Financial Applications of Bivariate Markov Processes

Abstract

This paper describes a methodology to approximate a bivariate Markov process by means of a proper Markov chain and presents possible financial applications in portfolio theory, option pricing and risk management. In particular, we first show how to model the joint distribution between market stochastic bounds and future wealth and propose an application to large-scale portfolio problems. Secondly, we examine an application to VaR estimation. Finally, we propose a methodology to price Asian options using a bivariate Markov process.