Working Paper

Exact Solutions for the Transient Densities of Continuous-Time Markov Switching Models – With an Application to the Poisson Multifractal Model

Kiel Working Papers, 1871

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.


Thomas Lux


Publication Date
JEL Classification
C13, C58, G12