Simulation and Estimation of Loss Given Default

by Stefan Hlawatsche of Otto-von-Guericke University, Magdeburg, and
Sebastian Ostrowski of Otto-von-Guericke University, Magdeburg

March 2010

Abstract: The aim of our paper is the development of an adequate estimation model for the loss given default, which incorporates the empirically observed bimodality and bounded nature of the distribution, Therefore we introduce an adjusted Expectation Maximization algorithm to estimate the parameters of a univariate mixture distribution, consisting of two beta distributions. Subsequently these estimations are compared with the Maximum Likelihood estimators to test the efficiency and accuracy of both algorithms. Furthermore we analyze our derived estimation model with estimation models proposed in the literature on a synthesized loan portfolio. The simulated loan portfolio consists of possibly loss-influencing parameters that are merged with loss given default observations via a quasi-random approach. Our results show that our proposed model exhibits more accurate loss given default estimators than the benchmark models for different simulated data sets comprising obligor-specific parameters with either high predictive power or low predictive power for the loss given default.

JEL Classification: C01, C13, C15, C16, C5.

Keywords: Bimodality, EM Algorithm, Loss Given Default, Maximum Likelihood, Mixture Distribution, Portfolio Simulation.

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