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Pricing and Hedging in Stochastic Volatility Regime Switching Models
Centre National de la Recherche Scientifique (CNRS)—Universit Paris 7 Diderot, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Paris, France
- 1 Centre National de la Recherche Scientifique (CNRS)—Universit Paris 7 Diderot, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Paris, France
Journal of Mathematical Finance·Volume 03 (2013)·Pages 70–80·Published 26 February 2013·DOI10.4236/jmf.2013.31006
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Abstract
We consider general regime switching stochastic volatility models where both the asset and the volatility dynamics depend on the values of a Markov jump process. Due to the stochastic volatility and the Markov regime switching, this financial market is thus incomplete and perfect pricing and hedging of options are not possible. Thus, we are interested in finding formulae to solve the problem of pricing and hedging options in this framework. For this, we use the local risk minimization approach to obtain pricing and hedging formulae based on solving a system of partial differential equations. Then we get also formulae to price volatility and variance swap options on these general regime switching stochastic volatility models.
KeywordsStochastic VolatilityMarkov SwitchingLocal Risk MinimizationHedgingVolatility Derivative
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