Distributions related to a Markov chain and Application in Finance

Distributions related to a Markov chain and Application in Finance

In this paper, we introduce a sequence of dependent Bernoulli trials, which forms a two state homogeneous Markov chain. Then we define two types of geometric and negative binomial distributions, as well as binomial distribution, related to this sequence. Some properties of the defined distributions are given. Recursion formulas and probability mass functions are derived. The application of the defined distributions is related to the Markov binomial model of financial market. The European call option pricing formula, according to this model is a generalization of the classical Cox - Ross -- Rubinstain formula (1979).