIaDx}} -} - -@MANUAL{Moudiki2013Rb, - title = {ycinterextra: Yield curve or zero-coupon prices interpolation and - extrapolation}, - author = {Thierry Moudiki}, - year = {2013}, - note = {R package version 0.1 available at \url{http://goo.gl/7MUWP2}} -} - -@ARTICLE{nelson1987parsimonious, - author = {Nelson, Charles R and Siegel, Andrew F}, - title = {Parsimonious modeling of yield curves}, - journal = {Journal of Business}, - year = {1987}, - pages = {473--489}, - publisher = {JSTOR} -} - -@TECHREPORT{pooter2007examining, - author = {de Pooter, MD}, - title = {Examining the Nelson-Siegel class of term structure models}, - institution = {Tinbergen Institute}, - year = {2007} -} - -@MANUAL{R2013, - title = {R: A Language and Environment for Statistical Computing}, - author = {{R Core Team}}, - organization = {R Foundation for Statistical Computing}, - address = {Vienna, Austria}, - year = {2013}, - note = {Available at \url{http://www.R-project.org/}} -} - -@TECHREPORT{smithwilson2001, - author = {Smith, A. and Wilson, T.}, - title = {Fitting Yield curves with long Term Constraints}, - institution = {Bacon \& Woodrow}, - year = {2001}, - note = {Research Notes, Bacon and Woodrow} -} - -@ARTICLE{svensson1995estimating, - author = {Svensson, Lars EO}, - title = {Estimating forward interest rates with the extended {N}elson \& {S}iegel - method}, - journal = {Sveriges Riksbank Quarterly Review}, - year = {1995}, - volume = {3}, - pages = {13--26}, - number = {1} -} - -@article{uhlenbeck1930theory, - title={On the theory of the Brownian motion}, - author={Uhlenbeck, George E and Ornstein, Leonard Salomon}, - journal={Physical review}, - volume={36}, - number={5}, - pages={823}, - year={1930}, - publisher={APS} -} - -@article{vasicek1977equilibrium, - title={An equilibrium characterization of the term structure}, - author={Vasicek, Oldrich}, - journal={Journal of financial economics}, - volume={5}, - number={2}, - pages={177--188}, - year={1977}, - publisher={Elsevier} -} - -@book{wickham2009ggplot2, - title={ggplot2: elegant graphics for data analysis}, - author={Wickham, Hadley}, - year={2009}, - publisher={Springer} -} - -@ARTICLE{wu2013inflation, - author = {Wu, Lixin}, - title = {Inflation-rate Derivatives: From Market Model to Foreign Currency - Analogy}, - journal = {arXiv preprint arXiv:1302.0574}, - year = {2013} -} - From 0af593f30aa1552a7d910d10782f4e31f5e739c6 Mon Sep 17 00:00:00 2001 From: thierrymoudiki Date: Tue, 6 Oct 2020 17:22:02 +0200 Subject: [PATCH 2/5] update docs - roxygen failing --- man/esgcortest.Rd | 2 +- man/esgplotbands.Rd | 6 +++--- man/simdiff.Rd | 14 +++++++------- man/simshocks.Rd | 25 +++++++++++++++++-------- 4 files changed, 28 insertions(+), 19 deletions(-) diff --git a/man/esgcortest.Rd b/man/esgcortest.Rd index 338081d..94e4f33 100644 --- a/man/esgcortest.Rd +++ b/man/esgcortest.Rd @@ -41,7 +41,7 @@ family = 1, par = 0.8) (test1 <- esgcortest(s0.par1)) (test2 <- esgcortest(s0.par2)) -par(mfrow=c(2, 1)) +#par(mfrow=c(2, 1)) esgplotbands(test1) esgplotbands(test2) diff --git a/man/esgplotbands.Rd b/man/esgplotbands.Rd index 1c2fb54..41054a7 100644 --- a/man/esgplotbands.Rd +++ b/man/esgplotbands.Rd @@ -31,9 +31,9 @@ frequency = "quart", model = "OU", x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) -par(mfrow=c(2,1)) +#par(mfrow=c(2,1)) esgplotbands(x, xlab = "time", ylab = "values") -matplot(time(x), x, type = 'l', xlab = "time", ylab = "series values") +matplot(as.vector(time(x)), x, type = 'l', xlab = "time", ylab = "series values") # Martingale test @@ -64,7 +64,7 @@ family = 1, par = 0.8) (test1 <- esgcortest(s0.par1)) (test2 <- esgcortest(s0.par2)) -par(mfrow=c(2, 1)) +#par(mfrow=c(2, 1)) esgplotbands(test1) esgplotbands(test2) } diff --git a/man/simdiff.Rd b/man/simdiff.Rd index 95465fd..881307e 100644 --- a/man/simdiff.Rd +++ b/man/simdiff.Rd @@ -118,9 +118,9 @@ sim.OU <- simdiff(n = 10, horizon = 5, model = "OU", x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) head(sim.OU) -par(mfrow=c(2,1)) +#par(mfrow=c(2,1)) esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") -matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") +matplot(as.vector(time(sim.OU)), sim.OU, type = 'l', main = "with matplot") # OU with simulated shocks (check the dimensions) @@ -130,9 +130,9 @@ sim.OU <- simdiff(n = 50, horizon = 5, frequency = "quart", model = "OU", x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3, eps = eps0) -par(mfrow=c(2,1)) +#par(mfrow=c(2,1)) esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") -matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") +matplot(as.vector(time(sim.OU)), sim.OU, type = 'l', main = "with matplot") # a different plot esgplotts(sim.OU) @@ -144,7 +144,7 @@ sim.CIR <- simdiff(n = 50, horizon = 5, model = "CIR", x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = 0.05) esgplotbands(sim.CIR, xlab = "time", ylab = "values", main = "with esgplotbands") -matplot(time(sim.CIR), sim.CIR, type = 'l', main = "with matplot") +matplot(as.vector(time(sim.CIR)), sim.CIR, type = 'l', main = "with matplot") @@ -156,7 +156,7 @@ sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", x0 = 100, theta1 = 0.03, theta2 = 0.1, eps = eps0) esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") -matplot(time(sim.GBM), sim.GBM, type = 'l', main = "with matplot") +matplot(as.vector(time(sim.GBM)), sim.GBM, type = 'l', main = "with matplot") eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") @@ -165,7 +165,7 @@ sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", x0 = 100, theta1 = 0.03, theta2 = 0.1, eps = eps0) esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") -matplot(time(sim.GBM), sim.GBM, type = 'l', main = "with matplot") +matplot(as.vector(time(sim.GBM)), sim.GBM, type = 'l', main = "with matplot") } \references{ Black, F., Scholes, M.S. (1973) The pricing of options and corporate liabilities, diff --git a/man/simshocks.Rd b/man/simshocks.Rd index a45d8d8..4c0d416 100644 --- a/man/simshocks.Rd +++ b/man/simshocks.Rd @@ -11,8 +11,9 @@ simshocks( method = c("classic", "antithetic", "mm", "hybridantimm", "TAG"), family = NULL, par = NULL, - par2 = NULL, - type = c("CVine", "DVine"), + par2 = rep(0, length(par)), + RVM = NULL, + type = c("CVine", "DVine", "RVine"), seed = 123 ) } @@ -28,7 +29,7 @@ simshocks( hybrid antithetic variates + moment matching or "TAG" (see the 4th reference for the latter).} -\item{family}{the same as \code{\link{CDVineSim}} from package \code{CDVine}. +\item{family}{ A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values 0 = independence copula, 1 = Gaussian copula, @@ -63,16 +64,20 @@ A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values 39 = rotated BB7 copula (270 degrees), 40 = rotated BB8 copula (270 degrees)} -\item{par}{the same as \code{\link{CDVineSim}} from package \code{CDVine}. +\item{par}{ A d*(d-1)/2 vector of pair-copula parameters.} -\item{par2}{the same as \code{\link{CDVineSim}} from package \code{CDVine}. +\item{par2}{ A d*(d-1)/2 vector of second parameters for pair-copula families with two parameters (t, BB1, BB6, BB7, BB8; no default).} -\item{type}{type of the vine model: -1 : C-vine -2 : D-vine} +\item{RVM}{An \code{\link[VineCopula]{RVineMatrix}} object containing the +information of the R-vine copula model. Optionally, a length-N list +of \code{VineCopula::RVineMatrix} objects sharing the same structure, but +possibly different family/parameter can be supplied. Must be not NULL for +type == "RVine", not used otherwise. See also VineCopula::RVineMatrix.} + +\item{type}{type of vine model: "CVine", "DVine" or "RVine"} \item{seed}{reproducibility seed} } @@ -140,6 +145,10 @@ mvtnorm: Multivariate Normal and t Distributions. R package version 0.9-9996. Genz, A. Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195., Springer-Verlag, Heidelberg. ISBN 978-3-642-01688-2. +Thomas Nagler, Ulf Schepsmeier, Jakob Stoeber, Eike Christian Brechmann, Benedikt +Graeler and Tobias Erhardt (2020). VineCopula: Statistical Inference of Vine Copulas. +R package version 2.4.0. https://CRAN.R-project.org/package=VineCopula + Nteukam T, O., & Planchet, F. (2012). Stochastic evaluation of life insurance contracts: Model point on asset trajectories and measurement of the error related to aggregation. Insurance: Mathematics and Economics, 51(3), 624-631. From c85f1da69171777416b936696c122336465f7c02 Mon Sep 17 00:00:00 2001 From: thierrymoudiki Date: Tue, 6 Oct 2020 17:23:46 +0200 Subject: [PATCH 3/5] use VineCopula package --- .DS_Store | Bin 6148 -> 6148 bytes DESCRIPTION | 17 +++--- ESGtoolkit.Rproj | 2 +- NAMESPACE | 1 - R/plots.R | 4 +- R/simulations.R | 140 ++++++++++++++++++++++++++++++----------------- R/tests.R | 32 ++++++----- R/zzz.R | 9 +++ README.md | 4 +- _pkgdown.yml | 3 + src/.DS_Store | Bin 0 -> 6148 bytes src/symbols.rds | Bin 17830 -> 5441 bytes 12 files changed, 135 insertions(+), 77 deletions(-) create mode 100644 R/zzz.R create mode 100644 src/.DS_Store diff --git a/.DS_Store b/.DS_Store index 50bb2658331e57091463470229ff11defc9587b6..85a07aa00702facd43dd31cc4187cf0382404a5b 100644 GIT binary patch delta 94 zcmZoMXfc@JFT%{gz`)4BAi$8Ela!yI1LQFqZZ)+ delta 75 zcmZoMXfc@JFUrWkzyQPo3=F9ZB|w +Version: 0.3.0 +Date: 2020-10-06 +Author: T. Moudiki +URL: https://www.example.com +Maintainer: T. Moudiki Description: A toolkit for Monte Carlo Simulations in Finance, Economics, Insurance, Physics. Multiple simulation models can be created by combining building blocks provided in the package. License: BSD_3_clause Clear + file LICENSE -Depends: CDVine, ggplot2, gridExtra, reshape2, ycinterextra +Depends: ggplot2, gridExtra, reshape2, ycinterextra, VineCopula Imports: Rcpp(>= 0.11.0) Suggests: - knitr, - fOptions, + devtools, testthat LinkingTo: Rcpp -VignetteBuilder: knitr -Collate: 'RcppExports.R' 'fwdrates.R' 'plots.R' 'simulations.R' 'tests.R' 'tools.R' +Collate: 'RcppExports.R' 'fwdrates.R' 'plots.R' 'simulations.R' 'tests.R' 'tools.R' 'zzz.R' Packaged: 2014-06-12 23:32:30 UTC; Thierry NeedsCompilation: yes Repository: CRAN diff --git a/ESGtoolkit.Rproj b/ESGtoolkit.Rproj index 5f46c9a..0232760 100644 --- a/ESGtoolkit.Rproj +++ b/ESGtoolkit.Rproj @@ -13,6 +13,6 @@ RnwWeave: knitr LaTeX: pdfLaTeX BuildType: Package -PackageUseDevtools: Yes PackageInstallArgs: --no-multiarch --with-keep.source PackageCheckArgs: --as-cran --no-vignettes +PackageRoxygenize: rd,collate,namespace diff --git a/NAMESPACE b/NAMESPACE index fa37ab5..36869ee 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -12,7 +12,6 @@ export(simshocks) importFrom(ggplot2, ggplot) importFrom(ggplot2, qplot) importFrom(gridExtra, grid.arrange) -importFrom(CDVine, CDVineSim) importFrom(reshape2, melt) importFrom(ycinterextra, ycinter) importFrom(ycinterextra, ycextra) diff --git a/R/plots.R b/R/plots.R index 39b61b2..51577db 100644 --- a/R/plots.R +++ b/R/plots.R @@ -35,7 +35,7 @@ #'model = "OU", #'x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) #' -#'par(mfrow=c(2,1)) +#'#par(mfrow=c(2,1)) #'esgplotbands(x, xlab = "time", ylab = "values") #'matplot(time(x), x, type = 'l', xlab = "time", ylab = "series values") #' @@ -68,7 +68,7 @@ #' #'(test1 <- esgcortest(s0.par1)) #'(test2 <- esgcortest(s0.par2)) -#'par(mfrow=c(2, 1)) +#'#par(mfrow=c(2, 1)) #'esgplotbands(test1) #'esgplotbands(test2) esgplotbands <- function(x, ...) diff --git a/R/simulations.R b/R/simulations.R index 851fa67..e7598d3 100644 --- a/R/simulations.R +++ b/R/simulations.R @@ -1,6 +1,38 @@ # simulation of gaussian shocks -------------------------------------------- +# util. function to reproduce results from package CDVine +CDRVineSim <- function(N, family, par=NULL, + par2 = rep(0, length(par)), + type=c("CVine", "DVine", "RVine"), + RVM=NULL) +{ + + type <- match.arg(type) + + if (type == "RVine") + { + + stopifnot(!is.null(RVM)) + + } else { + + stopifnot(!