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The Journal of Derivatives

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Primary Article

Valuation of Convertible Bonds With Credit Risk

E. Ayache, P.A. Forsyth and Kenneth R. Vetzal
The Journal of Derivatives Fall 2003, 11 (1) 9-29; DOI: https://doi.org/10.3905/jod.2003.319208
E. Ayache
President of ITO 33, S.A., in Paris.
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  • For correspondence: numbersix@ito33.com
P.A. Forsyth
A professor at the School of Computer Science, University of Waterloo, in Waterloo, Ontario.
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  • For correspondence: paforsyt@elora.math.uwaterloo.ca
Kenneth R. Vetzal
An associate professor at the Centre for Advanced Studies in Finance, University of Waterloo, in Waterloo Ontario.
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  • For correspondence: kvetzal@watarts.uwaterloo.ca
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Abstract

Applying the technology of option pricing and contingent claims modeling to credit risk is one of the major growth areas in derivatives research these days. It is an old idea to treat default as a firm's management rationally exercising the shareholders' option to go bankrupt rather than to make a required payment to the debtholders. But only in the last few years has this insight been extended and widely applied to practical bond valuation problems. Convertible bonds have also become much more popular in recent years, as the weak and volatile stock market has combined with low interest rates to create an environment in which the conversion option can be very attractive. One critical uncertainty in credit risk analysis that may not be fully appreciated by those who have not worked in this area, is what the payoff to bondholders will actually be in the event of a default. In this article, Ayache, Forsyth, and Vetzal explore the interactions among the multiple options embedded in convertibles that are subject to default risk, call provisions, and put provisions, in addition to the conversion option. Along with results that illustrate the interactions among these multiple options, the authors provide a straightforward valuation technique for convertibles, by applying principles of linear complementarity to the discretization of the fundamental PDE of contingent claims pricing.

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The Journal of Derivatives
Vol. 11, Issue 1
Fall 2003
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Valuation of Convertible Bonds With Credit Risk
E. Ayache, P.A. Forsyth, Kenneth R. Vetzal
The Journal of Derivatives Aug 2003, 11 (1) 9-29; DOI: 10.3905/jod.2003.319208

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Valuation of Convertible Bonds With Credit Risk
E. Ayache, P.A. Forsyth, Kenneth R. Vetzal
The Journal of Derivatives Aug 2003, 11 (1) 9-29; DOI: 10.3905/jod.2003.319208
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