Contingent credit default swaps: accurate and approximate pricing

Abstract

In this paper, we analyze the pricing of contingent credit default swaps (CCDSs), which provide protection against default losses in derivative transactions. In a framework with both asset and interest rate risk, we obtain a meaningful semi-analytical solution for CCDS prices with an interest rate swap as underlying. Our model yields three major contributions.1. CCDSs have several properties that fundamentally differ from those of CDSs, despite the similar nature of the two instruments.2. We propose simple approximate pricing formulas for CCDSs. While the first one only depends on the prices of observable traded assets, i.e., the CDS quote, the value of a swaption and a zero bond, the second approximation formula additionally requires volatility information.3. We find that the approximate formulas work well in practical situations and converge to the true value for a financial institution with low default risk.