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

Abstract EN

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.