An Urn-Based Generalized Extreme Shock Model for the Probability of Firms' Default

Abstract:     
In the literature, there are several methods to estimate the probability of firms' default, from simple judgement-based methods to more complicated artificial intelligence systems and statistical regression models. In this paper we propose a new stochastic model for the probability of firms' default, based on a stochastic urn process, characterized by a special triangular reinforcement matrix. In particular, assuming that a firm can experience three different levels of risk (no risk, risk and default), we introduce a dependence among the levels, so that the probability of default increases every time the firm enters the risky state, while it decreases (but does not disappear) the more the firm spends in the non-risky one. The levels of risk are determined on the basis of aggregate balance indices. Using this approach, we are both able to predict firms' default probabilities with a good degree of approximation and to obtain limit distributions that nicely reproduce the empirical results one can find in the literature.

Keywords: generalized extreme shock model, Polya urn, reinforcement, default

JEL Classifications: C15, C16, C19

Working Paper Series