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Option pricing in a regime switching stochastic volatility model. (English) Zbl 1393.91131

Summary: We consider a regime switching stochastic volatility model where the stock volatility dynamics is a semi-Markov modulated square root mean reverting process. Under this model assumption, we find the locally risk minimizing price of European type vanilla options. The price function is shown to satisfy a non-local degenerate parabolic PDE which can be viewed as a generalization of the Heston PDE. The related Cauchy problem involving the PDE is shown to be equivalent to an integral equation (IE). The existence and uniqueness of solution to the PDE is carried out by studying the IE and using the semigroup theory.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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