Risk Minimizing Option Pricing in a Regime Switching Market

Abstract

We study option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of a stock depends on a finite state Markov chain. Using a minimal martingale measure we show that the risk minimizing option price satisfies a system of Black–Scholes partial differential equations with weak coupling.

Keywords:

• Black–Scholes equations
• Minimal martingale measure
• Risk minimizing option price
• Regime switching market

Mathematics Subject Classification (2000):

• 91B28
• 91B70

This work is supported in part by a DST project: SR/S4/MS: 379/06, and in part by grants from UGC via DSA-SAP Phase IV.