Regime-Dependent Delta Hedging with SVI-Calibrated Volatility Surfaces: An Empirical Analysis of SPX Index Options
Regime-Dependent Delta Hedging with SVI-Calibrated Volatility Surfaces: An Empirical Analysis of SPX Index Options
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Original abstract
This paper investigates which volatility input minimizes delta-hedging error for S&P 500 index options across different market regimes. I compare five volatility inputs for computing Black-Scholes hedge deltas: (1) flat at-the-money implied volatility, (2) strike-specific implied volatility from a calibrated Gatheral SVI surface, (3) 21-day close-to-close realized volatility, (4) 21-day Parkinson realized volatility, and (5) 21-day Yang-Zhang realized volatility. Using OptionMetrics data on 2,000 stratified SPX options from January 2019 through December 2024, I conduct daily-rebalanced delta-hedging backtests across four VIXdefined regimes (Low, Normal, High, and Crisis). The results challenge prevailing intuition. Aggregate hedging performance ranks closeto-close realized volatility first, with a statistically significant 5.8% reduction in hedging error standard deviation versus the flat BSM benchmark (F = 0.89, p = 0.008). The SVI surface, despite achieving a median calibration RMSE of 19.5 basis points and 68.6% butterfly arbitrage-free rate, increases hedging error variance by 9.4% overall. However, the optimal volatility input is regime-and moneyness-dependent: SVI dominates for out-of-themoney calls (RMSE reductions of 6-12% versus flat BSM), while realized volatility estimators outperform for out-of-the-money puts. An El Karoui-style P&L decomposition reveals that higher-order residuals (vanna, volga, jumps) dominate variance attribution across all regimes (153-162%), while discrete rebalancing error and volatility misspecification contribute negatively through the gamma-theta offset. These findings suggest that the calibration noise introduced by SVI fitting outweighs its informational benefit for most option types, but that a regime-conditional approach selecting different volatility inputs by moneyness and VIX level could improve hedging outcomes relative to any single-input strategy.