A Unified Framework for Regime-Switching Models

Abstract

Regime-switching models have been widely used in many areas such as finance, biomedicine, and healthcare. However, the computations under these models are usually challenging due to the complexities incurred by regime changes. We provide a unified analytical approximation framework for accurate and efficient computations of the distributions of a variety of practically useful quantities, including first passage times, running extrema, and time integrals, under general regime-switching Markov models, where the state variable in each regime follows a general Markov process. Furthermore, based on our result about the first passage time distributions, we develop an EM algorithm to fit data related to the generalized phase-type distributions. We apply our framework to biomedicine and healthcare (e.g., HIV incubation time, modeling of carcinogenesis, and distribution fitting for service time in healthcare systems) and finance (e.g., implied volatilities, credit spreads, valuation of marketability, and pricing of path-dependent options). Numerical results indicate that adding regime switching can have significant effects on the modeling implications.

Keywords: Regime-Switching Markov Models; Continuous-Time Markov Chains; First Passage Times; Time Integrals; Generalized Phase-Type Distributions; EM Algorithm