Local volatility in the Heston model: a Malliavin calculus approach

Ewald, C.-O. (2005) Local volatility in the Heston model: a Malliavin calculus approach. Journal of Applied Mathematics and Stochastic Analysis, 2005(3), pp. 307-322. (doi: 10.1155/JAMSA.2005.307)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ewald, Professor Christian
• Authors: Ewald, C.-O.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Journal of Applied Mathematics and Stochastic Analysis
• ISSN: 1048-9533
• ISSN (Online): 1687-2177
• Copyright Holders: Copyright © 2005 Hindawi Publishing Corporation
• First Published: First published in Journal of Applied Mathematics and Stochastic Analysis 2005(3):307-322
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher