Delta Hedging Performance Under Different Volatility Measures

Key Takeaways

• SVI surface increases hedging error variance 9.4% over flat ATM
• Close‑to‑close realized volatility cuts error std dev 5.8%
• Parkinson estimator yields highest hedging error among realized measures
• OTM calls benefit from SVI; OTM puts favor realized volatility
• Hedge performance depends on moneyness and market regime

Pulse Analysis

Delta‑hedging an options book hinges on the quality of the volatility input used to compute deltas. Practitioners often assume that more sophisticated models—such as a full SVI‑calibrated implied volatility surface—will automatically reduce hedging errors. In reality, the calibration process introduces noise, and the extra smile information may not translate into better hedge ratios, especially when the underlying dynamics deviate from the model’s assumptions. This nuance is critical for desks that allocate significant resources to complex volatility modeling.

The Rutgers‑Business‑School thesis examined 2,000 stratified SPX options across four VIX regimes, covering the COVID‑19 crash and the 2022 rate‑hiking cycle. Five volatility measures were tested: flat ATM IV, SVI‑derived IV, close‑to‑close realized volatility, Parkinson’s range‑based estimator, and the Yang‑Zhang estimator. Results showed that the simple close‑to‑close realized volatility outperformed all others, reducing hedging error standard deviation by 5.8%, while the SVI surface actually increased error variance by 9.4% relative to flat ATM. Parkinson’s estimator performed worst, and the Yang‑Zhang estimator lagged behind the close‑to‑close approach despite its theoretical efficiency.

For traders and risk managers, the practical takeaway is to adopt a moneyness‑ and regime‑conditional hedging strategy. Out‑of‑the‑money calls benefit from the SVI smile, whereas out‑of‑the‑money puts are better hedged with realized volatility inputs. Moreover, higher‑order Greeks—vanna, volga—and jump risk dominate residual errors, suggesting that supplementing delta hedges with vega or gamma adjustments can further improve outcomes. As markets evolve, continuous empirical validation of volatility inputs remains essential to maintain hedge effectiveness.