A Default Risk Model Under Macroeconomic Conditions

Abstract

This paper presents a structural model of default risk under macroeconomic conditions. The macroeconomic conditions are assumed to be a finite state of a Markov chain. The innovation of our model is to characterize the firm default, the default-free pure discount bond price, the defaultable bond price and the credit spread associated with macroeconomic conditions. By using the Wiener-Hopf factorization, we show that there is a risk-neutral measure under regime-switching. Under macroeconomic conditions, we derive both the default-free bond price and the price of defaultable bond governed by fundamental systems of partial differential equations. Both the defaultable yield-to-maturity, the credit spread and the duration are related to the finite state of the Markov chain.