Pricing Callable Bonds with Stochastic Interest Rate and Stochastic Default Risk: A 3D Finite Difference Model

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Pricing Callable Bonds with Stochastic Interest Rate and Stochastic Default Risk: A 3D Finite Difference Model

by David Wang of Hsuan Chuang University

February 2005

Abstract: This paper presents a 3D model for pricing defaultable bonds with embedded call options. The pricing model incorporates three essential ingredients in the pricing of defaultable bonds: stochastic interest rate, stochastic default risk, and call provision. Both the stochastic interest rate and the stochastic default risk are modeled as a square-root diffusion process. The default risk process is allowed to be correlated with the default-free term structure. The call provision is modeled as a constraint on the value of the bond in the finite difference scheme. This paper can provide new insight for future research on defaultable bond pricing models.

JEL Classification: C00, G13.

Keywords: Defaultable bond, Embedded option, Partial differential equation, Finite difference method.

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