Valuing Risky Fixed Rate Debt: An Extension

TLDR

The paper develops a corporate bond valuation model that incorporates early default and interest‑rate risk. The model defines a fixed default barrier discounted at the risk‑free rate, triggers bondholder payouts as a fraction of remaining assets upon breach, and corrects prior pricing defects by allowing deviations from the absolute priority rule. By incorporating Gaussian interest‑rate uncertainty, default risk, and priority rule deviations, the model generates a wide range of yield‑spread term‑structure shapes.

Abstract

This paper develops a corporate bond valuation model that takes into account both early default and interest rate risk. It corrects a defect of recent contributions where pricing equations do not assure that the payment to bondholders upon bankruptcy is no greater than firm value. The bankruptcy-triggering mechanism is directly related to the payoff received by bondholders when early bankruptcy is forced upon the firm. More specifically, the default barrier is defined simply as a fixed quantity discounted at the riskless rate up to the maturity date of the risky corporate bond. As soon as this threshold is crossed, bondholders receive an exogenously specified fraction of the remaining assets. Deviations from the absolute priority rule also are captured. Because it accounts for Gaussian interest rate uncertainty, default risk, and deviations from the absolute priority rule, this model is capable of producing quite diverse shapes for the term structure of yield spreads.