Structural credit risk models have met with significant resistance in academic research. First, attempts to empirically implement models on individual corporate bond prices have not been successful. Second, subsequent efforts to calibrate models to observable moments including historical default rates uncovered what has become known as the credit spread puzzle the models are unable to match average credit spreads levels. Finally, econometric specification tests further document the difficulties that existing models encounter in explaining the dynamics of credit spreads and equity volatilities.
In this paper, we develop a structural model with time-varying asset volatility in order to address both the levels and dynamics of credit spreads. Our first contribution is to show that the presence of a variance risk premium resolves the credit spread puzzle in terms of levels. Second, we show that the modelling of stochastic asset volatility allows the model to explain time series of equity volatilities while doing a better job at fitting time series of credit spreads at the individual firm level. Finally, we provide estimates of the size of variance risk premia required to explain credit spread levels and benchmark these to existing empirical evidence.
The credit spread puzzle is defined as the inability of structural models, when calibrated to default probabilities, loss rates and Sharpe ratios, to predict spread levels across rating categories consistent with historical market spreads. Huang and Huang (2003), hereafter abbreviated HH, perform this calibration analysis for a broad and representative selection of models and find that, as an example, the latter never predict spreads in excess of a third of the observed levels for 4- and 10-year debt issued by A-rated firms. The performance is typically worse for more highly rated firms and somewhat better for low grade firms.
Huang and Zhou (2008) test a broad set of structural models by designing a GMM-based specification test that confronts the models with panels of CDS term structures and equity volatilities. In addition to ranking the models by rejection frequency, their paper provides insights into the specific shortcomings of the models. One important weakness that emerges from their study is the models’ inability to fit the dynamics of CDS prices and equity volatilities. In particular, the models find it difficult to generate time variation in the equity volatility of the same magnitude as is actually observed, suggesting that an extension to allow for stochastic asset volatility is desirable.
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Time-varying asset volatility and the credit spread puzzle
