The Term Structure of Defaultable Bond Prices

In this paper we present a new methodology for modelling the development of the prices of defaultable zero coupon bonds that is inspired by the Heath-Jarrow-Morton (HJM) approach to risk-free interest rate modelling. Instead of precisely specifying the mechanism that triggers the default we concentrate on modelling the development of the term structure of the defaultable bonds and give conditions under which these dynamics are arbitrage-free. These conditions are a drift restriction that is closely related to the HJM drift restriction for risk-free bonds, and the restriction that the defaultable short rate must always be not below the risk-free short rate. The same restrictions apply for the extended versions of the model that allow for restructuring of defaulted debt and multiple defaults, and loss quotas that are not predictable. In its most general version the model is set in a marked point process framework, to allow for jumps in the defaultable rates at times of default.