Multivariate European option pricing in a Markov-modulated Lévy framework

This paper studies the pricing of some multivariate European options, namely Exchange options and Quanto options, when the risky assets involved are modelled by Markov-Modulated Lévy Processes (MMLPs). Pricing formulae are based upon the characteristic exponents by using the well known FFT methodology. We study these pricing issues both under a risk neutral martingale measure and the historical measure. The dependence between the asset's components is incorporated in the joint characteristic function of the MMLPs. As an example, we concentrate upon a regime-switching version of the model of Ballotta et al. (2015) in which the dependence structure is introduced in a flexible way. Several numerical examples are provided to illustrate our results.