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binomial_model_IV.py
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# FILE: `StockTrader/garch_vol2.py`
from config import * # this imports all necessary packages and functions referenced but not explicitly defined below
#
# Use Binomial Pricing Model to Estimate Price of American Option Contract
#
def binomQL (underlying, strike_price, time_to_expiry, risk_free_rate, dividend_yield, volatility, option_type):
day_count = ql.Actual365Fixed();
calendar = ql.UnitedStates(ql.UnitedStates.NYSE);
todays_date = ql.Date.todaysDate();
settlement_date = calendar.advance(todays_date, ql.Period(2, ql.Days));
ql.Settings.instance().evaluationDate = settlement_date;
expiry_date = settlement_date + int(time_to_expiry * 365);
underlyingH = ql.QuoteHandle(ql.SimpleQuote(underlying));
risk_freeH = ql.YieldTermStructureHandle(ql.FlatForward(settlement_date, risk_free_rate, day_count));
div_yieldH = ql.YieldTermStructureHandle(ql.FlatForward(settlement_date, dividend_yield, day_count));
volH = ql.BlackVolTermStructureHandle(
ql.BlackConstantVol(settlement_date, calendar, volatility, day_count)
);
bsm_process = ql.BlackScholesMertonProcess(underlyingH, div_yieldH, risk_freeH, volH);
payoff = ql.PlainVanillaPayoff(ql.Option.Call if option_type == 'call' else ql.Option.Put, strike_price);
exercise = ql.AmericanExercise(settlement_date, expiry_date);
option_contract = ql.VanillaOption(payoff, exercise);
binom_engine = ql.BinomialVanillaEngine(bsm_process, 'crr', 100);
option_contract.setPricingEngine(binom_engine);
return option_contract;
def binomIV (midprice, underlying, strike_price, time_to_expiry, risk_free_rate, dividend_yield, option_type):
def objectiveIV (vol):
try:
binom_option = binomQL(underlying, strike_price, time_to_expiry, risk_free_rate, dividend_yield, vol, option_type);
return binom_option.NPV() - midprice;
except RuntimeError:
return 1e5;
try:
# result = root_scalar(objectiveIV, method='toms748', bracket=found_bracket, xtol=1e-6);
result = root_scalar(objectiveIV, method='toms748', bracket=[.005, 83], xtol=1e-6);
if result.converged:
return result.root;
else:
print('FAILED: TOMS748 CONVERGE')
return None;
except ValueError as e:
print(f'Root-finding failed: {str(e)}');
return None;
# >>> obj_binom_IV(h_price,strike,h_days_to_expiry/365,h_risk_free,h_div_yield,option_type,.005)
# 0.0
# >>> obj_binom_IV(h_price,strike,h_days_to_expiry/365,h_risk_free,h_div_yield,option_type,83)
# 144.97267785483393
def obj_binom_IV (underlying, strike_price, time_to_expiry, risk_free_rate, dividend_yield, option_type, vol):
binom = binomQL(underlying, strike_price, time_to_expiry, risk_free_rate, dividend_yield, vol, option_type);
print(binom.NPV());
# Hyatt Price: 150.26
h_price = quotes.get_quote_day("H", True);
print(f'Hyatt Price: {h_price}');
print(105*'-');
# H Expiry String: 2024-08-16
# H Days to Maturity: 21
h_expiry_str = options_data.get_closest_expiry(symbol='H', num_days=30);
h_expiry_dt = datetime.strptime(h_expiry_str, '%Y-%m-%d');
h_days_to_expiry = (h_expiry_dt - datetime.today()).days;
print(f'H Expiry String: {h_expiry_str}');
print(f'H Days to Maturity: {h_days_to_expiry}');
print(105*'-');
# Risk Free Rate [TB3MS]: 0.0524
# H Dividend Yield: 0.004
h_risk_free = fred_rate();
h_div_yield = dividend_yield('H', h_price);
print(f'Risk Free Rate [TB3MS]: {h_risk_free}');
print(f'H Dividend Yield: {h_div_yield}');
print(105*'-');
# Near Money Options:
# symbol volume bid ask strike bidsize asksize open_interest option_type
# 28 H240816P00140000 0 1.15 1.55 140.0 44 30 97 put
# 29 H240816C00140000 0 11.80 12.50 140.0 6 6 6 call
# 30 H240816P00145000 1 2.35 2.75 145.0 7 23 85 put
# 31 H240816C00145000 1 6.80 8.60 145.0 65 20 40 call
# 32 H240816P00150000 10 4.50 4.70 150.0 6 12 81 put
# 33 H240816C00150000 2 5.10 5.60 150.0 41 1 32 call
# 34 H240816P00155000 0 7.10 7.50 155.0 3 10 327 put
# 35 H240816C00155000 13 3.00 3.40 155.0 6 31 276 call
# 36 H240816P00160000 1 10.40 11.30 160.0 9 7 211 put
# 37 H240816C00160000 27 1.45 1.80 160.0 3 23 457 call
h_options = options_data.get_chain_day("H", options_data.get_closest_expiry('H', 30));
h_options.drop(
labels = ['last', 'change', 'open', 'high', 'low', 'change_percentage', 'last_volume', 'trade_date', 'prevclose', 'bidexch', 'bid_date', 'askexch', 'ask_date'],
axis = 1,
inplace= True
);
h_near_itm = h_options.loc[(h_options['strike'] >= (1-.0725)*h_price) & (h_options['strike'] <= (1+.0725)*h_price)];
print(f'Near Money Options:\n{h_near_itm}');
print(105*'-');
