|
| 1 | +""" |
| 2 | +Market-calibrated data generator for deep hedging evaluation. |
| 3 | +
|
| 4 | +This module calibrates stochastic models to publicly available market data |
| 5 | +and generates synthetic paths for model evaluation. |
| 6 | +""" |
| 7 | +import warnings |
| 8 | +from datetime import datetime |
| 9 | + |
| 10 | +import numpy as np |
| 11 | +import pandas as pd |
| 12 | +import yfinance as yf |
| 13 | + |
| 14 | +from quantlab.calibration.inverse import recover_heston_params_from_implied_vols |
| 15 | +from quantlab.calibration.utils import make_heston_object_wrapper |
| 16 | +from quantlab.market_data.market_state import MarketState |
| 17 | +from quantlab.models.heston.model import HestonParameters, HestonProcess |
| 18 | +from quantlab.pricing.heston.cos import price as cos_price |
| 19 | +from quantlab.sim.heston.paths import simulate_heston_paths_torch |
| 20 | + |
| 21 | +warnings.filterwarnings("ignore") |
| 22 | + |
| 23 | + |
| 24 | +class MarketCalibrator: |
| 25 | + """Calibrates Heston model to market data for realistic synthetic data generation.""" # noqa: E501 |
| 26 | + |
| 27 | + def __init__(self, risk_free_rate=None): |
| 28 | + """ |
| 29 | + Initialize with optional risk-free rate. |
| 30 | +
|
| 31 | + Args: |
| 32 | + risk_free_rate: Risk free rate. |
| 33 | + If None, will fetch from Treasury data. |
| 34 | + """ |
| 35 | + if risk_free_rate is None: |
| 36 | + self.risk_free_rate = self._fetch_risk_free_rate() |
| 37 | + else: |
| 38 | + self.risk_free_rate = risk_free_rate |
| 39 | + |
| 40 | + def _fetch_risk_free_rate(self, maturity_years=1.0): |
| 41 | + """ |
| 42 | + Fetch appropriate risk-free rate for the given maturity. |
| 43 | +
|
| 44 | + Args: |
| 45 | + maturity_years: Maturity of the derivatives being hedged |
| 46 | + """ |
| 47 | + try: |
| 48 | + # Map maturity to appropriate Treasury security |
| 49 | + if maturity_years <= 1.0: |
| 50 | + ticker = "^IRX" # 3-month Treasury |
| 51 | + elif maturity_years <= 5.0: |
| 52 | + ticker = "^FVX" # 5-year Treasury |
| 53 | + elif maturity_years <= 10.0: |
| 54 | + ticker = "^TNX" # 10-year Treasury |
| 55 | + else: # Longer maturity |
| 56 | + ticker = "^TYX" # 30-year Treasury |
| 57 | + |
| 58 | + treasury = yf.Ticker(ticker) |
| 59 | + hist = treasury.history(period="5d") |
| 60 | + rate_percent = hist["Close"].iloc[-1] # Annual percentage rate |
| 61 | + return rate_percent / 100 # Convert to decimal |
| 62 | + |
| 63 | + except Exception as e: |
| 64 | + print(f"Warning: Could not fetch Treasury data: {e}") |
| 65 | + # Fallback: reasonable estimate based on maturity |
| 66 | + if maturity_years <= 1.0: |
| 67 | + return 0.045 # Short-term rate |
| 68 | + else: |
| 69 | + return 0.050 # Long-term rate |
| 70 | + |
| 71 | + def _fetch_option_chain(self, ticker="SPY"): |
| 72 | + """Fetch option chain data for calibration.""" |
| 73 | + try: |
| 74 | + stock = yf.Ticker(ticker) |
| 75 | + |
| 76 | + # Get current stock price from historical data |
| 77 | + hist = stock.history(period="5d") |
| 78 | + S0 = hist["Close"].iloc[-1] |
| 79 | + |
| 80 | + # Get available expiration dates (using near-term options for calibration) |
| 81 | + exp_dates = stock.options[:3] # Use first 3 expiration dates |
| 82 | + |
| 83 | + if not exp_dates: |
