Article2009

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

36 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

Abstract

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

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1983Stochastic Differential Equations and Diffusion Processes 1997Martingale Methods in Financial Modelling 1990Hedging of contingent claims under incomplete information 2002AMERICAN OPTIONS WITH REGIME SWITCHING 2010A Guided Tour through Quadratic Hedging Approaches 2006Paul Wilmott on Quantitative Finance 1985Hedging of non-redundant contingent claims 2005Option pricing and Esscher transform under regime switching

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