Do Credit Spreads Reflect Stationary Leverage Ratios? Reconciling Structural and Reduced-Form Frameworks

Abstract

In contrast to the empirical findings of Helwege and Turner (1998), existing structural models of default predict that the term structure of credit spreads is downward sloping for speculative-grade debt. We demonstrate that this prediction is a consequence of the assumption that the default boundary remains constant over time, which in turn forces the expected leverage ratio to vanish over time. In practice, however, firms typically adjust their capital structure in response to changes in asset value, creating time-varying default thresholds, and mean reverting (stationary) leverage ratios. Below, we introduce a framework where the leverage ratio is modeled as a stationary process. Our framework generates term structures of credit spreads more in line with empirical findings. Further, our framework reconciles the credit-spread predictions of reduced-form models and structural models of default for long maturities. Generalizing the approach of Longstaff and Schwartz (1995), we provide a computationally efficient method for solving the first-passage-time density of a two-dimensional Gaussian process.