Analytic Correlation Risk for CDS

Abstract

We consider a rates credit hybrid model with the rates and the credit intensity governed by Hull-White and Black-Karasinski short-rate models, respectively. We report on and make use of a highly accurate analytic representation of a pricing kernel for European-style options and/or protection payments in powers of the credit spread (not of its lognormal volatility). We show how this can be applied to calculate analytically the impact of rates credit correlation on the pricing of credit default swaps (CDS), extinguishing interest rate swaps, and survival-contingent capped LIBOR flows. Very simple expressions are obtained in all cases for present values (PVs). Highly favorable comparison is found between even the first-order approximations and Monte Carlo simulations.