Predicting the Loss Given Default Distribution with the Zero-Inflated Censored Beta-Mixture Regression that Allows Probability Masses and Bimodality

Abstract

We propose a new procedure to predict the loss given default (LGD) distribution. Studies find empirical evidence that LGD values have a high concentration at the endpoint 0. Thus, we first use a logistic regression to determine the probability that the LGD value of a defaulted debt equals zero. Further, studies find empirical evidence that positive LGD values have a low concentration at the endpoint 1 and a bimodal distribution on the interval (0,1). Therefore, we use a right-tailed censored beta-mixture regression to model the distribution of positive LGD data. To implement the proposed procedure, we collect 5554 defaulted debts from Moody’s Default and Recovery Database and apply an expectation–maximization algorithm to estimate the LGD distribution. Using each of the k-fold cross-validation technique and the expanding rolling window approach, our empirical results confirm that the new procedure has better and more robust out-of-sample performance than its alternatives because it yields more accurate predictions of the LGD distribution.