Markov Chain applications to non parametric option pricing theory

In this paper we propose to use a Markov chain in order to price contingent claims. In particular, we describe a non parametric markovian approach to price American and European options. First, we discuss the risk neutral valuation of the non parametric approach. Secondly, we examine the problems of the computational complexity and of the stability with respect to the number of the states of the Markov chain. Finally, we propose an ex post comparison between the Markovian model and the Black and Scholes one.