An Analytic Approach for Pricing American Options with Regime Switching

Leunglung Chan,Song-Ping Zhu

doi:10.3390/jrfm14050188

Abstract

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

Highlights

Pricing financial derivative is an ative field of research in mathematical finance
Another example that has clearly demonstrated the use of regime switching models in finance practice is the two earlier papers that were published by Elliott et al (2003) and Elliott and Royal (2007), who used filtering methods to estimate the state of the economy from historical stock market data
We will extend the work of Zhu (2006) to obtain an explicit formula for pricing finite-horizon regime switching American options by means of the homotopy analysis method (HAM)

Summary

Introduction

Pricing financial derivative is an ative field of research in mathematical finance. The pioneering work of Black and Scholes (1973) and Merton (1973) laid the foundations of field and gave rise tto a branch of the research in option pricing theory. Two recent publications have discussed this issue (see He and Zhu (2018) and He and Zhu (2021), in addition to using real market data in calibration, so that a practical use of regime switching models is clearly demonstrated through convincing empirical evidence Another example that has clearly demonstrated the use of regime switching models in finance practice is the two earlier papers that were published by Elliott et al (2003) and Elliott and Royal (2007), who used filtering methods to estimate the state of the economy from historical stock market data. We will extend the work of Zhu (2006) to obtain an explicit formula for pricing finite-horizon regime switching American options by means of the homotopy analysis method (HAM). Zhu (2006) applied HAM to derive an explicit pricing formula for American options in the Black–Scholes–Merton framework. We derive an explicit formula for pricing American options with regime switching.

The Model Formulation

HAM Approach

The Common Continuation Region

Transition Region

Conclusions