The Valuation of Default Risk in Corporate Bonds and Interest Rate Swaps

Abstract

This paper implements a model for the valuation of the default risk implicit in the prices of corporate bonds and interest rate swaps. The analytical approach considers the two essential ingredients in the valuation of corporate bonds: interest rate uncertainty and default risk. The former is modeled as a diffusion process. The latter is modeled as a spread following a diffusion process, with the magnitude of this spread impacting on the probability of a Poisson process governing the arrival of the default event. We apply two variants of this model to the valuation of fixed-for-floating swaps. In the first, the swap is default-free, and the spread represents the appropriate discounted expected value of the instantaneous TED spread; in the second, we allow the swap to incorporate default risk. We test our models using the entire term structure of corporate bond prices for different ratings and industry categories, as well as the term structure of fixed-for-floating swaps.

JEL Classification: G13