Exact solutions for the transient densities of continuous-time Markov switching models : with an application to the poisson multifractal model

This paper shows how exact solutions for the transient density of a large class of continuous-time Markov switching models can be obtained. We illustrate the pertinent approach for both simple diffusion models with a small number of regimes as well as for the more complicated so-called Poisson multifractal model introduced by Calvet and Fisher (2001) with an arbitrarily large number of regimes. Our results can be immediately applied as well to various popular Markov switching models in financial economics. Closed-form solutions provide for the possibility of exact maximum likelihood estimation for discretely sampled Markov-switching diffusions and also facilitate the use of such models in applied tasks such as option pricing and portfolio management.