Stochastic Volatility of Financial Assets and Default Risk

We present the non-Gaussian extension of the traditional Merton framework, which takes into account slowly relaxing fluctuations of the volatility of the firm's market value of financial assets. The minimal version of the model depends on the Tsallis entropic parameter q and the generalized “distance to default”. For , related to the normal statistics, the new approach replicates results of traditional structural models. For q > 1, corresponding to complex systems with non-additive Tsallis entropy, the model leads to much higher 1-year probability of default for investment grade issuers. 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 q. Using Receiver Operating Characteristic curves, we demonstrate the high forecasting power of the model in prediction of 1-year defaults. We report excellent fitting capabilities of the derived formulae to multi-period default data in both investment-grade and high-yield categories of credit ratings initially assigned to future defaulters. Our study suggests that the level of complexity (“turbulence”) of the time series, quantified by q, should be taken into account to improve valuations of default risk