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| Pricing Corporate Bonds in an Arbitrary Jump-Diffusion Model Based on an Improved Brownian-bridge Algorithm by Johannes Ruf of the University of Ulm, and June 1, 2006 Abstract: In this paper, we provide an efficient algorithm for the computation of default probabilities and bond prices in a structural default model with jumps. Our algorithm allows jump-diffusion processes with arbitrary jump-size distribution as a model for the logarithm of the value process of a firm. Moreover, the algorithm is unbiased and is capable of capturing stochastic recovery rates, which are endogenously generated by structural default models with jumps. The algorithm requires the evaluation of integrals with the density of the first-passage time of a Brownian bridge as integrand. In order to further accelerate their barrier-option pricing algorithm, Metwally and Atiya (2002) suggested an approximation of these integrals. We significantly improve this approximation in terms of precision. It is well known that allowing a sudden default by jumps results in a positive limit of credit spreads at the short end of the term structure. We provide an explicit formula for this limit, which depends only on the Lévy measure of the logarithm of the firm-value process, the recovery rate, and the distance to default. Keywords: Corporate bonds, Jump-diffusion model, Structural default model, Brownian-bridge, Credit spreads, Laplace transform, Monte Carlo simulation. Books Referenced in this Paper: (what is this?)
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