NEW NUMERICAL SCHEME FOR PRICING AMERICAN OPTION WITH REGIME-SWITCHING

A. Q. M. Khaliq () and R. H. Liu ()
Additional contact information
A. Q. M. Khaliq: Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA
R. H. Liu: Department of Mathematics, University of Dayton, Dayton, Ohio, OH 45469-2316, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 03, 319-340

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 (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024909005245
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:12:y:2009:i:03:n:s0219024909005245

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024909005245

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().