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Modeling and pricing of variance and volatility swaps for local semi-Markov volatilities in financial engineering. (English) Zbl 1202.91355
Summary: We consider a semi-Markov modulated security market consisting of a riskless asset or bond with constant interest rate and risky asset or stock, whose dynamics follow gemoetric Brownian motion with volatility that depends on semi-Markov process. Two cases for semi-Markov volatilities are studied: local current and local semi-Markov volatilities. Using the martingale characterization of semi-Markov processes, we find the minimal martingale measure for this incomplete market. Then we model and price variance and volatility swaps for local semi-Markov stochastic volatilities.

91G80Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
91G30Interest rates (stochastic models)
91G20Derivative securities
Full Text: DOI EuDML
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