Pricing Interest Rate-Sensitive Credit Portfolio Derivatives

Abstract

In this paper we present a modelling framework for portfolio credit risk which incorporates the dependence between risk-free interest-rates and the default loss process. The contribution in this approach is that - besides the traditional diffusion based covariation between loss intensities and interest-rates - a direct dependence between interest-rates and the loss process is allowed, in particular default-free interest-rates can also depend on the loss history of the credit portfolio. Amongst other things this enables us to capture the effect that economy-wide default events are likely to have on government bond markets and/or central banks' interest-rate policies. Similar to Schonbucher (2005), the model is set up using a set of loss contingent forward interest-rates fn(t; T) and loss-contingent forward credit protection rates Fn(t; T) to parameterize the market prices of default-free bonds and credit-sensitive assets such as CDOs. We show that (up to weak regularity conditions), existence of such a parametrization is necessary and sufficient for the absence of static arbitrage opportunities in the underlying assets. We also give necessary conditions and sufficient conditions on the dynamics of the parametrization which ensure absence of dynamic arbitrage opportunities in the model. Similar to the HJM drift restrictions for default-free interest-rates, these conditions take the form of restrictions on the drifts of fn(t; T) and Fn(t; T), together with a set of regularity conditions.