Affiliations: Quantitative Management Group, Babson Capital Management LLC, 1500 Main Street, Suite 1000, Springfield, MA 01103, USA. Tel.: +1 860 805 1275; E-mail: VCLadyzhets@cox.net
Abstract: This paper presents the major results of a research and development project of building default models for pools of subprime mortgages. The models have been developed to assess the risk of investing into the Residential Mortgage-Backed Securities (RMBS) backed by those pools in a rapidly changing environment. These RMBS are over-the-counter financial securities, and the models serve as a major tool for their competitive pricing and marketing. It has been demonstrated that by modifying the definition of mortgage default – using so-called “implied default” – one can extract more realistic patterns of borrower behavior under adverse economic scenarios from the same historical data. Also, it has been shown that different types of decision trees, chi-square, entropy, and Gini index, can be effectively used to provide the best variable selection and to break the universe of mortgage borrowers into groups that exhibit significant differences with respect to their default propensity. The paper discusses several generations of models that were built and tested. It shows how the relatively simple G-based default model, which yields estimates of cumulative expected defaults for various groups of borrowers, can be generalized into a multidimensional stochastic process (stochastic G-based default model). The paper also discusses how the G-based default model can be expanded to deal with the mortgages that are in a negative equity position.
Keywords: Implied default, decision trees, variable selection, G-based default model