(is.null(par))) + + # solve length(family) = d * (d - 1) / 2 for d + d <- (1 + sqrt(1 + 8 * length(family))) / 2 + + order <- 1:d + + RVM <- switch(type, + "CVine" = VineCopula::C2RVine(order, family, par, par2), + "DVine" = VineCopula::D2RVine(order, family, par, par2)) + + } + + return(VineCopula::RVineSim(N, RVM)) +} + #'@title #' #'Underlying gaussian shocks for risk factors' simulation. @@ -60,16 +92,20 @@ #' 39 = rotated BB7 copula (270 degrees), #' 40 = rotated BB8 copula (270 degrees) #' -#'@param par the same as \code{\link{CDVineSim}} from package \code{CDVine}. -#'A d*(d-1)/2 vector of pair-copula parameters. +#'@param par A d*(d-1)/2 vector of pair-copula parameters. +#' +#'@param par2 A d*(d-1)/2 vector of second parameters for pair-copula +#'families with two parameters (optional; default: +#' par2 = rep(0,length(family))), necessary for the t-, BB1, BB6, BB7, +#' BB8, Tawn type 1 and type 2 copulas. #' -#'@param par2 the same as \code{\link{CDVineSim}} from package \code{CDVine}. -#'A d*(d-1)/2 vector of second parameters for pair-copula families with two -#'parameters (t, BB1, BB6, BB7, BB8; no default). +#'@param RVM An \code{\link{RVineMatrix()}} object containing the information of the R-vine +#'copula model. Optionally, a length-N list of \code{\link{RVineMatrix()}} +#'objects sharing the same structure, but possibly different family/parameter +#'can be supplied. Must be not NULL for +#'type == "RVine", not used otherwise. See also VineCopula::RVineMatrix. #' -#'@param type type of the vine model: -#' 1 : C-vine -#' 2 : D-vine +#'@param type type of vine model: "CVine", "DVine" or "RVine" #' #'@param seed reproducibility seed #' @@ -138,14 +174,18 @@ #' colMeans(s0[[5]]) #' apply(s0[[3]], 2, sd) #' apply(s0[[4]], 2, sd) -#' +#' +#' simshocks <- function(n, horizon, frequency = c("annual", "semi-annual", "quarterly", "monthly", "weekly", "daily"), method = c("classic", "antithetic", "mm", "hybridantimm", "TAG"), - family = NULL, par = NULL, par2 = NULL, type = c("CVine", "DVine"), + family = NULL, + par = NULL, par2 = rep(0, length(par)), + RVM = NULL, + type = c("CVine", "DVine", "RVine"), seed = 123) { if (floor(n) != n) stop("'n' must be an integer") @@ -159,6 +199,8 @@ simshocks <- function(n, horizon, "monthly" = 1/12, "weekly" = 1/52, "daily" = 1/252) + type <- match.arg(type) + method <- match.arg(method) m <- horizon/delta type <- match.arg(type) @@ -203,63 +245,63 @@ simshocks <- function(n, horizon, start = delta, end = horizon, deltat = delta)) } } - else # !is.null(family) && !is.null(par) - { + else # !is.null(family) && !is.null(par) # C, D, R-Vine + { nb.sim <- n*m - + if (method == "classic") { - shocks.sim <- qnorm(CDVineSim(N = nb.sim, - family, par, par2, type)) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), - start = delta, end = horizon, deltat = delta))) + shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, + family, par, par2, type)) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), + start = delta, end = horizon, deltat = delta))) } - + if (method == "antithetic") { half.nb.sim <- nb.sim/2 - if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") - temp <- qnorm(CDVineSim(N = half.nb.sim, - family, par, par2, type)) + if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") + temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, + family, par, par2, type)) shocks.sim <- rbind(temp, -temp) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), start = delta, end = horizon, deltat = delta))) } - - if (method == "mm") + + if (method == "mm") { - shocks.sim <- qnorm(CDVineSim(N = nb.sim, - family, par, par2, type)) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), - start = delta, end = horizon, deltat = delta))) + shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, + family, par, par2, type)) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), + start = delta, end = horizon, deltat = delta))) } - + if (method == "hybridantimm") { half.nb.sim <- nb.sim/2 if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") - temp <- qnorm(CDVineSim(N = half.nb.sim, - family, par, par2, type)) + temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, + family, par, par2, type)) shocks.sim <- rbind(temp, -temp) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), - start = delta, end = horizon, deltat = delta))) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), + start = delta, end = horizon, deltat = delta))) } - + if (method == "TAG") { - if (!is.null(family) && family > 0) warning("for method == 'TAG', only the independence copula is implemented") - return(lapply(1:d, function(i) - ts(data = TAG(n = n, m = m), - start = delta, end = horizon, deltat = delta))) - } + if (!is.null(family) && family > 0) warning("for method == 'TAG', only the independence copula is implemented") + return(lapply(1:d, function(i) + ts(data = TAG(n = n, m = m), + start = delta, end = horizon, deltat = delta))) + } } } simshocks <- cmpfun(simshocks) @@ -397,7 +439,7 @@ simshocks <- cmpfun(simshocks) #' model = "OU", #' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) #'head(sim.OU) -#'par(mfrow=c(2,1)) +#'#par(mfrow=c(2,1)) #'esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") #'matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") #' @@ -409,7 +451,7 @@ simshocks <- cmpfun(simshocks) #' model = "OU", #' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3, #' eps = eps0) -#'par(mfrow=c(2,1)) +#'#par(mfrow=c(2,1)) #'esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") #'matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") #'# a different plot diff --git a/R/tests.R b/R/tests.R index dae0068..537454d 100644 --- a/R/tests.R +++ b/R/tests.R @@ -402,20 +402,22 @@ esgmartingaletest <- function(r, X, p0, alpha = 0.05) #' #'@description #' -#'This function performs correlation tests for the shocks generated by \code{\link{simshocks}}. +#'This function performs correlation tests for the shocks generated by +#'\code{\link{simshocks}}. #' -#'@param x gaussian (bivariate) shocks, with correlation, generated by \code{\link{simshocks}}. -#' -#'@param alternative indicates the alternative hypothesis and must be one of "two.sided", -#'"greater" or "less". +#'@param x gaussian (bivariate) shocks, with correlation, generated by +#' \code{\link{simshocks}}. +#' +#'@param alternative indicates the alternative hypothesis and must be one of +#' "two.sided", "greater" or "less". #' -#'@param method which correlation coefficient is to be used for the test : -#'"pearson", "kendall", or "spearman". +#'@param method which correlation coefficient is to be used for the test : +#' "pearson", "kendall", or "spearman". #' #'@param conf.level confidence level. #' -#'@return a list with 2 components : estimated correlation coefficients, -#'and confidence intervals for the estimated correlations. +#'@return a list with 2 components : estimated correlation coefficients, and +#' confidence intervals for the estimated correlations. #' #'@export #' @@ -423,30 +425,32 @@ esgmartingaletest <- function(r, X, p0, alpha = 0.05) #' #'@references #' -#'D. J. Best & D. E. Roberts (1975), Algorithm AS 89: The Upper Tail +#'D. J. Best & D. E. Roberts (1975), Algorithm AS 89: The Upper Tail #'Probabilities of Spearman's rho. Applied Statistics, 24, 377-379. #' #'Myles Hollander & Douglas A. Wolfe (1973), Nonparametric Statistical Methods. -#' New York: John Wiley & Sons. Pages 185-194 (Kendall and Spearman tests). +#'New York: John Wiley & Sons. Pages 185-194 (Kendall and Spearman tests). #' -#'@author Thierry Moudiki + stats package +#'@author Thierry Moudiki + stats package #' #'@examples #' +#' #'nb <- 500 #' #'s0.par1 <- simshocks(n = nb, horizon = 3, frequency = "semi", #'family = 1, par = 0.2) #' -#'s0.par2 <- simshocks(n = nb, horizon = 3, frequency = "semi", +#'s0.par2 <- simshocks(n = nb, horizon = 3, frequency = "semi", #'family = 1, par = 0.8) #' #'(test1 <- esgcortest(s0.par1)) #'(test2 <- esgcortest(s0.par2)) -#'par(mfrow=c(2, 1)) +#'#par(mfrow=c(2, 1)) #'esgplotbands(test1) #'esgplotbands(test2) #' +#' esgcortest <- function(x, alternative = c("two.sided", "less", "greater"), method = c("pearson", "kendall", "spearman"), conf.level = 0.95) diff --git a/R/zzz.R b/R/zzz.R new file mode 100644 index 0000000..3791cad --- /dev/null +++ b/R/zzz.R @@ -0,0 +1,9 @@ +#.onAttach <- function(lib, pkg) { + #packageStartupMessage( + # ".