  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.
