On a Markov chain approximation method for option pricing with regime switching

Kun  Fan; Yang  Shen; Tak Kuen  Siu; Rongming Wang

doi:10.3934/jimo.2016.12.529

Article Contents

2016, Volume 12, Issue 2: 529-541. Doi: 10.3934/jimo.2016.12.529

This issue Previous Article A combinatorial optimization approach to the selection of statistical units Next Article Regularized multidimensional scaling with radial basis functions

On a Markov chain approximation method for option pricing with regime switching

1.
School of Finance and Statistics, East China Normal University, Shanghai, 200241
2.
School of Risk and Actuarial Studies and CEPAR, UNSW Business School, University of New South Wales, Sydney, NSW 2052
3.
Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109
4.
School of Finance and Statistics, Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241

Received: June 2013

Revised: March 2015

Published: April 2016

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Abstract

In this paper, we discuss a Markov chain approximation method to price European options, American options and barrier options in a Markovian regime-switching environment. The model parameters are modulated by a continuous-time, finite-state, observable Markov chain, whose states represent the states of an economy. After selecting an equivalent martingale measure by the regime-switching Esscher transform, we construct a discrete-time, inhomogeneous Markov chain to approximate the dynamics of the logarithmic stock price process. Numerical examples and empirical analysis are used to illustrate the practical implementation of the method.

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Mathematics Subject Classification: Primary: 91G20, 91G60; Secondary: 60J10.

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