On Default Correlation: A Copula Function Approach

TLDR

This paper studies the problem of default correlation. The study introduces a “time‑until‑default” variable and defines default correlation as the correlation coefficient between survival times of two credit risks. The authors argue that a copula function should specify the joint distribution of survival times after deriving marginal distributions from market data, and provide definitions and basic properties of copula functions. They demonstrate that CreditMetrics’ asset‑correlation method is equivalent to a normal copula and illustrate copula usage with numerical examples for credit derivatives such as credit default swaps and first‑to‑default contracts.

Abstract

This paper studies the problem of default correlation. We first introduce a random variable called "time-until-default" to denote the survival time of each defaultable entity or financial instrument, and define the default correlation between two credit risks as the correlation coefficient between their survival times. Then we argue why a copula function approach should be used to specify the joint distribution of survival times after marginal distributions of survival times are derived from market information, such as risky bond prices or asset swap spreads. The definition and some basic properties of copula functions are given. We show that the current CreditMetrics approach to default correlation through asset correlation is equivalent to using a normal copula function. Finally, we give some numerical examples to illustrate the use of copula functions in the valuation of some credit derivatives, such as credit default swaps and first-to-default contracts.