| 84 | + return None, None, None, S0 |
| 85 | + |
| 86 | + strikes = [] |
| 87 | + maturities = [] |
| 88 | + implied_vols = [] |
| 89 | + |
| 90 | + today = datetime.today() |
| 91 | + |
| 92 | + for exp_date in exp_dates: |
| 93 | + try: |
| 94 | + # Check if expiration date is in the future |
| 95 | + expiry = datetime.strptime(exp_date, "%Y-%m-%d") |
| 96 | + if expiry <= today: |
| 97 | + print(f"Skipping expired option date: {exp_date}") |
| 98 | + continue |
| 99 | + |
| 100 | + # Get options for this expiration |
| 101 | + opt = stock.option_chain(exp_date) |
| 102 | + |
| 103 | + # Filter to reasonable strikes around current price |
| 104 | + atm_strike = round(S0, -1) # Round to nearest 10 |
| 105 | + strike_range = [ |
| 106 | + atm_strike - 40, |
| 107 | + atm_strike + 40, |
| 108 | + ] # 80-strike range around ATM |
| 109 | + |
| 110 | + # Use calls with valid implied volatility and reasonable volume |
| 111 | + calls = opt.calls[ |
| 112 | + (opt.calls["strike"] >= strike_range[0]) |
| 113 | + & (opt.calls["strike"] <= strike_range[1]) |
| 114 | + & (opt.calls["impliedVolatility"] > 0) |
| 115 | + & (opt.calls["impliedVolatility"] < 1.0) # valid IVs |
| 116 | + & (opt.calls["volume"] > 10) # Exclude extremely high IVs |
| 117 | + & (pd.notna(opt.calls["lastPrice"])) # At least some volume |
| 118 | + & (opt.calls["lastPrice"] > 0) |
| 119 | + ].copy() |
| 120 | + |
| 121 | + if len(calls) == 0: |
| 122 | + continue |
| 123 | + |
| 124 | + # Calculate time to maturity in years |
| 125 | + T = (expiry - today).days / 365.25 |
| 126 | + if T <= 0: |
| 127 | + continue |
| 128 | + |
| 129 | + for _, row in calls.iterrows(): |
| 130 | + if row["impliedVolatility"] > 0 and row["lastPrice"] > 0: |
| 131 | + strikes.append(row["strike"]) |
| 132 | + maturities.append(T) |
| 133 | + implied_vols.append(row["impliedVolatility"]) |
| 134 | + |
| 135 | + except Exception as e: |
| 136 | + print(f"Warning: Could not get options for {exp_date}: {e}") |
| 137 | + continue |
| 138 | + |
| 139 | + if len(strikes) > 5: # Only return if we have enough data points |
| 140 | + return ( |
| 141 | + np.array(strikes), |
| 142 | + np.array(maturities), |
| 143 | + np.array(implied_vols), |
| 144 | + S0, |
| 145 | + ) |
| 146 | + else: |
| 147 | + return None, None, None, S0 # Not enough options data |
| 148 | + |
| 149 | + except Exception as e: |
| 150 | + print(f"Warning: Could not fetch option chain for {ticker}: {e}") |
| 151 | + print("Falling back to equity-based calibration...") |
| 152 | + |
| 153 | + # Still try to get S0 from equity data |
| 154 | + try: |
| 155 | + stock = yf.Ticker(ticker) |
| 156 | + hist = stock.history(period="5d") |
| 157 | + S0 = hist["Close"].iloc[-1] |
| 158 | + return None, None, None, S0 |
| 159 | + except Exception as e: |
| 160 | + print(f"Could not extract S0: {e}") |
| 161 | + return None, None, None, None |
| 162 | + |
| 163 | + def _calibrate_from_options(self, strikes, maturities, ivs, S0): |
| 164 | + """Calibrate using option market data.""" |
| 165 | + # Create market state |
| 166 | + market_state = MarketState( |
| 167 | + stock_price=S0, interest_rate=self.risk_free_rate, time=0.0 |
| 168 | + ) |
| 169 | + |
| 170 | + # Initial guess based on market conditions |
| 171 | + initial_guess = { |
| 172 | + "kappa": 2.0, |
