An Urn-Based Generalized Extreme Shock Model for the Probability of Firms' Default
IMSV University of Bern
University of Bern
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 Classification: C15, C16, C19
Date posted: April 8, 2008