Inflated Mixture Models: Applications to Multimodality in Loss Given Default

Abstract

In this paper, we propose an inflated mixture model to deal with multimodality in loss given default data. We propose a mixed of degenerate distributions, to handle zeros and ones excess, with a mixture of to-be-chosen bounded distributions for non-zeros and non-ones proportions. By applying the methodology in four retail portfolios of a large Brazilian commercial bank, we show that the inflated mixture of beta distributions plays better role minimizing model risk in fitting an inadequate model, in comparison with others considered competitive models. We explore the use of maximum likelihood estimation procedure. Monte Carlo simulations are carried out in order to check its finite sample performance.