Default risk in a market model

Abstract

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 finite-interval interest rates (such as LIBOR) which explicitly takes into account the possibility of default through the influence 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 find 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 fixed 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.