qGaussian model of default

TL;DR

This paper introduces a qGaussian extension of the Merton model that incorporates volatility fluctuations, demonstrating improved default risk prediction during the 2006-2012 financial crisis for North American firms.

Contribution

The paper develops a novel qGaussian-based model of default risk that accounts for fat-tailed return distributions and volatility fluctuations, enhancing predictive accuracy.

Findings

Model accurately predicts 1-year defaults.

Fat-tailed distributions observed in defaulters.

q parameter correlates with market volatility complexity.

Abstract

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.