\n") +#} + + +.onLoad <- function(libname, pkgname) { + +} diff --git a/README.md b/README.md index 1d43899..6938d46 100644 --- a/README.md +++ b/README.md @@ -16,7 +16,9 @@ devtools::install_github("thierrymoudiki/ESGtoolkit") - From CRAN: -TBD +``` +install.packages("ESGtoolkit") +``` # Contributing diff --git a/_pkgdown.yml b/_pkgdown.yml index e69de29..f1de3df 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -0,0 +1,3 @@ +template: + params: + bootswatch: darkly \ No newline at end of file diff --git a/src/.DS_Store b/src/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6 GIT binary patch literal 6148 zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3 zem<@ulZcFPQ@L2!n>{z**++&mCkOWA81W14cNZlEfg7;MkzE(HCqgga^y>{tEnwC%0;vJ&^%eQ zLs35+`xjp>T0PdY@HIV|s8E zSia|EqQ<~yNSLCbbIO>95r{P;PDmq%R>~jna(ZDQRflBA%=~y7Wrk#I1tVd$K%6a*W(#ESGFCu?QF4Y${PX=Y zE5f|}^FCu8j4)P^oH=fUOTvJ8aD>&EL}3D*mzp4+F+p0GTurFx0MoQ^8dRGzBUi@A zyQFUpNPp1l9v>3(>7Yd8#e+wO6|_@xfAFk_(7rq0@+~s>n-lZd;}T=8(T4IQ{AVYAe+a1A}Gb& 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e8675ee713c50bc3cfd36b335d48ac064f69e0e1 Mon Sep 17 00:00:00 2001 From: thierrymoudiki Date: Wed, 7 Oct 2020 10:04:07 +0200 Subject: [PATCH 4/5] create docs --- .DS_Store | Bin 6148 -> 8196 bytes CHANGES.md | 10 - DESCRIPTION | 16 +- ESGtoolkit.Rproj | 3 +- NAMESPACE | 5 + NEWS.md | 17 ++ R/fwdrates.R | 67 +---- R/plots.R | 183 +----------- R/simulations.R | 626 --------------------------------------- R/simulations_risks.R | 139 +++++++++ R/simulations_shocks.R | 166 +++++++++++ R/tests.R | 256 +--------------- README.md | 50 +++- _pkgdown.yml | 18 +- man/esgcortest.Rd | 6 +- man/esgdiscountfactor.Rd | 2 +- man/esgfwdrates.Rd | 18 +- man/esgmartingaletest.Rd | 4 +- man/esgmccv.Rd | 2 +- man/esgmcprices.Rd | 2 +- man/esgplotbands.Rd | 7 +- man/esgplotshocks.Rd | 6 +- man/esgplotts.Rd | 2 +- man/simdiff.Rd | 2 +- man/simshocks.Rd | 10 +- 25 files changed, 447 insertions(+), 1170 deletions(-) delete mode 100644 CHANGES.md create mode 100644 NEWS.md delete mode 100644 R/simulations.R create mode 100644 R/simulations_risks.R create mode 100644 R/simulations_shocks.R diff --git a/.DS_Store b/.DS_Store index 85a07aa00702facd43dd31cc4187cf0382404a5b..1c65d35d2ef30237090763f28a002378936b2998 100644 GIT binary patch literal 8196 zcmeHLTWl3Y82VZ7rA6_CP6@6gj0AsFXct7rJq~Th8t| zhf-^5BJo9x8jZKa#PEj5lSX;*#Y>3BOAJPd;Xz+~G#X8OGX68Or{U5QUkH-8b29VK z{Fj}XZ@$?%vjBkIIkOd@9so4TLh{8_%#(y&U4 zLLfrmRs_VhDTfI#z%~8r@9zhTO|jw1!G|nlu2(V0gAFIZ1q%ZDS>UG&{$$$m(iCtx zJ?Yqf(9-ffmX%j5Shz^jDz(b0%EwdVULh42LC)_svPVSgfDw$R!}5$wO;2xrxTQJX(K6Ehk{ z>T;ZvecJMe1M5^EYKMI<8}vxWVVh!wZj3J#@%@v5?YaJ-mGwz7_Rf-JD_5_5ux0b3 zJCawb?y2TAOBp*%$hm=i+_tiZ3bq-Hj~IT&a!uPkF_gD`JMCBlt}$WNU_WD5mekhLc-9PXi+UL z4lNy;VLR-C!;qo9P=M#)EIbcyz&W@G@4-j#8GHd>!PoE&T!o+D7x)c+hd)54CO)3Q zXG2E5jIZEZc$v+BkDe`o3M|F^Nn z=ur^@5dwD`0$7nuCA(=Y{zvD(q~HIx_y-Y_6j}fP delta 112 zcmZp1XfcprU|?W$DortDU=RQ@Ie-{MGqg=C6q~50$jCe~z?zYHGLL}8#u8`t#q1m$ xg3KU!pfYYC;R?iU8w Description: A toolkit for Monte Carlo Simulations in Finance, Economics, Insurance, Physics. Multiple simulation models can be created by combining building blocks provided in the package. License: BSD_3_clause Clear + file LICENSE -Depends: ggplot2, gridExtra, reshape2, ycinterextra, VineCopula +Depends: ggplot2, gridExtra, reshape2, ycinterextra, VineCopula, randtoolbox Imports: Rcpp(>= 0.11.0) Suggests: devtools, testthat LinkingTo: Rcpp -Collate: 'RcppExports.R' 'fwdrates.R' 'plots.R' 'simulations.R' 'tests.R' 'tools.R' 'zzz.R' +Collate: 'RcppExports.R' 'fwdrates.R' 'plots.R' 'simulations_risks.R' 'simulations_shocks.R' 'tests.R' 'tools.R' 'zzz.R' Packaged: 2014-06-12 23:32:30 UTC; Thierry NeedsCompilation: yes Repository: CRAN Date/Publication: 2014-06-13 06:17:14 -RoxygenNote: 7.1.1 +RoxygenNote: 7.1.1 \ No newline at end of file diff --git a/ESGtoolkit.Rproj b/ESGtoolkit.Rproj index 0232760..6801ae5 100644 --- a/ESGtoolkit.Rproj +++ b/ESGtoolkit.Rproj @@ -14,5 +14,4 @@ LaTeX: pdfLaTeX BuildType: Package PackageInstallArgs: --no-multiarch --with-keep.source -PackageCheckArgs: --as-cran --no-vignettes -PackageRoxygenize: rd,collate,namespace +PackageCheckArgs: --as-cran diff --git a/NAMESPACE b/NAMESPACE index 36869ee..47af7fe 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -12,7 +12,12 @@ export(simshocks) importFrom(ggplot2, ggplot) importFrom(ggplot2, qplot) importFrom(gridExtra, grid.arrange) +importFrom(randtoolbox, sobol) +importFrom(randtoolbox, halton) importFrom(reshape2, melt) +importFrom(VineCopula, C2RVine) +importFrom(VineCopula, D2RVine) +importFrom(VineCopula, RVineSim) importFrom(ycinterextra, ycinter) importFrom(ycinterextra, ycextra) importFrom(ycinterextra, fitted) diff --git a/NEWS.md b/NEWS.md new file mode 100644 index 0000000..c08fa76 --- /dev/null +++ b/NEWS.md @@ -0,0 +1,17 @@ +# version 0.3.0 + +- Use [VineCopula](http://tnagler.github.io/VineCopula/) package instead of CDVine (archived) for dependency simulation (means there's also now VineCopula's R-Vine Copulas simulation) +- Remove roxygen2 comments +- Create website with pkgdown, including docs --> https://techtonique.github.io/ESGtoolkit/ + + +# version 0.2.0 + +- refactor files +- add reproductibility seeds +- update vignette +- update LICENSE + +# version 0.1.0 + +- Initial version \ No newline at end of file diff --git a/R/fwdrates.R b/R/fwdrates.R index 2d51cf1..b6cf231 100644 --- a/R/fwdrates.R +++ b/R/fwdrates.R @@ -1,69 +1,7 @@ # Instantaneous forward rates --------------------------------------------- -#'@title -#' -#'Instantaneous forward rates -#' -#'@description -#' -#'This function provides instantaneous forward rates. They can be used -#'in no-arbitrage short rate models, to fit the yield curve exactly. -#' -#'@param in.maturities input maturities -#' -#'@param in.zerorates input zero rates -#' -#'@param n number of independent observations -#' -#'@param horizon horizon of projection -#' -#'@param out.frequency either "annual", "semi-annual", "quarterly", "monthly", -#'"weekly", or "daily" (1, 1/2, 1/4, 1/12, 1/52, 1/252) -#' -#'@param ... additional parameters provided to \code{\link{ycinter}} -#' -#'@author -#' -#'Thierry Moudiki -#' -#'@references -#' -#' Thierry Moudiki (2013). ycinterextra: Yield curve or zero-coupon prices interpolation and extrapolation. R package version 0.1. URL -#'\url{https://CRAN.R-project.org/package=ycinterextra} -#' -#'@examples -#' -#'# Yield to maturities -#'txZC <- c(0.01422,0.01309,0.01380,0.01549,0.01747,0.01940,0.02104,0.02236,0.02348, -#' 0.02446,0.02535,0.02614,0.02679,0.02727,0.02760,0.02779,0.02787,0.02786,0.02776 -#' ,0.02762,0.02745,0.02727,0.02707,0.02686,0.02663,0.02640,0.02618,0.02597,0.02578,0.02563) -#' -#'# Observed maturities -#'u <- 1:30 -#' -#'\dontrun{ -#'par(mfrow=c(2,2)) -#'fwdNS <- esgfwdrates(in.maturities = u, in.zerorates = txZC, -#' n = 10, horizon = 20, -#' out.frequency = "semi-annual", method = "NS") -#'matplot(time(fwdNS), fwdNS, type = 'l') -#' -#'fwdSV <- esgfwdrates(in.maturities = u, in.zerorates = txZC, -#' n = 10, horizon = 20, -#' out.frequency = "semi-annual", method = "SV") -#'matplot(time(fwdSV), fwdSV, type = 'l') -#' -#'fwdSW <- esgfwdrates(in.maturities = u, in.zerorates = txZC, -#' n = 10, horizon = 20, -#' out.frequency = "semi-annual", method = "SW") -#'matplot(time(fwdSW), fwdSW, type = 'l') -#' -#'fwdHCSPL <- esgfwdrates(in.maturities = u, in.zerorates = txZC, -#' n = 10, horizon = 20, -#' out.frequency = "semi-annual", method = "HCSPL") -#'matplot(time(fwdHCSPL), fwdHCSPL, type = 'l') -#'} +# Instantaneous forward rates esgfwdrates <- function(in.maturities, in.zerorates, n, horizon, out.frequency = c("annual", "semi-annual", @@ -124,5 +62,4 @@ esgfwdrates <- function(in.maturities, in.zerorates, return(ts(replicate(n, fwdrates), start = 0, deltat = delta)) -} -esgfwdrates <- cmpfun(esgfwdrates) \ No newline at end of file +} \ No newline at end of file diff --git a/R/plots.R b/R/plots.R index 51577db..2078264 100644 --- a/R/plots.R +++ b/R/plots.R @@ -2,75 +2,7 @@ # Misc plots -------------------------------------------------------------- -#'@title Plot time series percentiles and confidence intervals -#' -#'@description -#' -#'This function plots colored bands for time series percentiles and confidence -#'intervals. You can use it for outputs from \code{link{simdiff}}, -#'\code{link{esgmartingaletest}}, \code{link{esgcortest}}. -#' -#'@param x a times series object -#' -#'@param ... additionnal (optional) parameters provided to \code{plot} -#' -#'@export -#' -#'@author Thierry Moudiki -#' -#'@seealso \code{\link{esgplotts}} -#' -#'@examples -#' -#'# Times series -#' -#'kappa <- 1.5 -#'V0 <- theta <- 0.04 -#'sigma <- 0.2 -#'theta1 <- kappa*theta -#'theta2 <- kappa -#'theta3 <- sigma -#'x <- simdiff(n = 100, horizon = 5, -#'frequency = "quart", -#'model = "OU", -#'x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) -#' -#'#par(mfrow=c(2,1)) -#'esgplotbands(x, xlab = "time", ylab = "values") -#'matplot(time(x), x, type = 'l', xlab = "time", ylab = "series values") -#' -#'# Martingale test -#' -#'r0 <- 0.03 -#'S0 <- 100 -#'sigma0 <- 0.1 -#'nbScenarios <- 100 -#'horizon0 <- 10 -#'eps0 <- simshocks(n = nbScenarios, horizon = horizon0, frequency = "quart", -#' method = "anti") -#'sim.GBM <- simdiff(n = nbScenarios, horizon = horizon0, frequency = "quart", -#' model = "GBM", -#' x0 = S0, theta1 = r0, theta2 = sigma0, -#' eps = eps0) -#' -#'mc.test <- esgmartingaletest(r = r0, X = sim.GBM, p0 = S0, alpha = 0.05) -#'esgplotbands(mc.test) -#' -#'# Correlation test -#' -#'nb <- 500 -#' -#'s0.par1 <- simshocks(n = nb, horizon = 3, frequency = "semi", -#'family = 1, par = 0.2) -#' -#'s0.par2 <- simshocks(n = nb, horizon = 3, frequency = "semi", -#'family = 1, par = 0.8) -#' -#'(test1 <- esgcortest(s0.par1)) -#'(test2 <- esgcortest(s0.par2)) -#'#par(mfrow=c(2, 1)) -#'esgplotbands(test1) -#'esgplotbands(test2) +# Plot time series percentiles and confidence intervals esgplotbands <- function(x, ...) { if (is.ts(x)) @@ -143,7 +75,7 @@ esgplotbands <- function(x, ...) abs <- as.numeric(time(x$conf.int)) y.mean <- rep(0, length(abs)) - par(mfrow = c(2, 1)) + par(mfrow = c(1, 2)) bands.plot(abs, y.mean, ci.upper = x$conf.int[, 2], ci.lower = x$conf.int[, 1], col = "gray80", ylim = c(min(x$conf.int[, 1]), max(x$conf.int[, 2])), xlab = "time", ylab = "conf. int.", @@ -162,42 +94,7 @@ esgplotbands <- function(x, ...) } - -#'@title Plot time series objects -#' -#'@description This function plots outputs from \code{\link{simdiff}}. -#' -#'@details For a large number of simulations, it's preferable to use -#'\code{\link{esgplotbands}} for a synthetic view by percentiles. -#' -#'@param x a time series object, an output from \code{\link{simdiff}}. -#' -#'@seealso \code{\link{simdiff}}, \code{\link{esgplotbands}} -#' -#'@author -#' -#'Thierry Moudiki -#' -#'@export -#' -#'@references -#' -#'H. Wickham (2009), ggplot2: elegant