Malliavin Differentiability of the Heston Volatility and Applications to Option Pricing

27 Pages Posted: 16 May 2007

See all articles by Elisa Alos

Elisa Alos

University of Pompeu Fabra - Department of Economics

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Date Written: May 14, 2007

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 the first author in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.

Keywords: Malliavin calculus, stochastic volatility models, Heston model, Cox-Ingersoll-Ross process, Hull and White formula, Option pricing

JEL Classification: C02, G13

Suggested Citation

Alos, Elisa and Ewald, Christian-Oliver, Malliavin Differentiability of the Heston Volatility and Applications to Option Pricing (May 14, 2007). Available at SSRN: https://ssrn.com/abstract=986316 or http://dx.doi.org/10.2139/ssrn.986316

Elisa Alos

University of Pompeu Fabra - Department of Economics ( email )

c/o Ramon Trias Fargas 25-27
08005 Barcelona
Spain
34 93 542 19 25 (Phone)
34 93 542 17 46 (Fax)

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

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