| 173 | + "theta": np.mean(ivs) ** 2, # Rough estimate from average IV |
| 174 | + "eta": 0.3, |
| 175 | + "rho": -0.7, |
| 176 | + "v0": np.mean(ivs) ** 2, # Start with average IV squared |
| 177 | + } |
| 178 | + |
| 179 | + # Calibration bounds |
| 180 | + bounds = { |
| 181 | + "kappa": (0.1, 10.0), |
| 182 | + "theta": (0.001, 0.5), |
| 183 | + "eta": (0.01, 2.0), |
| 184 | + "rho": (-0.99, 0.99), |
| 185 | + "v0": (0.001, 0.5), |
| 186 | + } |
| 187 | + |
| 188 | + # Create wrapper |
| 189 | + cos_wrapper = make_heston_object_wrapper( |
| 190 | + pricer_func=cos_price, |
| 191 | + market_state_for_calibration=market_state, |
| 192 | + pricer_kwargs={"n_points": 2048}, |
| 193 | + ) |
| 194 | + |
| 195 | + # Perform calibration |
| 196 | + calibrated_params = recover_heston_params_from_implied_vols( |
| 197 | + strikes=strikes, |
| 198 | + maturities=maturities, |
| 199 | + target_implied_vols=ivs, |
| 200 | + market_state=market_state, |
| 201 | + initial_guess=initial_guess, |
| 202 | + pricing_func=cos_wrapper, |
| 203 | + pricing_kwargs={}, |
| 204 | + bounds=bounds, |
| 205 | + weights=None, # Equal weighting |
| 206 | + method="differential_evolution", |
| 207 | + optimizer_options={ |
| 208 | + "maxiter": 100, |
| 209 | + "seed": 42, |
| 210 | + "polish": True, |
| 211 | + "disp": True, |
| 212 | + }, |
| 213 | + verbose=False, |
| 214 | + ) |
| 215 | + |
| 216 | + calibrated_heston_params = HestonParameters( |
| 217 | + v0=calibrated_params["v0"], |
| 218 | + kappa=calibrated_params["kappa"], |
| 219 | + theta=calibrated_params["theta"], |
| 220 | + eta=calibrated_params["eta"], |
| 221 | + rho=calibrated_params["rho"], |
| 222 | + ) |
| 223 | + |
| 224 | + print("Option-based calibration successful!") |
| 225 | + self._print_calibration_results(calibrated_heston_params) |
| 226 | + |
| 227 | + return HestonProcess(calibrated_heston_params, market_state) |
| 228 | + |
| 229 | + def _calibrate_from_equity_prices(self, ticker, period): |
| 230 | + """Calibrate using equity price returns.""" |
| 231 | + # Fetch historical data |
| 232 | + data = yf.download(ticker, period=period) |
| 233 | + prices = data["Close"].values |
| 234 | + returns = np.diff(np.log(prices)) |
| 235 | + |
| 236 | + # Only proceed if we have enough data points for meaningful statistics |
| 237 | + if len(returns) < 2: |
| 238 | + print(f"Warning: Insufficient data for {ticker}, using default parameters") |
| 239 | + S0 = prices[-1] if len(prices) > 0 else 100.0 |
| 240 | + else: |
| 241 | + # Calculate target statistics |
| 242 | + target_vol = np.std(returns) * np.sqrt(252) |
| 243 | + target_drift = np.mean(returns) * 252 |
| 244 | + |
| 245 | + print(f"Target volatility: {target_vol:.4f}") |
| 246 | + print(f"Target drift: {target_drift:.4f}") |
| 247 | + |
| 248 | + S0 = prices[-1] |
| 249 | + |
| 250 | + # Create market state and parameters |
| 251 | + market_state = MarketState( |
| 252 | + stock_price=S0, |
| 253 | + interest_rate=self.risk_free_rate, |
| 254 | + time=0.0, |
| 255 | + ) |
| 256 | + |
| 257 | + initial_params = HestonParameters( |
| 258 | + v0=target_vol**2, # Square of target volatility |
| 259 | + kappa=2.0, # Mean reversion speed (typical value) |
| 260 | + theta=target_vol**2, # Long-term variance (matches target) |
| 261 | + eta=0.3, # Vol of vol (typical value) |
