Default risk in a market model

This paper presents a theoretical model of default risk in the context of t he "market" model approach to interest rate dynamics. We propose a model fo r finite-interval interest rates (such as LIBOR) which explicitly takes int o account the possibility of default through the influence of a point proce ss with deterministic intensity. We relate the defaultable interest rate to the non-defaultable interest rate and to the credit risk characteristics d efault intensity and recovery rate. We find that the spread between default able 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 uni lateral and bilateral default risk and derive the fair fixed swap rate in b oth cases. Under the condition that both counterparties are of the same ris k 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 withou t default risk. (C) 2000 Elsevier Science B.V. All rights reserved. JEL cla ssification. G30; G33; E43.