Derivative Pricing Models with Regime Switching

Abstract

Several different approaches to modeling returns processes with time–varying volatility have been developed in recent years. The affine jump–diffusion (AJD) class of stochastic processes, in which volatility can be a function of an arbitrary number of underlying stochastic state variables that follow correlated mean–reverting square root jump–diffusions, is perhaps the most tractable, since transform methods allow prices of derivatives tied to those processes to be expressed in (more or less) closed form. Without that, numerical solution techniques can entail a very heavy computational burden. But despite their flexibility, AJD processes still significantly restrict the behavior of the state variables. In this article, Edwards introduces a new regime–switching approach that can be adapted to a broad array of alternative processes. The key is to model the volatile regime using a stochastic time change.