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Variance-Optimal Hedging in General Affine Stochastic Volatility Models

Part of: Stochastic systems and control Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jan Kallsen  and
Arnd Pauwels
Jan Kallsen*
Affiliation:
Christian-Albrechts-Universität zu Kiel
Arnd Pauwels*
Affiliation:
MEAG AssetManagement GmbH
*
∗ Postal address: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. Email address: [email protected]
∗∗ Postal address: MEAG AssetManagement GmbH, Abteilung Risikocontrolling, Oskar-von-Miller-Ring 18, 80333 München, Germany. Email address: [email protected]
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Abstract

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We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

Keywords

Variance-optimal hedgingstochastic volatilityGaltchouk-Kunita-Watanabe decompositionaffine processLaplace transform

MSC classification

Primary: 60H05: Stochastic integrals 60G48: Generalizations of martingales 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 83 - 105
Copyright
Copyright © Applied Probability Trust 2010 

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