A Direct Solution Method for Pricing Options in Regime-switching Models

TL;DR

This paper introduces a direct method for pricing options in regime-switching models by reducing complex problems to simpler non-switching optimal stopping problems, enabling explicit solutions and broad applicability.

Contribution

It presents a novel systematic approach to solve regime-switching optimal stopping problems by transforming them into non-switching problems, facilitating explicit value function derivation.

Findings

Explicit form of value functions obtained

Method applied to complex option pricing problems

Simplifies solving regime-switching models

Abstract

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two-regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.