Option Valuation under a Multivariate Markov Chain Model

In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model.