qGaussian model of default
We present the qGaussian generalization of the Merton framework, which takes into account slow fluctuations of the volatility of the firms market value of financial assets. The minimal version of the model depends on the Tsallis entropic parameter q and the generalized distance to default. The empirical foundation and implications of the model are illustrated by the study of 645 North American industrial firms during the financial crisis, 2006 - 2012. All defaulters in the sample have exceptionally large, corresponding to unusually fat-tailed unconditional distributions of log-asset-returns. Using Receiver Operating Characteristic curves, we demonstrate the high forecasting power of the model in prediction of 1-year defaults. Our study suggests that the level of complexity of the realized time series, quantified by q, should be taken into account to improve valuations of default risk.