Generalized maximum expected utility models for default risk: a comparison of models with different dependence structures

Stephan Höcht, Rudi Zagst

Abstract

ABSTRACT

We compare different ways of modeling real world probabilities of default over a fixed time horizon conditioned on a vector of explanatory variables. Besides a simple logistic regression, we introduce an extended version of the logistic regression that allows for modeling further dependencies. We also discuss a maximum expected utility (MEU) approach, which chooses the model measure from a one-parameter family of pareto-optimal measures defined in terms of consistency with the data and a prior measure. We apply this setting to a very general class of utility functions, namely the class of hyperbolic absolute risk aversion (HARA) utility functions. The numerical comparison based on Fitch Risk’s North American Loan Loss Database shows mainly three things: the logarithmic utility function leads to good results in the MEU approach and can be used as a proxy for other utility functions in the HARA class, a more complex dependence structure leads to a better performance, and the extended version of the logistic regression outperforms the MEU model in-sample.