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Zbl 1202.91355
Swishchuk, Anatoliy; Manca, Raimondo
Modeling and pricing of variance and volatility swaps for local semi-Markov volatilities in financial engineering. (English)
[J] Math. Probl. Eng. 2010, Article ID 537571, 17 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

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.

MSC 2000:: *91G80
91G30
91G20

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Zentralblatt MATH Berlin [Germany]