Specification Analysis of Structural Credit Risk Models

Empirical studies of structural credit risk models so far are often based on calibration, rolling estimation, or regressions. This paper proposes a GMM-based method that allows us to estimate model parameters and test model-implied restrictions in a unified framework. We conduct a specification analysis of five representative structural models based on the proposed GMM procedure, using information from both equity volatility and the term structure of single-name credit default swap (CDS) spreads. Our test results strongly reject the Merton (1974) model and two diffusion-based models with a flat default boundary. The other two models, one with jumps and one with stationary leverage ratios, do improve the overall fit of CDS spreads and equity volatility. However, all five models have difficulty capturing the dynamic behavior of both equity volatility and CDS spreads, especially for investment-grade names. On the other hand, these models have a much better ability to explain the sensitivity of CDS spreads to equity returns.