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

Abstract

We propose a numerical method to price corporate bonds based on the model of default 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 the bond very efficiently. More precisely, we consider both the first‐ and second‐order power series expansions of the survival probability in powers of the model parameter c. The zero‐order coefficient 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 the Laplace transform. Extensive simulation is carried out on several test cases where the parameters of the model of Madan and Unal are chosen from Grundke and Riedel, and bonds with different maturities are considered. The numerical experiments performed reveal that the numerical method proposed in this paper is accurate and computationally efficient.

Keywords:

• Credit risk
• defaultable bonds
• asymptotic expansion