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Hedging with Stochastic Local Volatility

Carol Alexander 

University of Reading - ICMA Centre

Leonardo M. Nogueira 

Banco Central do Brasil - Foreign Reserves Department; University of Reading - ICMA Centre
July 2004

ISMA Centre Discussion Paper No. DP2004-11 
Abstract:      
The delta hedging performance of deterministic local volatility models is poor, with most studies showing that even the simple constant volatility Black-Scholes model performs better. But when the local volatility model is extended to capture stochastic dynamics for the spot volatility process, the hedge ratios change. Here, we derive the local volatility hedge ratios that are consistent with a stochastic spot volatility and show that the stochastic local volatility model is equivalent to the market model for implied volatilities. We also quantify the hedging error that arises from residual hedging uncertainty and provide an empirical example based on a stochastic normal mixture diffusion model for asset returns.