Predictive Modeling and Expectable Loss Analysis for Borrower Defaults of Mortgage Loans

Abstract

Home mortgage loan lending firms are exposed to many business risks. This paper focuses on the mortgage loan borrower risks and proposes a prospective loss analysis approach in regard to loan repayment defaults of borrowers.For this purpose, a predictive modeling is presented in three stages. In the first stage, occurrence of borrower defaults in a mortgage loans portfolio is modeled through the generalized linear models (GLMs) type regressions for which we specify a logistic distribution for default events. The second stage of modeling develops a survival analysis in order to estimate survival probability and hazard rate functions for individual loans. Ultimately, an expectable loss amount model is presented in the third stage as a function of conditional survival probabilities and corresponding hazard rates at loan levels. Throughout all modeling stages, a large and real data set is used as an empirical analysis case by which detailed interpretations and practical implications of the obtained results are stated.The remaining part of the paper is organized as follows. Next section gives a review of the literature in relevance to the subject matter of this paper. Thereafter, we describe the data that we use as an empirical case analysis in our modeling steps. In the fourth section, we pursue the construction of GLMs type logistic and classified logistic regression models to identify the major predictors of default occurrences and to estimate default event probabilities. Section five concentrates on the lifetimes of observed defaulted loans and active loans in a mortgage loans portfolio and presents a log-logistic type survival modeling and hazard rate analysis for default predictions. In the same section, we propose and compute a measure of expectable loss amounts on the loans that are detected in no default status over a given time period, and discuss the practical implications of this measure. An overall discussion of the obtained results is given in section six and the last section concludes the paper. PREDICTIVE MODELING AND EXPECTABLE LOSS ANALYSIS 233Irish residential mortgage market with the U.S. subprime mortgage crises, Danis and Pennington-Cross (2008) applied a multinomial logit model and discussed the reasons for mortgage delinquencies in a certain geographical location at several borrower age classes and several housing market factors, Mian and Sufi (2009) investigated the U.S. mortgage default crisis as a consequence of the expanding size of the mortgage loans at the time, Qi and Yang (2009) presented a study on the loss-given-default measure for a large set of residential mortgage loan data that involve high loan-to-value ratios, Tsai, Liao, and Chiang (2009) presented an analysis on the yield, duration and convexity features of the mortgages that are risky due to the prepayment and ability-to-payment problems, Ali and Daly (2010) investigated an evidence on the macroeconomic determinants of credit risks in a cross country study, Bastos (2010) investigated the bank loans loss-given-default amounts ...