Option pricing under two-state Markov chain market model

Abstract

This paper analyses a two-state Markov chain model, which is a discrete-time model of a financial market. The uncertainty in a financial market is presented as the changes of the risky asset are modulated by a discrete-time, two-state, Markov chain. It examines two versions of our Markov chain market model: first, where the model has a recombinant tree, and second, with a non-recombinant tree. Risk-neutral probability measure in the Markov chain market model was also discussed and defined. Considering the European call option in the case of recombinant tree, which is the simplest departure from independency of underlying asset from the classical option price model, the risk neutral probability measure is the same as in the Cox-Ross-Rubinstein model, and consequently the price of option. In the case of non-recombinant tree a method for valuation of option in the Markov chain model using calibration to the market option price is presented. The suggested two-state Markov chain market model has the bull and bear features of the underlying asset price fluctuations and it gives better results with the evaluation of option price of companies from DJIA.