A New Scheme for Static Hedging of European Derivatives under Stochastic Volatility Models

Abstract

This paper proposes a new scheme for static hedging of European path-independent derivatives under stochastic volatility models. First, we show that pricing European path-independent derivatives under stochastic volatility models is transformed to pricing those under one-factor local volatility models. Next, applying an efficient static replication method for one-dimensional price processes developed by Takahashi and Yamazaki (2007), we present a static hedging scheme for European path-independent derivatives. Finally, a numerical example comparing our method with a dynamic hedging method under the Heston (1993) stochastic volatility model is used to demonstrate that our hedging scheme is effective in practice.

Keywords: Static Hedging, Stochastic Volatility, Markovian Projection, Plain Vanilla Option, Heston Model