SPY Option Hedging: Comparing Implied Volatility and Historical Volatility

This study empirically compares the effectiveness of implied volatility (IV) and historical volatility (HV) as inputs for delta-hedging SPY options under the Black-Scholes-Merton framework. Through a structured daily rebalancing strategy and high-frequency empirical data, the analysis reveals that HV consistently outperforms IV in hedging precision, yielding a substantially lower hedging error of $5.69 compared to $13.12 from the IV-based approach. This performance gap stems from IVs inherent sensitivity to market sentiment and risk premia, which led to volatility overestimation and consequently excessive and inefficient hedging positions. In contrast, HVthough backward-lookingprovided a more stable and reliable measure of realized market risk, facilitating higher and more responsive delta values that strengthened hedging responsiveness and reduced replication errors. The findings underscore the practical implications for derivative risk management: while IV remains a valuable forward-looking indicator, its tendency to embed volatility risk premia can distort hedge ratios and increase transaction costs. HV, by comparison, offers a more robust basis for delta hedging in stable or moderately volatile markets. Nonetheless, IV may still provide critical signals during abrupt market regime shifts. This study highlights the context-dependent utility of volatility measures and suggests that hybrid approachesor regime-aware selection of HV and IVcould further optimize hedging performance. Further research extending to multiple option classes and varying macroeconomic environments is warranted to enhance the generalizability of these insights.