On the estimation of regime-switching Lévy models

Abstract

AbstractThe regime-switching Lévy model combines jump-diffusion under the form of a Lévy process, and Markov regime-switching where all parameters depend on the value of a continuous time Markov chain. We start by giving general stochastic results. Estimation is performed following a two-step procedure. The EM-algorithm is extended to this new class of jump-diffusion regime-switching models. Simulations are proposed, alongside an empirical application dedicated to the study of financial and commodity time series. When comparing the results with (i) non regime-switching models, and (ii) continuous regime-switching models (where the Lévy process is replaced by a classic Brownian motion), the Lévy regime-switching model outperforms other competitors.