Default risk in a market model

This paper presents a theoretical model of default risk in the context of the ``market'' model approach to interest rate dynamics. We propose a model for ®nite-interval interest rates (such as LIBOR) which explicitly takes into account the possibility of default through the in ̄uence of a point process with deterministic intensity. We relate the defaultable interest rate to the non-defaultable interest rate and to the credit risk characteristics default intensity and recovery rate. We ®nd that the spread between defaultable and non-defaultable rate depends on the non-defaultable rate even when the default intensity is deterministic. Prices of a cap on the defaultable rate and of a credit spread option are derived. We consider swaps with unilateral and bilateral default risk and derive the fair ®xed swap rate in both cases. Under the condition that both counterparties are of the same risk class, we show that for a monotonously increasing term structure the swap rate for a defaultable swap will lie below the swap rate for a swap without default risk. Ó 2000 Elsevier Science B.V. All rights reserved. JEL classi®cation: G30; G33; E43