Abstract
We propose an alternative approach to the modeling of the positive dependence between the probability of default and the loss given default in a portfolio of exposures, using a bivariate urn process. The model combines the power of Bayesian nonparametrics and statistical learning, allowing for the elicitation and the exploitation of experts’ judgements, and for the constant update of this information over time, every time new data is available. A real-world application on mortgages is described using the Single Family Loan-Level Dataset by Freddie Mac.
Highlights
The ambition of this paper is to present a new way of modeling the empirically-verified positive dependence between the Probability of Default (PD) and the Loss Given Default (LGD) using a Bayesian nonparametric approach, based on urns and beta-Stacy processes (Walker and Muliere 1997)
The results we obtain are promising and suggest that the bivariate urn model can represent an interesting way of modeling PD and LGD dependence for banks and practitioners
The present section has no ambition of being a complete empirical study on the PD–LGD dependence in the Freddie
Summary
The ambition of this paper is to present a new way of modeling the empirically-verified positive dependence between the Probability of Default (PD) and the Loss Given Default (LGD) using a Bayesian nonparametric approach, based on urns and beta-Stacy processes (Walker and Muliere 1997). Our contribution to this open problem is represented by the present paper, which finds its root in the recent literature about the use of urn models in credit risk management (Amerio et al 2004; Cheng and Cirillo 2018; Cirillo et al 2010; Peluso et al 2015), and more in general in the Bayesian modeling of credit risk—see, for example, Baesens et al (2016); Cerchiello and Giudici (2014); Giudici (2001); Giudici et al (2003); McNeil and Wendin (2007). Peluso et al (2015) and Cheng and Cirillo (2018)
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