# Hyatt Bar Data:
# date open high low close volume log_return
# 0 2023-07-27 121.37 124.360 121.075 122.30 539682 NaN
# 1 2023-07-28 123.26 125.620 123.260 125.18 591237 0.023276
# 2 2023-07-31 125.79 127.800 125.790 126.35 782804 0.009303
# 3 2023-08-01 125.75 126.350 123.455 125.03 754097 -0.010502
# 4 2023-08-02 123.55 124.720 122.300 122.34 1050326 -0.021750
# .. ... ... ... ... ... ... ...
# 246 2024-07-19 153.44 154.730 152.000 154.61 444559 0.010860
# 247 2024-07-22 152.68 154.700 151.800 153.97 286304 -0.004148
# 248 2024-07-23 154.80 155.990 154.010 155.07 240798 0.007119
# 249 2024-07-24 153.79 154.645 150.270 150.31 417710 -0.031177
# 250 2024-07-25 149.79 151.560 147.950 150.26 663501 -0.000333
# [251 rows x 7 columns]
h_bars = quotes.get_historical_quotes(
symbol = 'H',
start_date = (datetime.today()-timedelta(weeks=52)).strftime("%Y-%m-%d"),
end_date = datetime.today().strftime("%Y-%m-%d")
);
h_bars['log_return'] = np.log(h_bars['close']).diff();
print(f'Hyatt Bar Data:\n{h_bars}');
print(105*'-');
# H Historical Volatility: 0.2747
h_historical_vol = estimate_historical_vol(h_bars);
print(f'H Historical Volatility: {h_historical_vol:.4f}');
print(105*'-');
h_contract = h_near_itm.loc[(h_near_itm['strike'] == 145.00) & (h_near_itm['option_type'] == 'put')];
h_strike = h_contract.iloc[0]['strike'];
h_option_type = h_contract.iloc[0]['option_type'];
h_contract_midprice = .5*(h_contract.iloc[0]['bid'] + h_contract.iloc[0]['ask']);
print(f'Contract for Testing:\n{h_contract}');
print(105*'-');
# Testing Contract QuantLib Object:
# <QuantLib.QuantLib.VanillaOption; proxy of <Swig Object of type 'ext::shared_ptr< VanillaOption > *' at 0x13b73a340> >
h_contract_ql = binomQL(
underlying = h_price,
strike_price = h_contract.iloc[0]['strike'],
time_to_expiry = h_days_to_expiry/365,
risk_free_rate = h_risk_free,
dividend_yield = h_div_yield,
volatility = h_historical_vol,
option_type = h_contract.iloc[0]['option_type']
);
print(f'Testing Contract QuantLib Object:\n{h_contract_ql}');
print(105*'-');
# Contract Example Midprice: 2.5500
# Contract Example NPV: 1.6792
# Contract Example Delta: -0.2700
# Contract Example Gamma: 0.0339
h_contract_npv = h_contract_ql.NPV();
h_contract_delta = h_contract_ql.delta();
h_contract_gamma = h_contract_ql.gamma();
h_contract_theta = h_contract_ql.theta();
npv_and_greeks = [h_contract_midprice, h_contract_npv, h_contract_delta, h_contract_gamma, h_contract_theta];
tmp_vars = ['Midprice', 'NPV', 'Delta', 'Gamma', 'Theta'];
for x in range(0,4):
print(f"Contract Example {tmp_vars[x]}: {npv_and_greeks[x]:.4f}");
print(105*'-');
# Binom IV: 0.3451
sigma_IV = binomIV(
midprice = .5*(h_contract.iloc[0]['bid'] + h_contract.iloc[0]['ask']),
underlying = h_price,
strike_price = h_contract.iloc[0]['strike'],
time_to_expiry = h_days_to_expiry/365,
risk_free_rate = h_risk_free,
dividend_yield = h_div_yield,
option_type = h_contract.iloc[0]['option_type']
);
print(f"Binom IV: {sigma_IV:.4f}");
print(105*'-');
# Binom Contract Price with σ_iv: 2.5500
# Broker Midprice: 2.55
h_contract_IV = binomQL(
underlying = h_price,
strike_price = h_strike,
time_to_expiry = h_days_to_expiry/365,
risk_free_rate = h_risk_free,
dividend_yield = h_div_yield,
volatility = sigma_IV,
option_type = h_option_type
);
print(f"Binom Contract Price with σ_iv: {h_contract_IV.NPV():.4f}");
print(f"Broker Midprice: {h_contract_midprice}");
print(125*'-');