Specification Analysis of Structural Credit Risk Models

February 1, 2020

Specification Analysis of Structural Credit Risk Models
Jing-Zhi Huang, Zhan Shi, Hao Zhou
Review of Finance, Volume 24, Issue 1, February 2020, Pages 45–98, https://doi.org/10.1093/rof/rfz006

Empirical studies of structural credit risk models are usually carried out using calibration, rolling window estimation, or regression analysis. This paper proposes an alternative approach to testing such models. This alternative method allows us to directly estimate structural models, as well as test whether all the restrictions of a given model are satisfied, among other things.

Specifically, we construct a specification test based on certain model-implied variables, such as credit spreads and equity volatility. By assuming that both equity and credit markets are efficient and that the underlying structural model is correct, we obtain moment restrictions on model parameters. We then use generalized method of moments (GMM) to conduct parameter estimation as well as a specification analysis of the structural model.

For illustration, we apply the proposed approach to five representative structural models that incorporate various economic considerations. For each of the five models, we construct its moment conditions using equity volatility and term structures of single-name credit default swap (CDS) spreads. We then test whether all the restrictions of the model are satisfied using the GMM. In addition, we examine the ability of the model to explain equity volatility, the CDS term structure, default rates, sensitivity of CDS spreads to equity returns, etc.

We focus on the Merton (1974) model and its four extensions with an exogenous default boundary in our empirical analysis. The extensions are the Black and Cox (1976) model, the Longstaff and Schwartz (1995) model with stochastic interest rates, the Collin-Dufresne and Goldstein (2001) model with a stationary leverage, and the double-exponential jump diffusion model used in Huang and Huang (2002, 2012) and Kou (2002).

Results from our specification tests strongly reject the Merton, Black and Cox, and Longstaff and Schwartz models. However, the results also indicate that jumps and stationary leverage help improve the overall fit of CDS spreads and equity volatility. Nonetheless, all five models have difficulty capturing the dynamic behavior of both equity volatility and CDS spread curves, especially for investment-grade names. On the other hand, we find that these models have a much better ability to explain the average sensitivity of CDS spreads to equity returns than their ability to explain the average CDS spread and equity volatility. Surprisingly, the Merton model provides the best hedging performance among all five models.

Overall, the main findings of this study, together with those of Bao and Pan (2013) on excess corporate bond return volatility, suggest a need for new structural models that can explain not only the credit spread puzzle (Huang and Huang 2002) but also those second moment variables.