A Dynamic Programming Approach for Pricing Options Embedded in Bonds

Posted: 4 Jul 2006 Last revised: 29 Feb 2012

See all articles by Hatem Ben Ameur

Hatem Ben Ameur

HEC Montreal - Department of Management Sciences

Michèle Breton

HEC Montreal - Department of Management Sciences

Lotfi Karoui

Goldman, Sachs & Co

Pierre L'Ecuyer

University of Montreal

Abstract

We propose a Dynamic Programming (DP) approach for pricing options embedded in bonds, the focus being on call and put options with advance notice. An efficient procedure is developed for the cases where the interest-rate process follows the Vasicek, Cox-Ingersoll-Ross (CIR), or generalized Vasicek models. Our DP methodology uses the exact joint distribution of the interest rate and integrated interest rate at a future date, conditional on the current value of the interest rate. We provide numerical illustrations, for the Vasicek and CIR models, comparing our DP method with finite difference methods. Our procedure compares quite favorably in terms of both efficiency and accuracy. An important advantage of the our DP approach is that it can be applied to more general models calibrated to capture the term structure of interest rates (e.g.,the generalized Vasicek model).

Keywords: Option pricing, Bond pricing, Dynamic Programming, Options embedded in bonds

JEL Classification: C63, G13

Suggested Citation

Ben Ameur, Hatem and Breton, Michèle and Karoui, Lotfi and L'Ecuyer, Pierre, A Dynamic Programming Approach for Pricing Options Embedded in Bonds. Journal of Economic Dynamics and Control, Vol. 31, No. 7, pp. 2212-2233, July 2007. Available at SSRN: https://ssrn.com/abstract=912337

Hatem Ben Ameur (Contact Author)

HEC Montreal - Department of Management Sciences ( email )

Montreal, Quebec H3T 2A7
Canada
514-340-6480 (Phone)
514-340-5634 (Fax)

Michèle Breton

HEC Montreal - Department of Management Sciences ( email )

Montreal, Quebec H3T 2A7
Canada
514-340-6490 (Phone)
514-340-5634 (Fax)

Lotfi Karoui

Goldman, Sachs & Co ( email )

1 New York Plaza
New York, NY 10004
United States

Pierre L'Ecuyer

University of Montreal ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7
Canada

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