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.
Highlights
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
We propose in this paper to apply the local risk minimization approach to a more global class of stochastic volatility models since we will assume in the sequel that all parameters of the model depend on the values of a Markov jump process
We studied the problem of pricing and hedging options based on an asset which is modeled by a regime switching stochastic volatility model
Summary
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. We propose in this paper to apply the local risk minimization approach to a more global class of stochastic volatility models since we will assume in the sequel that all parameters of the model depend on the values of a Markov jump process. Elliott et al in [10] developed a model for pricing the same class of derivatives but under a Markov-modulated version of this stochastic volatility model In their paper, they only considered the case where not all the parameters of the model depend on the state of the Markov process.
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