New Numerical Scheme for Pricing American Option with Regime-Switching

International Journal of Theoretical and Applied Finance, Vol. 12, No. 3, pp. 319-340, 2009

Posted: 16 Apr 2010 Last revised: 21 Apr 2010

See all articles by Abdul Q. M. Khaliq

Abdul Q. M. Khaliq

Middle Tennessee State University

R. H. Liu

University of Dayton - Department of Mathematics

Date Written: May 5, 2008

Abstract

This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes.

Keywords: American Option, Regime-Switching, Implicit Scheme, Penalty Method, Θ-Method, Free Boundary Value Problem

Suggested Citation

Khaliq, Abdul Q. M. and Liu, R. H., New Numerical Scheme for Pricing American Option with Regime-Switching (May 5, 2008). International Journal of Theoretical and Applied Finance, Vol. 12, No. 3, pp. 319-340, 2009. Available at SSRN: https://ssrn.com/abstract=1515475

Abdul Q. M. Khaliq (Contact Author)

Middle Tennessee State University ( email )

P.O. Box 50
Murfreesboro, TN 37132
United States

R. H. Liu

University of Dayton - Department of Mathematics ( email )

300 College Park
Dayton, OH 45469
United States
(937) 229-1021 (Phone)
(937) 229-2566 (Fax)

HOME PAGE: http://academic.udayton.edu/ruihualiu/

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