Continuous time Markov chain model of asset prices distribution

Abstract

The aim of this paper is to introduce a new model of a financial asset prices distribution. It is known that the probability distribution of an asset prices or returns is unknown in reality. The general model of asset prices based on continuous time Markov chains is proposed. For this reason the interarrivals between two price states are approximated by mixture of exponential distributions. Numerical-analytic approach is used to obtain the probability distribution of asset prices. The developed software allows creating the space of an asset prices, the matrix of transition rates among states, a system of equations to find the steady state probabilities of price states and solves the system of equations by method of imbedded Markov chains. © 2009 Springer Berlin Heidelberg.