Analytic Correlation Risk for CDS

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 credit-rates 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 PVs. Highly favourable comparison is found between even the first order approximations and Monte Carlo simulations