Empirical Dynamic Asset Pricing: Model Specification and Econometric Assessment

By Kenneth J. Singleton | Go to book overview

14
Term Structures of Corporate
Bond Spreads

IF THE ISSUER of a fixed-income security might default prior to the maturity date T then, in addition to the risk of changes in r, both the magnitude and the timing of payoffs to investors may be uncertain. How these additional default risks affect pricing depends on how the default event is defined and how recovery in the event of a default is specified.This chapter presents several of the most widely studied models for pricing defaultable bonds and reviews the evidence on the empirical fits of these models.


14.1. DTSMs of Defaultable Bonds

At the broadest level, the two most commonly studied default processes are those of reduced-form and structural models. The former treat default as an unpredictable event, essentially the outcome of a jump process and its associated intensity or the arrival rate of default events. In contrast, the latter often provide an explicit characterization of the default event, like the first time that a firm’s assets fall below the value of its liabilities. Hybrid models that combine aspects of both approaches have also been examined.

In the case where an issuer might default, we view a zero-coupon bond as a portfolio of two securities: (1) a security that pays $1 at date T contingent on survival of the issuer to the maturity date T; and (2) a security that pays the (possibly random) recovery w received at default, if default occurs before maturity. More precisely, we let τ denote the random default time and 1{τ>t} be the indicator function for the event that τ > t. The price of this defaultable zero-coupon bond, B(t, T), is given by

The practical challenge in extending our pricing models to accommodate default is the evaluation of the two expectations in (14.1). The first involves

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