A Default Risk Model under Macroeconomic Conditions

Abstract

This article 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 the author’s 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, the author shows that there is a risk-neutral measure under regime switching. Under macroeconomic conditions, he derives both the default-free bond price and the price of the defaultable bond governed by fundamental systems of partial differential equations. The defaultable yield to maturity, credit spread, and duration are related to the finite state of the Markov chain.