Contingent Claims Pricing in Markovian Switching Model with Consumption

The pricing of the derivatives is a hot topic among recent problems in economics and finance. This paper modifies the classical Black-Scholes model by replacing his constant drift and volatility with a finite-state Markov chain. In addition, we take the consumption into consideration. With a Girasnov-like change of measure, we derive the price of the contingent claim and also give an explicit formula to the European call option in a risk-neutral world.