Credit Value Adjustment for Credit Default Swaps via the Structural Default Model

Abstract

We propose a structural default model to evaluate the counterparty risk by trading in credit default swap (CDS) contracts. We model the joint evolution of the firm value of the entity underlying the CDS contract and the counterparty using a correlated jump-diffusion process. Unlike the reduced-form default model, where the default event is always a sudden event, in our model, the default event is triggered by a sudden drop in the value of the credit entity and subsequent deterioration of its credit quality, which is the pattern observed in practice, in particular, for financial institutions. Thus, our model might provide a better tool to model the value of financial institutions and their creditworthiness. We develop robust semi-analytical and numerical methods for the model calibration and solving the pricing problem, which will be presented somewhere else. In this article we show how to apply our model to analyze the counterparty risk in credit default swaps and evaluate the counterparty charge. Using the market data of JP Morgan and Citigroup for illustrations, we show that in our model the counterparty charge is significant, 5%-30% compared to the present value of the default leg of the underlying CDS, and it is sensitive to both correlation and volatility parameters. Our results indicate that the counterparty risk in credit derivatives trading cannot be neglected and should be actively managed.

Keywords: counterparty risk, jump-to-default

JEL Classification: C00