A Numerical Method to Price Defaultable Bonds Based on the Madan and Unal Credit Risk Model

摘要

We propose a numerical method to price corporate bonds based on the model ofdefault risk developed by Madan and Unal. Using a perturbation approach, we derive two semi-explicit formulae that allow us to approximate the survival probability of the firm issuing thebond very efficiently. More precisely, we consider both the first- and second-order power seriesexpansions of the survival probability in powers of the model parameter c. The zero-ordercoefficient of the series is evaluated using an exact analytical formula. The first- and second-order coefficients of the series are computed using an approximation algorithm based on theLaplace transform. Extensive simulation is carried out on several test cases where the parametersof the model of Madan and Unal are chosen from Grundke and Riedel, and bonds with differentmaturities are considered. The numerical experiments performed reveal that the numericalmethod proposed in this paper is accurate and computationally efficient.