Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

Abstract

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121-160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.

A revised version of the Cathcart & El-Jahel model and its application to CDS market

“…Employed in Ballestra et al. ( 2017 ) for pricing CDSs, it assumes that default occurs at the first jump of a Poisson process as in reduced-form models. However, the intensity of default accounts for structural informations.…”

Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion

“…Later, the problem that a new model of credit risk was proposed combining structural information with the reduced-form approach also was studied by Ballestra (2014) [13] and a closed-form approximate solution was derived by perturbation approach and the Laplace transform. A quasianalytical approximation of the survival probability was derived based on Madan's credit risk model, and a quasianalytical approximate expression for CDS par spreads was obtained by Ballestra (2017) [14]. All the discussions above are based on the underlying asset price obeying the geometric Brownian motion, which implies that the changes of underlying asset price are mutually independent random variables and the return on assets obeys the normal distribution.…”