| 262 | + rho=-0.7, # Leverage effect (typical for equities) |
| 263 | + ) |
| 264 | + |
| 265 | + print("Equity-based calibration successful!") |
| 266 | + self._print_calibration_results(initial_params) |
| 267 | + |
| 268 | + return HestonProcess(initial_params, market_state) |
| 269 | + |
| 270 | + def _print_calibration_results(self, params: HestonParameters): |
| 271 | + """Print calibration results for debugging.""" |
| 272 | + print("Calibrated parameters:") |
| 273 | + print(f" v0 (initial variance): {params.v0:.6f}") |
| 274 | + print(f" kappa (mean reversion): {params.kappa:.6f}") |
| 275 | + print(f" theta (long-term var): {params.theta:.6f}") |
| 276 | + print(f" eta (vol of vol): {params.eta:.6f}") |
| 277 | + print(f" rho (correlation): {params.rho:.6f}") |
| 278 | + |
| 279 | + def calibrate_to_market_data( |
| 280 | + self, ticker="SPY", period="2y", use_options_if_available=True |
| 281 | + ): |
| 282 | + """ |
| 283 | + Calibrate Heston model to market data. |
| 284 | +
|
| 285 | + Args: |
| 286 | + ticker: Stock/ETF symbol (e.g., 'SPY', 'QQQ') |
| 287 | + period: Historical period ('1y', '2y', '5y') |
| 288 | + use_options_if_available: Whether to try option data first |
| 289 | +
|
| 290 | + Returns: |
| 291 | + Calibrated HestonProcess object |
| 292 | + """ |
| 293 | + print(f"Calibrating Heston model to {ticker} market data...") |
| 294 | + |
| 295 | + if use_options_if_available: |
| 296 | + strikes, maturities, ivs, S0 = self._fetch_option_chain(ticker) |
| 297 | + |
| 298 | + if strikes is not None and len(strikes) > 5: # Have enough option data |
| 299 | + print(f"Found {len(strikes)} option quotes, using for calibration...") |
| 300 | + return self._calibrate_from_options(strikes, maturities, ivs, S0) |
| 301 | + |
| 302 | + print("Using equity price data for calibration...") |
| 303 | + return self._calibrate_from_equity_prices(ticker, period) |
| 304 | + |
| 305 | + |
| 306 | +def generate_market_calibrated_paths( |
| 307 | + ticker="SPY", n_paths=10000, maturity=1.0, n_steps=252 |
| 308 | +): |
| 309 | + """ |
| 310 | + Generate market-calibrated synthetic paths for evaluation. |
| 311 | +
|
| 312 | + Args: |
| 313 | + ticker: Equity symbol to calibrate to |
| 314 | + n_paths: Number of paths to generate |
| 315 | + maturity: Time to maturity in years |
| 316 | + n_steps: Number of time steps per path |
| 317 | +
|
| 318 | + Returns: |
| 319 | + torch.Tensor of shape (n_paths, n_steps + 1) containing asset paths |
| 320 | + """ |
| 321 | + calibrator = MarketCalibrator() |
| 322 | + calibrated_process = calibrator.calibrate_to_market_data(ticker, period="2y") |
| 323 | + |
| 324 | + paths, _ = simulate_heston_paths_torch( |
| 325 | + calibrated_process, T=maturity, N=n_paths, M=n_steps, device="cpu" |
| 326 | + ) |
| 327 | + |
| 328 | + return paths.float() |
| 329 | + |
| 330 | + |
| 331 | +if __name__ == "__main__": |
| 332 | + try: |
| 333 | + paths = generate_market_calibrated_paths( |
| 334 | + "SPY", n_paths=100, maturity=1.0, n_steps=252 |
| 335 | + ) |
| 336 | + print(f"Generated paths shape: {paths.shape}") |
| 337 | + print(f"Sample path: {paths[0, :10]}") # First 10 points of first path |
| 338 | + except Exception as e: |
| 339 | + print(f"Error in generation: {e}") |
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