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Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering

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  • Anatoliy Swishchuk
  • Raimondo Manca

Abstract

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.

Suggested Citation

  • Anatoliy Swishchuk & Raimondo Manca, 2010. "Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-17, November.
    • Handle: RePEc:hin:jnlmpe:537571
    DOI: 10.1155/2010/537571
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