Journal of Applied Mathematics and Stochastic Analysis 
Volume 2005 (2005), Issue 3, Pages 307-322
doi:10.1155/JAMSA.2005.307

Local volatility in the Heston model: a Malliavin calculus approach

Christian-Oliver Ewald

 School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
Received 23 October 2003; Revised 30 September 2004

Abstract

We implement the Heston stochastic volatility model by using multidimensional Ornstein-Uhlenbeck processes and a special Girsanov transformation, and consider the Malliavin calculus of this model. We derive explicit formulas for the Malliavin derivatives of the Heston volatility and the log-price, and give a formula for the local volatility which is approachable by Monte-Carlo methods.