Collateralized CDS and Default Dependence

TL;DR

This paper analyzes the pricing of fully collateralized CDS, revealing persistent default dependence effects in prices even with perfect collateralization, and explores implications for risk management.

Contribution

It introduces a straightforward pricing formula using the survival measure that captures default dependence effects despite perfect collateralization.

Findings

Default dependence influences CDS prices even under perfect collateralization.

The hazard rates of counterparty and investor do not appear in the pricing formula.

Numerical examples show how default dependence affects fair CDS premiums.

Abstract

In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way. As a result, we have found that there exists irremovable trace of the counter party as well as the investor in the price of CDS through their default dependence even under the perfect collateralization, although the hazard rates of the two parties are totally absent from the pricing formula. As an important implication, we have also studied the situation where the investor enters an offsetting back-to-back trade with another counter party. We have provided simple numerical examples to demonstrate the change of a fair CDS premium according to the strength of default dependence among the relevant names, and then discussed its possible implications for the risk management of the central counter parties.