graphics for data analysis. Springer -#'New York. -#' -#'@examples -#'kappa <- 1.5 -#'V0 <- theta <- 0.04 -#'sigma <- 0.2 -#'theta1 <- kappa*theta -#'theta2 <- kappa -#'theta3 <- sigma -#'x <- simdiff(n = 10, horizon = 5, frequency = "quart", -#'model = "OU", -#'x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) -#' -#'esgplotts(x) -#' +# Plot time series objects esgplotts <- function(x) { x0 <- start(x)[1] @@ -209,77 +106,9 @@ esgplotts <- function(x) xlab("Maturity") + ylab("Values") + ggplot2::theme(legend.position = "none") } -esgplotts <- cmpfun(esgplotts) - -#'@title Visualize the dependence between 2 gaussian shocks -#' -#'@description -#' -#'This function helps you in visualizing the dependence between 2 gaussian -#' shocks. -#' -#'@param x an output from \code{\link{simshocks}}, a list with 2 components. -#' -#'@param y an output from \code{\link{simshocks}}, a list with 2 components -#'(Optional). -#' -#'@export -#' -#'@seealso \code{\link{simshocks}} -#' -#'@author Thierry Moudiki + some nice blogs :) -#' -#'@references -#' -#'H. Wickham (2009), ggplot2: elegant graphics for data analysis. Springer -#'New York. -#' -#'@examples -#' -#'# Number of risk factors -#'d <- 2 -#' -#'# Number of possible combinations of the risk factors -#'dd <- d*(d-1)/2 -#' -#'# Family : Gaussian copula -#'fam1 <- rep(1,dd) -#'# Correlation coefficients between the risk factors (d*(d-1)/2) -#'par0.1 <- 0.1 -#'par0.2 <- -0.9 -#' -#'# Family : Rotated Clayton (180 degrees) -#'fam2 <- 13 -#'par0.3 <- 2 -#' -#'# Family : Rotated Clayton (90 degrees) -#'fam3 <- 23 -#'par0.4 <- -2 -#' -#'# number of simulations -#'nb <- 500 -#' -#'# Simulation of shocks for the d risk factors -#'s0.par1 <- simshocks(n = nb, horizon = 4, -#'family = fam1, par = par0.1) -#' -#'s0.par2 <- simshocks(n = nb, horizon = 4, -#'family = fam1, par = par0.2) -#' -#'s0.par3 <- simshocks(n = nb, horizon = 4, -#'family = fam2, par = par0.3) -#' -#'s0.par4 <- simshocks(n = nb, horizon = 4, -#'family = fam3, par = par0.4) -#' -#'\dontrun{ -#'esgplotshocks(s0.par1, s0.par2) -#'esgplotshocks(s0.par2, s0.par3) -#'esgplotshocks(s0.par2, s0.par4) -#'esgplotshocks(s0.par1, s0.par4)} -#' +# Visualize the dependence between 2 gaussian shocks esgplotshocks <- function(x, y = NULL) { x <- matrix(unlist(x), ncol = 2) @@ -338,6 +167,4 @@ esgplotshocks <- function(x, y = NULL) #arrange the plots together, with appropriate height and width for each row and column grid.arrange(plot_top, empty, scatter, plot_right, ncol=2, nrow=2, widths=c(4, 1), heights=c(1, 4)) -} -esgplotshocks <- cmpfun(esgplotshocks) - +} \ No newline at end of file diff --git a/R/simulations.R b/R/simulations.R deleted file mode 100644 index e7598d3..0000000 --- a/R/simulations.R +++ /dev/null @@ -1,626 +0,0 @@ - -# simulation of gaussian shocks -------------------------------------------- - -# util. function to reproduce results from package CDVine -CDRVineSim <- function(N, family, par=NULL, - par2 = rep(0, length(par)), - type=c("CVine", "DVine", "RVine"), - RVM=NULL) -{ - - type <- match.arg(type) - - if (type == "RVine") - { - - stopifnot(!is.null(RVM)) - - } else { - - stopifnot(!(is.null(par))) - - # solve length(family) = d * (d - 1) / 2 for d - d <- (1 + sqrt(1 + 8 * length(family))) / 2 - - order <- 1:d - - RVM <- switch(type, - "CVine" = VineCopula::C2RVine(order, family, par, par2), - "DVine" = VineCopula::D2RVine(order, family, par, par2)) - - } - - return(VineCopula::RVineSim(N, RVM)) -} - -#'@title -#' -#'Underlying gaussian shocks for risk factors' simulation. -#' -#'@description -#' -#'This function makes simulations of correlated or dependent gaussian shocks for risk factors. -#' -#'@details The function shall be used along with \code{\link{simdiff}}, in order to embed -#'correlated or dependent random gaussian shocks into simulated diffusions. -#'\code{\link{esgplotshocks}} can help in visualizing the type of dependence -#'between the shocks. -#' -#'@param n number of independent observations for each risk factor. -#' -#'@param horizon horizon of projection. -#' -#'@param frequency either "annual", "semi-annual", "quarterly", "monthly", -#'"weekly", or "daily" (1, 1/2, 1/4, 1/12, 1/52, 1/252). -#' -#'@param method either classic monte carlo, antithetic variates, moment matching, -#'hybrid antithetic variates + moment matching or "TAG" (see the 4th reference for -#'the latter). -#' -#'@param family the same as \code{\link{CDVineSim}} from package \code{CDVine}. -#'A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values -#' 0 = independence copula, -#' 1 = Gaussian copula, -#' 2 = Student t copula (t-copula), -#' 3 = Clayton copula, -#' 4 = Gumbel copula, -#' 5 = Frank copula, -#' 6 = Joe copula, -#' 7 = BB1 copula, -#' 8 = BB6 copula, -#' 9 = BB7 copula, -#' 10 = BB8 copula, -#' 13 = rotated Clayton copula (180 degrees; "survival Clayton"), -#' 14 = rotated Gumbel copula (180 degrees; "survival Gumbel"), -#' 16 = rotated Joe copula (180 degrees; "survival Joe"), -#' 17 = rotated BB1 copula (180 degrees; "survival BB1"), -#' 18 = rotated BB6 copula (180 degrees; "survival BB6"), -#' 19 = rotated BB7 copula (180 degrees; "survival BB7"), -#' 20 = rotated BB8 copula (180 degrees; "survival BB8"), -#' 23 = rotated Clayton copula (90 degrees), -#' 24 = rotated Gumbel copula (90 degrees), -#' 26 = rotated Joe copula (90 degrees), -#' 27 = rotated BB1 copula (90 degrees), -#' 28 = rotated BB6 copula (90 degrees), -#' 29 = rotated BB7 copula (90 degrees), -#' 30 = rotated BB8 copula (90 degrees), -#' 33 = rotated Clayton copula (270 degrees), -#' 34 = rotated Gumbel copula (270 degrees), -#' 36 = rotated Joe copula (270 degrees), -#' 37 = rotated BB1 copula (270 degrees), -#' 38 = rotated BB6 copula (270 degrees), -#' 39 = rotated BB7 copula (270 degrees), -#' 40 = rotated BB8 copula (270 degrees) -#' -#'@param par A d*(d-1)/2 vector of pair-copula parameters. -#' -#'@param par2 A d*(d-1)/2 vector of second parameters for pair-copula -#'families with two parameters (optional; default: -#' par2 = rep(0,length(family))), necessary for the t-, BB1, BB6, BB7, -#' BB8, Tawn type 1 and type 2 copulas. -#' -#'@param RVM An \code{\link{RVineMatrix()}} object containing the information of the R-vine -#'copula model. Optionally, a length-N list of \code{\link{RVineMatrix()}} -#'objects sharing the same structure, but possibly different family/parameter -#'can be supplied. Must be not NULL for -#'type == "RVine", not used otherwise. See also VineCopula::RVineMatrix. -#' -#'@param type type of vine model: "CVine", "DVine" or "RVine" -#' -#'@param seed reproducibility seed -#' -#'@return -#'If \code{family} and \code{par} are not provided, a univariate time -#'series object with simulated gaussian shocks for one risk factor. Otherwise, -#'a list of time series objects, containing gaussian shocks for each risk factor. -#' -#'@author Thierry Moudiki -#' -#'@references -#' -#'Brechmann, E., Schepsmeier, U. (2013). Modeling Dependence with C- -#'and D-Vine Copulas: The R Package CDVine. Journal of Statistical Software, -#'52(3), 1-27. URL \url{http://www.jstatsoft.org/v52/i03/}. -#' -#'Genz, A. Bretz, F., Miwa, T. Mi, X., Leisch, F., Scheipl, F., Hothorn, T. (2013). -#' mvtnorm: Multivariate Normal and t Distributions. R package version 0.9-9996. -#' -#'Genz, A. Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. -#'Lecture Notes in Statistics, Vol. 195., Springer-Verlag, Heidelberg. ISBN 978-3-642-01688-2. -#' -#'Nteukam T, O., & Planchet, F. (2012). Stochastic evaluation of life insurance -#'contracts: Model point on asset trajectories and measurement of the error -#'related to aggregation. Insurance: Mathematics and Economics, 51(3), 624-631. -#'URL \url{http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/ab539dcebcc4e77ac12576c6004afa67/$FILE/Article_US_v1.5.pdf} -#' -#'@export -#' -#'@seealso \code{\link{simdiff}}, \code{\link{esgplotshocks}} -#' -#'@examples -#' -#'# Number of risk factors -#'d <- 6 -#' -#'# Number of possible combinations of the risk factors -#'dd <- d*(d-1)/2 -#' -#'# Family : Gaussian copula for all -#'fam1 <- rep(1,dd) -#' -#'# Correlation coefficients between the risk factors (d*(d-1)/2) -#'par1 <- c(0.2,0.69,0.73,0.22,-0.09,0.51,0.32,0.01,0.82,0.01, -#' -0.2,-0.32,-0.19,-0.17,-0.06) -#' -#' -#'# Simulation of shocks for the 6 risk factors -#'simshocks(n = 10, horizon = 5, family = fam1, par = par1) -#' -#' -#'# Simulation of shocks for the 6 risk factors -#'# on a quarterly basis -#'simshocks(n = 10, frequency = "quarterly", horizon = 2, family = fam1, -#'par = par1) -#' -#' -#'# Simulation of shocks for the 6 risk factors simulation -#'# on a quarterly basis, with antithetic variates and moment matching. -#'s0 <- simshocks(n = 10, method = "hyb", horizon = 4, -#'family = fam1, par = par1) -#' -#' -#' s0[[2]] -#' colMeans(s0[[1]]) -#' colMeans(s0[[5]]) -#' apply(s0[[3]], 2, sd) -#' apply(s0[[4]], 2, sd) -#' -#' -simshocks <- function(n, horizon, - frequency = c("annual", "semi-annual", - "quarterly", "monthly", - "weekly", "daily"), - method = c("classic", "antithetic", - "mm", "hybridantimm", "TAG"), - family = NULL, - par = NULL, par2 = rep(0, length(par)), - RVM = NULL, - type = c("CVine", "DVine", "RVine"), - seed = 123) -{ - if (floor(n) != n) stop("'n' must be an integer") - if (n <= 1) stop("'n' must be > 1") - if (floor(horizon) != horizon) stop("'horizon' must be an integer") - frequency <- match.arg(frequency) - delta <- switch(frequency, - "annual" = 1, - "semi-annual" = 0.5, - "quarterly" = 0.25, - "monthly" = 1/12, - "weekly" = 1/52, - "daily" = 1/252) - type <- match.arg(type) - - method <- match.arg(method) - m <- horizon/delta - type <- match.arg(type) - - set.seed(seed) - - if (is.null(family) && is.null(par)) - { - if (method == "classic") - { - return(ts(data = rnormESGcpp(N = n, M = m), - start = delta, end = horizon, deltat = delta)) - } - - if (method == "antithetic") - { - half.n <- n/2 - if(floor(half.n) != half.n) stop("'n' must be divisible by 2") - temp <- rnormESGcpp(N = half.n, M = m) - return(ts(data = cbind(temp, -temp), - start = delta, end = horizon, deltat = delta)) - } - - if (method == "mm") - { - return(ts(data = scaleESG(rnormESGcpp(N = n, M = m)), - start = delta, end = horizon, deltat = delta)) - } - - if (method == "hybridantimm") - { - half.n <- n/2 - if(floor(half.n) != half.n) stop("'n' must be divisible by 2") - temp <- rnormESGcpp(N = half.n, M = m) - return(ts(data = scaleESG(cbind(temp, -temp)), - start = delta, end = horizon, deltat = delta)) - } - - if (method == "TAG") - { - return(ts(data = TAG(n, m), - start = delta, end = horizon, deltat = delta)) - } - } - else # !is.null(family) && !is.null(par) # C, D, R-Vine - { - nb.sim <- n*m - - if (method == "classic") - { - shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, - family, par, par2, type)) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), - start = delta, end = horizon, deltat = delta))) - } - - if (method == "antithetic") - { - half.nb.sim <- nb.sim/2 - if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") - temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, - family, par, par2, type)) - shocks.sim <- rbind(temp, -temp) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), - start = delta, end = horizon, deltat = delta))) - } - - if (method == "mm") - { - shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, - family, par, par2, type)) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), - start = delta, end = horizon, deltat = delta))) - } - - if (method == "hybridantimm") - { - half.nb.sim <- nb.sim/2 - if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") - temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, - family, par, par2, type)) - shocks.sim <- rbind(temp, -temp) - d <- dim(shocks.sim)[2] - return(lapply(1:d, function(i) - ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), - start = delta, end = horizon, deltat = delta))) - } - - if (method == "TAG") - { - if (!is.null(family) && family > 0) warning("for method == 'TAG', only the independence copula is implemented") - return(lapply(1:d, function(i) - ts(data = TAG(n = n, m = m), - start = delta, end = horizon, deltat = delta))) - } - } -} -simshocks <- cmpfun(simshocks) - - -# simulation of risk factors ---------------------------------------------- - -#'@title -#' -#'Simulation of diffusion processes. -#' -#'@description -#' -#'This function makes simulations of diffusion processes, that are building -#'blocks for various risk factors' models. -#' -#'@param n number of independent observations. -#' -#'@param horizon horizon of projection. -#' -#'@param frequency either "annual", "semi-annual", "quarterly", "monthly", -#'"weekly", or "daily" (1, 1/2, 1/4, 1/12, 1/52, 1/252). -#' -#'@param model either Geometric Brownian motion-like (\code{"GBM"}), -#'Cox-Ingersoll-Ross (\code{"CIR"}), or Ornstein-Uhlenbeck -#'(\code{"OU"}). -#' -#' GBM-like (GBM, Merton, Kou, Heston, Bates) -#' -#'\deqn{dX_t = \theta_1(t) X_t dt + \theta_2(t) X_t dW_t + X_t JdN_t} -#' -#' CIR -#' -#'\deqn{dX_t = (\theta_1 - \theta_2 X_t) dt + \theta_3\sqrt(X_t) dW_t} -#' -#' Ornstein-Uhlenbeck -#'\deqn{dX_t = (\theta_1 - \theta_2 X_t)dt + \theta_3 dW_t} -#' -#'Where \eqn{(W_t)_t} is a standard brownian motion : -#' -#' \deqn{dW_t ~~ \epsilon \sqrt(dt)} -#' -#'and \deqn{\epsilon ~~ N(0, 1)} -#' -#'The \eqn{\epsilon} is a gaussian increment that -#'can be an output from \code{\link{simshocks}}. -#' -#'For 'GBM-like', \eqn{\theta_1} and \eqn{\theta_2} can be held constant, and the -#' jumps part \eqn{JdN_t} is optional. In case the jumps are used, they arise -#' following a Poisson process \eqn{(N_t)}, with intensities \eqn{J} drawn either -#'from lognormal or asymmetric double-exponential distribution. -#' -#'@param x0 starting value of the process. -#' -#'@param theta1 a \code{numeric} for \code{model = "GBM"}, \code{model = "CIR"}, -#'\code{model = "OU"}. Can also be a time series object (an output from -#'\code{simdiff} with the same number of scenarios, horizon and frequency) for -#'\code{model = "GBM"}, and time-varying parameters. -#' -#'@param theta2 a \code{numeric} for \code{model = "GBM"}, \code{model = "CIR"}, -#'\code{model = "OU"}. Can also be a time series object (an output from -#'\code{simdiff} with the same number of scenarios, horizon and frequency) -#'for \code{model = "GBM"}, and time-varying parameters. -#' -#'@param theta3 a \code{numeric}, volatility for \code{model = "CIR"} and -#'\code{model = "OU"}. -#' -#'@param lambda intensity of the Poisson process counting the jumps. Optional. -#' -#'@param mu_z mean parameter for the lognormal jumps size. Optional. -#' -#'@param sigma_z standard deviation parameter for the lognormal jumps size. -#'Optional. -#' -#'@param p probability of positive jumps. Must belong to ]0, 1[. Optional. -#' -#'@param eta_up mean of positive jumps in Kou's model. Must belong to -#']0, 1[. Optional. -#' -#'@param eta_down mean of negative jumps. Must belong to ]0, 1[. Optional. -#' -#'@param eps gaussian shocks. If not provided, independent shocks are -#'generated internally by the function. Otherwise, for custom shocks, -#'must be an output from \code{\link{simshocks}}. -#' -#'@param seed reproducibility seed -#' -#'@return a time series object. -#' -#'@seealso \code{\link{simshocks}}, \code{\link{esgplotts}} -#' -#'@author Thierry Moudiki -#' -#'@references -#' -#'Black, F., Scholes, M.S. (1973) The pricing of options and corporate liabilities, -#'Journal of Political Economy, 81, 637-654. -#' -#'Cox, J.C., Ingersoll, J.E., Ross, S.A. (1985) A theory of the term structure of -#' interest rates, Econometrica, 53, 385-408. -#' -#'Iacus, S. M. (2009). Simulation and inference for stochastic differential -#'equations: with R examples (Vol. 1). Springer. -#' -#'Glasserman, P. (2004). Monte Carlo methods in financial engineering (Vol. 53). -#'Springer. -#' -#'Kou S, (2002), A jump diffusion model for option pricing, Management Sci- -#'ence Vol. 48, 1086-1101. -#' -#'Merton, R. C. (1976). Option pricing when underlying stock returns are -#'discontinuous. Journal of financial economics, 3(1), 125-144. -#' -#'Uhlenbeck, G. E., Ornstein, L. S. (1930) On the theory of Brownian motion, -#'Phys. Rev., 36, 823-841. -#' -#'Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure, -#'Journal of Financial Economics, 5, 177-188. -#' -#'@export -#' -#'@examples -#' -#'kappa <- 1.5 -#'V0 <- theta <- 0.04 -#'sigma_v <- 0.2 -#'theta1 <- kappa*theta -#'theta2 <- kappa -#'theta3 <- sigma_v -#' -#'# OU -#' -#'sim.OU <- simdiff(n = 10, horizon = 5, -#' frequency = "quart", -#' model = "OU", -#' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) -#'head(sim.OU) -#'#par(mfrow=c(2,1)) -#'esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") -#'matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") -#' -#' -#'# OU with simulated shocks (check the dimensions) -#' -#'eps0 <- simshocks(n = 50, horizon = 5, frequency = "quart", method = "anti") -#'sim.OU <- simdiff(n = 50, horizon = 5, frequency = "quart", -#' model = "OU", -#' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3, -#' eps = eps0) -#'#par(mfrow=c(2,1)) -#'esgplotbands(sim.OU, xlab = "time", ylab = "values", main = "with esgplotbands") -#'matplot(time(sim.OU), sim.OU, type = 'l', main = "with matplot") -#'# a different plot -#'esgplotts(sim.OU) -#' -#' -#'# CIR -#' -#'sim.CIR <- simdiff(n = 50, horizon = 5, -#' frequency = "quart", -#' model = "CIR", -#' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = 0.05) -#'esgplotbands(sim.CIR, xlab = "time", ylab = "values", main = "with esgplotbands") -#'matplot(time(sim.CIR), sim.CIR, type = 'l', main = "with matplot") -#' -#' -#' -#'# GBM -#' -#'eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") -#'sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", -#' model = "GBM", -#' x0 = 100, theta1 = 0.03, theta2 = 0.1, -#' eps = eps0) -#'esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") -#'matplot(time(sim.GBM), sim.GBM, type = 'l', main = "with matplot") -#' -#' -#'eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") -#'sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", -#' model = "GBM", -#' x0 = 100, theta1 = 0.03, theta2 = 0.1, -#' eps = eps0) -#'esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") -#'matplot(time(sim.GBM), sim.GBM, type = 'l', main = "with matplot") -simdiff <- function(n, horizon, - frequency = c("annual", "semi-annual", - "quarterly", "monthly", - "weekly", "daily"), - model = c("GBM", "CIR", "OU"), - x0, theta1 = NULL, theta2 = NULL, theta3 = NULL, - lambda = NULL, mu_z = NULL, sigma_z = NULL, - p = NULL, eta_up = NULL, eta_down = NULL, - eps = NULL, seed = 123) -{ - if (floor(n) != n) stop("'n' must be an integer") - if (n <= 1) stop("'n' must be > 1") - if (floor(horizon) != horizon) stop("'horizon' must be an integer") - frequency <- match.arg(frequency) - delta <- switch(frequency, - "annual" = 1, - "semi-annual" = 0.5, - "quarterly" = 0.25, - "monthly" = 1/12, - "weekly" = 1/52, - "daily" = 1/252) - m <- horizon/delta - nbdates <- m + 1 - model <- match.arg(model) - - set.seed(seed) - - if (is.null(eps)) - { - eps <- rnormESGcpp(N = n, M = m) - } - else - { - if(!all.equal(dim(eps), c(m, n))) - stop(paste("dimensions required for 'eps' : nrow (observation dates) = " - , m, "\n and ncol (number of scenarios) = ", n, ".