Malliavin differentiability of the Heston volatility and applications to option pricing

Alos, E. and Ewald, C.-O. (2008) Malliavin differentiability of the Heston volatility and applications to option pricing. Advances in Applied Probability, 40(1), pp. 144-162. (doi: 10.1239/aap/1208358890)

Abstract

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ewald, Professor Christian
• Authors: Alos, E., and Ewald, C.-O.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Advances in Applied Probability
• ISSN: 0001-8678