Smile-Implied Hedging with Volatility Risk

Abstract

Options can be dynamically replicated using model-free Greeks extracted from the volatility smile. However, smile-implied delta and delta-gamma hedging do not achieve minimum variance in the presence of price-volatility correlation, and these strategies have shown poor performance relative to the Black-Scholes benchmark. We propose a way to extend smile-implied option replication with volatility risk management. Large-scale evidence on S&P 500 index options indicates that smile-implied delta-gamma-vega hedging strategies outperform the Black-Scholes approach as well as more sophisticated option hedging frameworks including stochastic volatility and jumps.