Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

Abstract

In this paper we present a class of regime switching diffusion models described by a pair (X(t), Y(t)) ∈ R n × S, S ={ 1, 2 ,..., N}, Y(t) being a Markov chain, for which the marginal probability of the diffusive component X(t) is a given mixture. Our main motivation is to extend to a multivariate setting the class of mixture models proposed by Brigo and Mercurio in a series of papers. Furthermore, a simple algorithm is available for simulating paths through a thinning mechanism. The application to option pricing is considered by proposing a mixture version for the Margrabe Option formula and the Heston stochastic volatility formula for a plain vanilla.