Modelling bonds and credit default swaps using a structural model with contagion

Abstract

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.

Modeling basket credit default swaps with default contagion

“…On an Intel Xeon CPU 3.5 Ghz x2 machine, it takes about eight minutes to generate default probabilities for a given value of correlation at 200 points in a ten-year period. Comparing default probabilities with those obtained analytically in Haworth et al (2006), using 10 uniform refinements and 200 time-steps gives results accurate to five decimal places. We have gone for accuracy over speed; to generate the same results accurate to three decimal places takes just thirty seconds.…”

“…In another approach, Luciano and Schoutens (2005), Moosbrucker (2006) and Baxter (2006) assume that firm values are driven by Levy processes rather than geometric Brownian motions and model credit derivatives using Variance Gamma processes. Haworth et al (2006) build on the approach of Zhou (2001) to derive closed-form solutions for corporate bond yields in the presence of default contagion and correlated two-firm basket credit default swaps. This paper is a generalisation of the analytical approach of Haworth et al (2006), incorporating a more flexible and realistic specification of the default contagion mechanism and allowing for rapid valuation of three-firm credit default swap (CDS) baskets.…”

“…Haworth et al (2006) build on the approach of Zhou (2001) to derive closed-form solutions for corporate bond yields in the presence of default contagion and correlated two-firm basket credit default swaps. This paper is a generalisation of the analytical approach of Haworth et al (2006), incorporating a more flexible and realistic specification of the default contagion mechanism and allowing for rapid valuation of three-firm credit default swap (CDS) baskets. It is organised as follows.…”

An Entropy Model of Credit Risk Contagion in the CRT Market

“…This parameter denotes the effect of the change in external environment on credit risk contagion in the CRT market, including macroeconomic environment, financial environment, industry environment, and legal environment. According to (13), the entropy spatial model of credit risk contagion can maximize the entropy of credit risk contagion in the CRT network that satisfies the given constraints and can depict the effects of the spatial distance and nonlinear coupling between banks and investors. The model also presents the ability of banks to transfer credit risk, the appetite for risk of investors, the credit status of the debtors, and external environment on credit risk contagion of the CRT network.…”

“…However, credit risk transfer can also induce contagion and lead to a Pareto reduction in welfare. Haworth et al [13] developed a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Jorion and Zhang [14] provided the first empirical analysis of credit contagion via direct counterparty effects and found that bankruptcy announcements cause negative abnormal equity returns and increases in CDS spreads for creditors.…”