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Malliavin differentiability of the Heston volatility and applications to option pricing

Published online by Cambridge University Press:  01 July 2016

Elisa Alòs*
Affiliation:
University Pompeu Fabra Barcelona
Christian-Oliver Ewald*
Affiliation:
University of St Andrews
*
Postal address: Department of Economics, University Pompeu Fabra Barcelona, c/Ramon Trias fargas, 25-27, 08005 Barcelona, Spain. Email address: [email protected]
∗∗ Postal address: Department of Economics, University of St Andrews, St Salvator's College, St Andrews, Fife KY16 9AL, UK. Email address: [email protected]
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Abstract

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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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2008 

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