\n Use 'simshocks' function - with same number of observations, horizon and frequency to obtain 'eps'")) - } - - if(model == "GBM") - { - if (!is.null(theta3)) - warning("unused parameter : 'theta3'") - - if(length(theta1) == 1) - { - theta1 <- matrix(data = theta1, nrow = nbdates, ncol = n) - } - else - { - if(prod(dim(theta1) == c(nbdates, n)) == 0) - stop(paste("dimensions required for 'theta1' : a numeric or nrow (observation dates) = " - , nbdates, "\n and ncol (number of scenarios) = ", n)) - } - - if(length(theta2) == 1) - { - theta2 <- matrix(data = theta2, nrow = nbdates, ncol = n) - } - else - { - if(prod(dim(theta2) == c(nbdates, n)) == 0) - stop(paste("dimensions required for 'theta2' : a numeric or nrow (observation dates) = " - , nbdates, "\n and ncol (number of scenarios) = ", n)) - } - } - - if (model == "CIR") - { - if (is.null(theta1) || is.null(theta2) || is.null(theta3)) - stop("'theta1', 'theta2' and 'theta3' must be provided") - - if(length(theta1) != 1 || length(theta2) != 1 || length(theta3) != 1) - stop(paste("length required for 'theta1', 'theta2' and 'theta3' : 1")) - - # rCIRESGcpp(const int N, const int horizon, const double Delta, const double x0, - # NumericVector theta, NumericMatrix eps) - return(ts(rCIRESGcppexact(N = n, horizon = horizon, Delta = delta, x0 = x0, - theta = c(theta1, theta2, theta3), eps = eps), - start = 0, end = horizon, deltat = delta)) - } - - if (model == "OU") - { - if (is.null(theta1) || is.null(theta2) || is.null(theta3)) - stop("'theta1', 'theta2' and 'theta3' must be provided") - - if(length(theta1) != 1 || length(theta2) != 1 || length(theta3) != 1) - stop(paste("length required for 'theta1', 'theta2' and 'theta3' : 1")) - - # rOUESGcpp(const int N, const int horizon, const double Delta, const double x0, - # NumericVector theta, NumericMatrix eps) - return(ts(rOUESGcppexact(N = n, horizon = horizon, Delta = delta, x0 = x0, - theta = c(theta1, theta2, theta3), eps = eps), - start = 0, end = horizon, deltat = delta)) - } - - if (model == "GBM") - { - if (is.null(mu_z) && is.null(sigma_z) && is.null(p) && is.null(eta_up) && is.null(eta_down)) - { - # rGBMESGcpp(const int N, const int horizon, const double Delta, const double x0, - # NumericMatrix theta1, NumericMatrix theta2, NumericMatrix eps) - return(ts(rGBMESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, - theta1 = theta1, theta2 = theta2, eps = eps), - start = 0, end = horizon, deltat = delta)) - } - - if (!is.null(lambda) && !is.null(mu_z) && !is.null(sigma_z)) - { - # rGBMjumpsnormESGcpp(const int N, const int horizon, const double Delta, - # const double x0, NumericMatrix theta1, NumericMatrix theta2, - # const double lambda, const double mu, const double sigma, - # NumericMatrix eps) - return(ts(rGBMjumpsnormESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, - theta1 = theta1, theta2 = theta2, - lambda = lambda, mu = mu_z, sigma = sigma_z, - eps = eps), start = 0, end = horizon, deltat = delta)) - } - - if (!is.null(lambda) && !is.null(p) && !is.null(eta_up) && !is.null(eta_down)) - { - # rGBMjumpskouESGcpp(const int N, const int horizon, const double Delta, - # const double x0, NumericMatrix theta1, NumericMatrix theta2, - # const double lambda, const double eta_up, const double eta_down, - # const double p, NumericMatrix eps) - return(ts(rGBMjumpskouESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, - theta1 = theta1, theta2 = theta2, - lambda = lambda, eta_up = eta_up, eta_down = eta_down, - p = p, eps = eps), - start = 0, end = horizon, deltat = delta)) - } - } - } -simdiff <- cmpfun(simdiff) - - diff --git a/R/simulations_risks.R b/R/simulations_risks.R new file mode 100644 index 0000000..e56ee51 --- /dev/null +++ b/R/simulations_risks.R @@ -0,0 +1,139 @@ +# simulation of risk factors ---------------------------------------------- + + +# Simulation of diffusion processes. +simdiff <- function(n, horizon, + frequency = c("annual", "semi-annual", + "quarterly", "monthly", + "weekly", "daily"), + model = c("GBM", "CIR", "OU"), + x0, theta1 = NULL, theta2 = NULL, theta3 = NULL, + lambda = NULL, mu_z = NULL, sigma_z = NULL, + p = NULL, eta_up = NULL, eta_down = NULL, + eps = NULL, seed = 123) +{ + if (floor(n) != n) stop("'n' must be an integer") + if (n <= 1) stop("'n' must be > 1") + if (floor(horizon) != horizon) stop("'horizon' must be an integer") + frequency <- match.arg(frequency) + delta <- switch(frequency, + "annual" = 1, + "semi-annual" = 0.5, + "quarterly" = 0.25, + "monthly" = 1/12, + "weekly" = 1/52, + "daily" = 1/252) + m <- horizon/delta + nbdates <- m + 1 + model <- match.arg(model) + + set.seed(seed) + + if (is.null(eps)) + { + eps <- rnormESGcpp(N = n, M = m) + } + else + { + if(!all.equal(dim(eps), c(m, n))) + stop(paste("dimensions required for 'eps' : nrow (observation dates) = " + , m, "\n and ncol (number of scenarios) = ", n, ".\n Use 'simshocks' function + with same number of observations, horizon and frequency to obtain 'eps'")) + } + + if(model == "GBM") + { + if (!is.null(theta3)) + warning("unused parameter : 'theta3'") + + if(length(theta1) == 1) + { + theta1 <- matrix(data = theta1, nrow = nbdates, ncol = n) + } + else + { + if(prod(dim(theta1) == c(nbdates, n)) == 0) + stop(paste("dimensions required for 'theta1' : a numeric or nrow (observation dates) = " + , nbdates, "\n and ncol (number of scenarios) = ", n)) + } + + if(length(theta2) == 1) + { + theta2 <- matrix(data = theta2, nrow = nbdates, ncol = n) + } + else + { + if(prod(dim(theta2) == c(nbdates, n)) == 0) + stop(paste("dimensions required for 'theta2' : a numeric or nrow (observation dates) = " + , nbdates, "\n and ncol (number of scenarios) = ", n)) + } + } + + if (model == "CIR") + { + if (is.null(theta1) || is.null(theta2) || is.null(theta3)) + stop("'theta1', 'theta2' and 'theta3' must be provided") + + if(length(theta1) != 1 || length(theta2) != 1 || length(theta3) != 1) + stop(paste("length required for 'theta1', 'theta2' and 'theta3' : 1")) + + # rCIRESGcpp(const int N, const int horizon, const double Delta, const double x0, + # NumericVector theta, NumericMatrix eps) + return(ts(rCIRESGcppexact(N = n, horizon = horizon, Delta = delta, x0 = x0, + theta = c(theta1, theta2, theta3), eps = eps), + start = 0, end = horizon, deltat = delta)) + } + + if (model == "OU") + { + if (is.null(theta1) || is.null(theta2) || is.null(theta3)) + stop("'theta1', 'theta2' and 'theta3' must be provided") + + if(length(theta1) != 1 || length(theta2) != 1 || length(theta3) != 1) + stop(paste("length required for 'theta1', 'theta2' and 'theta3' : 1")) + + # rOUESGcpp(const int N, const int horizon, const double Delta, const double x0, + # NumericVector theta, NumericMatrix eps) + return(ts(rOUESGcppexact(N = n, horizon = horizon, Delta = delta, x0 = x0, + theta = c(theta1, theta2, theta3), eps = eps), + start = 0, end = horizon, deltat = delta)) + } + + if (model == "GBM") + { + if (is.null(mu_z) && is.null(sigma_z) && is.null(p) && is.null(eta_up) && is.null(eta_down)) + { + # rGBMESGcpp(const int N, const int horizon, const double Delta, const double x0, + # NumericMatrix theta1, NumericMatrix theta2, NumericMatrix eps) + return(ts(rGBMESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, + theta1 = theta1, theta2 = theta2, eps = eps), + start = 0, end = horizon, deltat = delta)) + } + + if (!is.null(lambda) && !is.null(mu_z) && !is.null(sigma_z)) + { + # rGBMjumpsnormESGcpp(const int N, const int horizon, const double Delta, + # const double x0, NumericMatrix theta1, NumericMatrix theta2, + # const double lambda, const double mu, const double sigma, + # NumericMatrix eps) + return(ts(rGBMjumpsnormESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, + theta1 = theta1, theta2 = theta2, + lambda = lambda, mu = mu_z, sigma = sigma_z, + eps = eps), start = 0, end = horizon, deltat = delta)) + } + + if (!is.null(lambda) && !is.null(p) && !is.null(eta_up) && !is.null(eta_down)) + { + # rGBMjumpskouESGcpp(const int N, const int horizon, const double Delta, + # const double x0, NumericMatrix theta1, NumericMatrix theta2, + # const double lambda, const double eta_up, const double eta_down, + # const double p, NumericMatrix eps) + return(ts(rGBMjumpskouESGcpp(N = n, horizon = horizon, Delta = delta, x0 = x0, + theta1 = theta1, theta2 = theta2, + lambda = lambda, eta_up = eta_up, eta_down = eta_down, + p = p, eps = eps), + start = 0, end = horizon, deltat = delta)) + } + } +} + diff --git a/R/simulations_shocks.R b/R/simulations_shocks.R new file mode 100644 index 0000000..76b7c42 --- /dev/null +++ b/R/simulations_shocks.R @@ -0,0 +1,166 @@ + +# simulation of gaussian shocks -------------------------------------------- + + +# util. function to reproduce results from package CDVine +CDRVineSim <- function(N, family, par=NULL, + par2 = rep(0, length(par)), + type=c("CVine", "DVine", "RVine"), + RVM=NULL, U=NULL) +{ + + type <- match.arg(type) + + if (type == "RVine") + { + + stopifnot(!is.null(RVM)) + + } else { + + stopifnot(!(is.null(par))) + + # solve length(family) = d * (d - 1) / 2 for d + d <- (1 + sqrt(1 + 8 * length(family))) / 2 + + order <- 1:d + + RVM <- switch(type, + "CVine" = VineCopula::C2RVine(order, family, par, par2), + "DVine" = VineCopula::D2RVine(order, family, par, par2)) + + } + + return(VineCopula::RVineSim(N, RVM, U)) +} + + +# Underlying gaussian shocks for risk factors' simulation. +simshocks <- function(n, horizon, + frequency = c("annual", "semi-annual", + "quarterly", "monthly", + "weekly", "daily"), + method = c("classic", "antithetic", + "mm", "hybridantimm", "TAG"), + family = NULL, + par = NULL, par2 = rep(0, length(par)), + RVM = NULL, + type = c("CVine", "DVine", "RVine"), + seed = 123) +{ + if (floor(n) != n) stop("'n' must be an integer") + if (n <= 1) stop("'n' must be > 1") + if (floor(horizon) != horizon) stop("'horizon' must be an integer") + frequency <- match.arg(frequency) + delta <- switch(frequency, + "annual" = 1, + "semi-annual" = 0.5, + "quarterly" = 0.25, + "monthly" = 1/12, + "weekly" = 1/52, + "daily" = 1/252) + type <- match.arg(type) + + method <- match.arg(method) + m <- horizon/delta + type <- match.arg(type) + + set.seed(seed) + + if (is.null(family) && is.null(par)) # independent + { + if (method == "classic") + { + return(ts(data = rnormESGcpp(N = n, M = m), + start = delta, end = horizon, deltat = delta)) + } + + if (method == "antithetic") + { + half.n <- n/2 + if(floor(half.n) != half.n) stop("'n' must be divisible by 2") + temp <- rnormESGcpp(N = half.n, M = m) + return(ts(data = cbind(temp, -temp), + start = delta, end = horizon, deltat = delta)) + } + + if (method == "mm") + { + return(ts(data = scaleESG(rnormESGcpp(N = n, M = m)), + start = delta, end = horizon, deltat = delta)) + } + + if (method == "hybridantimm") + { + half.n <- n/2 + if(floor(half.n) != half.n) stop("'n' must be divisible by 2") + temp <- rnormESGcpp(N = half.n, M = m) + return(ts(data = scaleESG(cbind(temp, -temp)), + start = delta, end = horizon, deltat = delta)) + } + + if (method == "TAG") + { + return(ts(data = TAG(n, m), + start = delta, end = horizon, deltat = delta)) + } + } + else # !is.null(family) && !is.null(par) # C, D, R-Vine + { + nb.sim <- n*m + + if (method == "classic") + { + shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, + family, par, par2, type)) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), + start = delta, end = horizon, deltat = delta))) + } + + if (method == "antithetic") + { + half.nb.sim <- nb.sim/2 + if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") + temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, + family, par, par2, type)) + shocks.sim <- rbind(temp, -temp) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = matrix(shocks.sim[ , i], nrow = m, ncol = n), + start = delta, end = horizon, deltat = delta))) + } + + if (method == "mm") + { + shocks.sim <- qnorm(CDRVineSim(N = nb.sim, RVM=RVM, + family, par, par2, type)) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), + start = delta, end = horizon, deltat = delta))) + } + + if (method == "hybridantimm") + { + half.nb.sim <- nb.sim/2 + if(floor(half.nb.sim) != half.nb.sim) stop("'n' must be divisible by 2") + temp <- qnorm(CDRVineSim(N = half.nb.sim, RVM=RVM, + family, par, par2, type)) + shocks.sim <- rbind(temp, -temp) + d <- dim(shocks.sim)[2] + return(lapply(1:d, function(i) + ts(data = scaleESG(matrix(shocks.sim[ , i], nrow = m, ncol = n)), + start = delta, end = horizon, deltat = delta))) + } + + if (method == "TAG") + { + if (!is.null(family) && family > 0) warning("for method == 'TAG', only the independence copula is implemented") + return(lapply(1:d, function(i) + ts(data = TAG(n = n, m = m), + start = delta, end = horizon, deltat = delta))) + } + } +} \ No newline at end of file diff --git a/R/tests.R b/R/tests.R index 537454d..5fbaa6c 100644 --- a/R/tests.R +++ b/R/tests.R @@ -1,51 +1,6 @@ # Martingale Tests and Monte Carlo convergence -------------------------------------------------- -#'@title Stochastic discount factors or discounted values -#' -#'@description -#' -#'This function provides calculation of stochastic discount factors -#'or discounted values -#' -#'@details -#' -#'The function result is : -#' -#'\deqn{X_t exp(-\int_0^t r_s ds)} -#' -#'where \eqn{X_t} is an asset value at a given maturity \eqn{t}, and -#'\eqn{(r_s)_s} is the risk-free rate. -#' -#'@param r the short rate, a \code{numeric} (constant rate) or a time series object -#' -#'@param X the asset's price, a \code{numeric} (constant payoff or asset price) or a time series -#'object -#' -#'@seealso \code{\link{esgmcprices}}, \code{\link{esgmccv}} -#' -#'@author -#' -#'Thierry Moudiki -#' -#'@export -#' -#'@examples -#' -#'kappa <- 1.5 -#'V0 <- theta <- 0.04 -#'sigma_v <- 0.2 -#'theta1 <- kappa*theta -#'theta2 <- kappa -#'theta3 <- sigma_v -#' -#'# OU -#'r <- simdiff(n = 10, horizon = 5, -#' frequency = "quart", -#' model = "OU", -#' x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3) -#' -#'# Stochastic discount factors -#' esgdiscountfactor(r, 1) +# Stochastic discount factors or discounted values esgdiscountfactor <- function(r, X) { if(missing(r) || missing(X)) @@ -114,54 +69,9 @@ esgdiscountfactor <- function(r, X) } } } -esgdiscountfactor <- cmpfun(esgdiscountfactor) -#'@title -#' -#'Estimation of discounted asset prices -#' -#'@description -#' -#'This function computes estimators (sample mean) of -#' -#'\deqn{E[X_T exp(-\int_0^T r_s ds)]} -#' -#'where \eqn{X_T} is an asset value at given maturities \eqn{T}, and -#'\eqn{(r_s)_s} is the risk-free rate. -#' -#'@param r a \code{numeric} or a time series object, the risk-free rate(s). -#' -#'@param X asset prices obtained with \code{\link{simdiff}} -#' -#'@param maturity the corresponding maturity (optional). If missing, all the maturities -#'available in \code{X} are used. -#' -#'@seealso \code{\link{esgdiscountfactor}}, \code{\link{esgmccv}} -#' -#'@author -#' -#'Thierry Moudiki -#' -#'@export -#' -#'@examples -#' -#'# GBM -#' -#'r <- 0.03 -#' -#'eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") -#'sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", -#' model = "GBM", -#' x0 = 100, theta1 = 0.03, theta2 = 0.1, -#' eps = eps0) -#' -#'# monte carlo prices -#'esgmcprices(r, sim.GBM) -#' -#'# monte carlo price for a given maturity -#'esgmcprices(r, sim.GBM, 2) -#' + +# Estimation of discounted asset prices esgmcprices <- function(r, X, maturity = NULL) { if(missing(r) || missing(X)) @@ -193,59 +103,9 @@ esgmcprices <- function(r, X, maturity = NULL) } } -esgmcprices <- cmpfun(esgmcprices) -#'@title -#' -#'Convergence of Monte Carlo prices -#' -#'@description -#' -#'This function computes and plots confidence intervals around the estimated -#'average price, as functions of the number of simulations. -#' -#'@details -#' -#'Studying the convergence of the sample mean of : -#' -#'\deqn{E[X_T exp(-\int_0^T r_s ds)]} -#' -#'towards its true value. -#' -#'@param r a \code{numeric} or a time series object, the risk-free rate(s). -#' -#'@param X asset prices obtained with \code{\link{simdiff}} -#' -#'@param maturity the corresponding maturity (optional). If missing, all the maturities -#'available in \code{X} are used. -#' -#'@param plot if \code{TRUE} (default), a plot of the convergence is displayed. -#' -#'@param ... additional parameters provided to \code{\link{matplot}} -#' -#'@return a list with estimated average prices and the confidence intervals around them. -#' -#'@author -#' -#'Thierry Moudiki -#' -#'@examples -#' -#'r <- 0.03 -#' -#'set.seed(1) -#'eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") -#'sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", -#' model = "GBM", -#' x0 = 100, theta1 = 0.03, theta2 = 0.1, -#' eps = eps0) -#' -#'# monte carlo prices -#'esgmcprices(r, sim.GBM) -#' -#'# convergence to a specific price -#'(esgmccv(r, sim.GBM, 2)) -#' + +# Convergence of Monte Carlo prices esgmccv <- function(r, X, maturity, plot = TRUE, ...) { if(missing(r) || missing(X) || missing(maturity)) @@ -277,56 +137,9 @@ esgmccv <- function(r, X, maturity, plot = TRUE, ...) invisible(list(avg.price = avg.price, conf.int = conf.int)) } -esgmccv <- cmpfun(esgmccv) -#'@title Martingale and market consistency tests -#' -#'@description -#' -#'This function performs martingale and market consistency (t-)tests. -#' -#'@param r a \code{numeric} or a time series object, the risk-free rate(s). -#' -#'@param X a time series object, containing payoffs or projected asset values. -#' -#'@param p0 a \code{numeric} or a vector or a univariate time series containing -#'initial price(s) of an asset. -#' -#'@param alpha 1 - confidence level for the test. Default value is 0.05. -#' -#'@return The function result can be just displayed. Otherwise, you can get a list -#'by an assignation, containing (for each maturity) : -#'\itemize{ -#'\item the Student t values -#'\item the p-values -#'\item the estimated mean -#'of the martingale difference -#'\item Monte Carlo prices -#'} -#' -#'@export -#' -#'@seealso \code{\link{esgplotbands}} -#' -#'@author Thierry Moudiki -#' -#'@examples -#' -#'r0 <- 0.03 -#'S0 <- 100 -#' -#'set.seed(10) -#'eps0 <- simshocks(n = 100, horizon = 3, frequency = "quart") -#'sim.GBM <- simdiff(n = 100, horizon = 3, frequency = "quart", -#' model = "GBM", -#' x0 = S0, theta1 = r0, theta2 = 0.1, -#' eps = eps0) -#' -#'mc.test <- esgmartingaletest(r = r0, X = sim.GBM, p0 = S0, -#'alpha = 0.05) -#'esgplotbands(mc.test) -#' +# Martingale and market consistency tests esgmartingaletest <- function(r, X, p0, alpha = 0.05) { delta_X <- deltat(X) @@ -398,59 +211,8 @@ esgmartingaletest <- function(r, X, p0, alpha = 0.05) # Correlation test for shocks -------------------------------------------------------- -#'@title Correlation tests for the shocks -#' -#'@description -#' -#'This function performs correlation tests for the shocks generated by -#'\code{\link{simshocks}}. -#' -#'@param x gaussian (bivariate) shocks, with correlation, generated by -#' \code{\link{simshocks}}. -#' -#'@param alternative indicates the alternative hypothesis and must be one of -#' "two.sided", "greater" or "less". -#' -#'@param method which correlation coefficient is to be used for the test : -#' "pearson", "kendall", or "spearman". -#' -#'@param conf.level confidence level. -#' -#'@return a list with 2 components : estimated correlation coefficients, and -#' confidence intervals for the estimated correlations. -#' -#'@export -#' -#'@seealso \code{\link{esgplotbands}} -#' -#'@references -#' -#'D. J. Best & D. E. Roberts (1975), Algorithm AS 89: The Upper Tail -#'Probabilities of Spearman's rho. Applied Statistics, 24, 377-379. -#' -#'Myles Hollander & Douglas A. Wolfe (1973), Nonparametric Statistical Methods. -#'New York: John Wiley & Sons. Pages 185-194 (Kendall and Spearman tests). -#' -#'@author Thierry Moudiki + stats package -#' -#'@examples -#' -#' -#'nb <- 500 -#' -#'s0.par1 <- simshocks(n = nb, horizon = 3, frequency = "semi", -#'family = 1, par = 0.2) -#' -#'s0.par2 <- simshocks(n = nb, horizon = 3, frequency = "semi", -#'family = 1, par = 0.8) -#' -#'(test1 <- esgcortest(s0.par1)) -#'(test2 <- esgcortest(s0.par2)) -#'#par(mfrow=c(2, 1)) -#'esgplotbands(test1) -#'esgplotbands(test2) -#' -#' + +# Correlation tests for the shocks esgcortest <- function(x, alternative = c("two.sided", "less", "greater"), method = c("pearson", "kendall", "spearman"), conf.level = 0.95) @@ -473,5 +235,3 @@ esgcortest <- function(x, alternative = c("two.sided", "less", "greater"), conf.level = conf.level)$conf.int)), start = delta_x, deltat = delta_x))) } -esgcortest <- cmpfun(esgcortest) - diff --git a/README.md b/README.md index 6938d46..5cb0eec 100644 --- a/README.md +++ b/README.md @@ -3,23 +3,67 @@ ESGtoolkit [![Downloads](https://cranlogs.r-pkg.org/badges/ESGtoolkit)](https://cran.r-project.org/package=ESGtoolkit) -Tools for Stochastic Simulations. For more details, please read the package [vignette](https://www.researchgate.net/publication/338549100_ESGtoolkit_a_tool_for_stochastic_simulation_v020). +A toolkit for Monte Carlo Simulations in Finance, Economics, Insurance, Physics. Multiple simulation models can be created by combining building blocks provided in the package. + +For __more details__, you can read the package [vignette on +ResearchGate](https://www.researchgate.net/publication/338549100_ESGtoolkit_a_tool_for_stochastic_simulation_v020). Functions' documentation can be found in section 'Reference' of the [website](https://techtonique.github.io/ESGtoolkit/). + +# Table of Contents + +- [Installation](#Installation) +- [Quickstart](#Quickstart) +- [Contributing](#Contributing) +- [License](#License) + # Installation - From Github: -``` +```r library(devtools) devtools::install_github("thierrymoudiki/ESGtoolkit") ``` - From CRAN: -``` +```r install.packages("ESGtoolkit") ``` +# Quickstart + +In addition to the example below, you can read: +- [this blog](https://thierrymoudiki.wordpress.com/)'s archives +- the functions' examples in section 'Reference' on [the website](https://techtonique.github.io/ESGtoolkit/) +contain code + a lot graphs + + +```r +library(ESGtoolkit) + +# Geometric Brownian Motion (https://en.wikipedia.org/wiki/Geometric_Brownian_motion) + +eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") +sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", + model = "GBM", + x0 = 100, theta1 = 0.03, theta2 = 0.1, + eps = eps0) +esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") +matplot(as.vector(time(sim.GBM)), sim.GBM, type = 'l', main = "with matplot") + + +eps0 <- simshocks(n = 100, horizon = 5, frequency = "quart") +sim.GBM <- simdiff(n = 100, horizon = 5, frequency = "quart", + model = "GBM", + x0 = 100, theta1 = 0.03, theta2 = 0.1, + eps = eps0) +esgplotbands(sim.GBM, xlab = "time", ylab = "values", main = "with esgplotbands") +matplot(as.vector(time(sim.GBM)), sim.GBM, type = 'l', main = "with matplot") + +``` + + # Contributing Your contributions are welcome, and valuable. Please, make sure to __read__ the [Code of Conduct](CONTRIBUTING.md) first. diff --git a/_pkgdown.yml b/_pkgdown.yml index f1de3df..33d7be5 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -1,3 +1,19 @@ template: params: - bootswatch: darkly \ No newline at end of file + bootswatch: darkly +url: https://techtonique.github.io/ESGtoolkit/ +home: + title: A Toolkit for Monte Carlo Simulations + description: > + A toolkit for Monte Carlo Simulations in Finance, Economics, Insurance, Physics. + Multiple simulation models can be created by combining building blocks provided in the package. +authors: + T. Moudiki: + href: https://thierrymoudiki.github.io/ +repo: + url: + home: https://github.com/Techtonique/ + source: https://github.com/Techtonique/ESGtoolkit/ + issue: https://github.com/Techtonique/ESGtoolkit/issues + user: https://github.com/Techtonique/ + \ No newline at end of file diff --git a/man/esgcortest.Rd b/man/esgcortest.Rd index 94e4f33..03e4ccc 100644 --- a/man/esgcortest.Rd +++ b/man/esgcortest.Rd @@ -2,7 +2,7 @@ % Please edit documentation in R/tests.R \name{esgcortest} \alias{esgcortest} -\title{Correlation tests for the shocks} +\title{Correlation tests for the shocks (if Gaussian copula)} \usage{ esgcortest( x, @@ -12,7 +12,7 @@ esgcortest( ) } \arguments{ -\item{x}{gaussian (bivariate) shocks, with correlation, generated by \code{\link{simshocks}}.} +\item{x}{gaussian (bivariate) shocks, with correlation, generated by \code{\link{simshocks}} (if Gaussian copula).} \item{alternative}{indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less".} @@ -57,5 +57,5 @@ New York: John Wiley & Sons. Pages 185-194 (Kendall and Spearman tests). \code{\link{esgplotbands}} } \author{ -Thierry Moudiki + stats package +T. Moudiki + stats package } diff --git a/man/esgdiscountfactor.Rd b/man/esgdiscountfactor.Rd index 31a4011..41f5e38 100644 --- a/man/esgdiscountfactor.Rd +++ b/man/esgdiscountfactor.Rd @@ -46,5 +46,5 @@ esgdiscountfactor(r, 1) \code{\link{esgmcprices}}, \code{\link{esgmccv}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgfwdrates.Rd b/man/esgfwdrates.Rd index 68444f7..0d7a68f 100644 --- a/man/esgfwdrates.Rd +++ b/man/esgfwdrates.Rd @@ -41,33 +41,29 @@ txZC <- c(0.01422,0.01309,0.01380,0.01549,0.01747,0.01940,0.02104,0.02236,0.0234 # Observed maturities u <- 1:30 -\dontrun{ par(mfrow=c(2,2)) fwdNS <- esgfwdrates(in.maturities = u, in.zerorates = txZC, n = 10, horizon = 20, out.frequency = "semi-annual", method = "NS") -matplot(time(fwdNS), fwdNS, type = 'l') +matplot(as.vector(time(fwdNS)), fwdNS, type = 'l') fwdSV <- esgfwdrates(in.maturities = u, in.zerorates = txZC, n = 10, horizon = 20, out.frequency = "semi-annual", method = "SV") -matplot(time(fwdSV), fwdSV, type = 'l') +matplot(as.vector(time(fwdSV)), fwdSV, type = 'l') fwdSW <- esgfwdrates(in.maturities = u, in.zerorates = txZC, n = 10, horizon = 20, out.frequency = "semi-annual", method = "SW") -matplot(time(fwdSW), fwdSW, type = 'l') +matplot(as.vector(time(fwdSW)), fwdSW, type = 'l') fwdHCSPL <- esgfwdrates(in.maturities = u, in.zerorates = txZC, n = 10, horizon = 20, out.frequency = "semi-annual", method = "HCSPL") -matplot(time(fwdHCSPL), fwdHCSPL, type = 'l') -} -} -\references{ -Thierry Moudiki (2013). ycinterextra: Yield curve or zero-coupon prices interpolation and extrapolation. R package version 0.1. URL -\url{https://CRAN.R-project.org/package=ycinterextra} +matplot(as.vector(time(fwdHCSPL)), fwdHCSPL, type = 'l') + } + \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgmartingaletest.Rd b/man/esgmartingaletest.Rd index 5a791ac..61418e4 100644 --- a/man/esgmartingaletest.Rd +++ b/man/esgmartingaletest.Rd @@ -40,7 +40,7 @@ eps0 <- simshocks(n = 100, horizon = 3, frequency = "quart") sim.GBM <- simdiff(n = 100, horizon = 3, frequency = "quart", model = "GBM", x0 = S0, theta1 = r0, theta2 = 0.1, - eps = eps0) + eps = eps0, seed=10) mc.test <- esgmartingaletest(r = r0, X = sim.GBM, p0 = S0, alpha = 0.05) @@ -51,5 +51,5 @@ esgplotbands(mc.test) \code{\link{esgplotbands}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgmccv.Rd b/man/esgmccv.Rd index 79e1ea6..3c4f205 100644 --- a/man/esgmccv.Rd +++ b/man/esgmccv.Rd @@ -51,5 +51,5 @@ esgmcprices(r, sim.GBM) } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgmcprices.Rd b/man/esgmcprices.Rd index 642c712..63b7997 100644 --- a/man/esgmcprices.Rd +++ b/man/esgmcprices.Rd @@ -45,5 +45,5 @@ esgmcprices(r, sim.GBM, 2) \code{\link{esgdiscountfactor}}, \code{\link{esgmccv}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgplotbands.Rd b/man/esgplotbands.Rd index 41054a7..528d5b9 100644 --- a/man/esgplotbands.Rd +++ b/man/esgplotbands.Rd @@ -13,8 +13,9 @@ esgplotbands(x, ...) } \description{ This function plots colored bands for time series percentiles and confidence -intervals. You can use it for outputs from \code{link{simdiff}}, -\code{link{esgmartingaletest}}, \code{link{esgcortest}}. +intervals. You can use it for outputs from \code{\link[ESGtoolkit]{simdiff}}, +\code{\link[ESGtoolkit]{esgmartingaletest}}, \code{\link[ESGtoolkit]{esgcortest}}. + } \examples{ @@ -72,5 +73,5 @@ esgplotbands(test2) \code{\link{esgplotts}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/esgplotshocks.Rd b/man/esgplotshocks.Rd index 9fd03c5..269099f 100644 --- a/man/esgplotshocks.Rd +++ b/man/esgplotshocks.Rd @@ -54,11 +54,11 @@ family = fam2, par = par0.3) s0.par4 <- simshocks(n = nb, horizon = 4, family = fam3, par = par0.4) -\dontrun{ + esgplotshocks(s0.par1, s0.par2) esgplotshocks(s0.par2, s0.par3) esgplotshocks(s0.par2, s0.par4) -esgplotshocks(s0.par1, s0.par4)} +esgplotshocks(s0.par1, s0.par4) } \references{ @@ -69,5 +69,5 @@ New York. \code{\link{simshocks}} } \author{ -Thierry Moudiki + some nice blogs :) +T. Moudiki + some nice blogs :) } diff --git a/man/esgplotts.Rd b/man/esgplotts.Rd index df68b42..8e84f25 100644 --- a/man/esgplotts.Rd +++ b/man/esgplotts.Rd @@ -38,5 +38,5 @@ New York. \code{\link{simdiff}}, \code{\link{esgplotbands}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/simdiff.Rd b/man/simdiff.Rd index 881307e..c9cb88c 100644 --- a/man/simdiff.Rd +++ b/man/simdiff.Rd @@ -196,5 +196,5 @@ Journal of Financial Economics, 5, 177-188. \code{\link{simshocks}}, \code{\link{esgplotts}} } \author{ -Thierry Moudiki +T. Moudiki } diff --git a/man/simshocks.Rd b/man/simshocks.Rd index 4c0d416..e3f92d7 100644 --- a/man/simshocks.Rd +++ b/man/simshocks.Rd @@ -8,7 +8,7 @@ simshocks( n, horizon, frequency = c("annual", "semi-annual", "quarterly", "monthly", "weekly", "daily"), - method = c("classic", "antithetic", "mm", "hybridantimm", "TAG"), + method = c("classic", "antithetic", "mm", "hybridantimm", "TAG", "sobol", "halton"), family = NULL, par = NULL, par2 = rep(0, length(par)), @@ -26,8 +26,10 @@ simshocks( "weekly", or "daily" (1, 1/2, 1/4, 1/12, 1/52, 1/252).} \item{method}{either classic monte carlo, antithetic variates, moment matching, -hybrid antithetic variates + moment matching or "TAG" (see the 4th reference for -the latter).} +hybrid antithetic variates + moment matching, "TAG" (see the 4th reference for +the latter, sobol, halton. Options: "classic", "antithetic", + "mm", "hybridantimm", "TAG", + "sobol", "halton".} \item{family}{ A d*(d-1)/2 integer vector of C-/D-vine pair-copula families with values @@ -158,5 +160,5 @@ URL \url{http://www.ressources-actuarielles.net/EXT/ISFA/1226.nsf/0/ab539dcebcc4 \code{\link{simdiff}}, \code{\link{esgplotshocks}} } \author{ -Thierry Moudiki +T. Moudiki } From d92d98f66af30ed49f3dae21217acb75cdb577fd Mon Sep 17 00:00:00 2001 From: thierrymoudiki Date: Wed, 7 Oct 2020 11:14:25 +0200 Subject: [PATCH 5/5] create docs Pt.2 --- .DS_Store | Bin 8196 -> 8196 bytes README.md | 5 ++++- _pkgdown.yml | 8 +++++++- 3 files changed, 11 insertions(+), 2 deletions(-) diff --git a/.DS_Store b/.DS_Store index 1c65d35d2ef30237090763f28a002378936b2998..0f967ed1d299822f93d044222fd80fd656afec38 100644 GIT binary patch delta 100 zcmZp1XmOa}FT}~fz`)4BAi$7PoSc)CpP$3Hv2Ysu#0G)Q>>Ml{VjyW2h7^W;hGd3f oxRS{{0*WF)83tyCVum7yWS9iQW=DaI?3>vozOih6A;QiK0K7;Ub^rhX delta 87 zcmZp1XmOa}FU-Nfz`)4BAi$8Ela!yI1LQGmOjydknVo}$gOOvhqJW|ZP?~|6p_rkF lAvvWOqKt8}gP_>v9D&*F6AMH)vrBwq*(@abm1$yu5CBdc70dtt diff --git a/README.md b/README.md index 5cb0eec..9f47f89 100644 --- a/README.md +++ b/README.md @@ -3,6 +3,9 @@ ESGtoolkit [![Downloads](https://cranlogs.r-pkg.org/badges/ESGtoolkit)](https://cran.r-project.org/package=ESGtoolkit) +[![Last Commit](https://img.shields.io/github/last-commit/Techtonique/ESGtoolkit)](https://github.com/Techtonique/ESGtoolkit) + + A toolkit for Monte Carlo Simulations in Finance, Economics, Insurance, Physics. Multiple simulation models can be created by combining building blocks provided in the package. For __more details__, you can read the package [vignette on @@ -72,4 +75,4 @@ If you're not comfortable with Git/Version Control yet, please use [this form](h # License -[BSD 3-Clause Clear](LICENSE) © Thierry Moudiki, 2014. +[BSD 3-Clause Clear](https://techtonique.github.io/ESGtoolkit/LICENSE-text.html) © Thierry Moudiki, 2014. diff --git a/_pkgdown.yml b/_pkgdown.yml index 33d7be5..d1c80e8 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -16,4 +16,10 @@ repo: source: https://github.com/Techtonique/ESGtoolkit/ issue: https://github.com/Techtonique/ESGtoolkit/issues user: https://github.com/Techtonique/ - \ No newline at end of file +navbar: + structure: + left: [home, intro, reference, articles, tutorials, news, Techtonique] + right: [github] + components: + Techtonique: + href: ../ \ No newline at end of file