The GARCH Structural Credit Risk Model: Simulation Analysis and Application to the Bank CDS Market During the 2007-2008 Crisis

Abstract

We develop a structural credit risk model in which the unobserved asset volatility of the firm follows a GARCH process, as in Heston and Nandi (2000). We estimate our model using an Expectation Maximization algorithm, and benchmark it using simulated data against the Merton (1974) model, both when the latter is calibrated, and when its parameters are estimated using maximum likelihood techniques as in Duan (1994). The Duan method slightly outperforms GARCH when asset volatility is constant, and GARCH significantly outperforms both the Merton and Duan models when the asset follows a GARCH process. An application of the three models studied to the CDS market for the debt of US banks and financial corporations during the period 2007-2008 indicates high levels of asset volatility and financial leverage for many major banks during this period, although only moderate evidence of stochastic volatility. The GARCH model outperforms both the Duan and Merton models in out-of-sample CDS spread prediction. We document a wide incidence of inversion of the spread term structure in the CDS market, both in 2007 and 2008, and all three models exhibit an inverted spread term structure for all banks studied. The group of banks in which the models are able to generate nontrivial spreads is characterized by significantly higher equity time series volatility, higher average CDS spreads across all maturities, and a higher incidence of spread term structure inversion.