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

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.