A Jump Diffusion Model for Contingent CDS Valuation

Abstract

We study the valuation of contingent credit default swaps (C-CDS) where the underlying is an interest rate swap and swap rate follows a diffusion process with a one-time jump at default. Our method extends the standard Black (1976) model for interest rate swaption to (1) swaption expires at a ran- dom time (as in C-CDS); and (2) swap rate jumps to a fraction of its value when default occurs. A semi-analytic solution is obtained for the C-CDS value under the linear swap rate model assumption of Pelsser (2001). We also show how to calibrate default rates and survival probabilities to credit default swaps under the many annuity measure needed in the C-CDS valuation.