استفاده از داده کاوی برای ناهمگونی فضایی وام های مسکن مسدودشده

The loss given a default (LGD) is a key component when calculating the credit risk associated with an asset portfolio. However, the issue of default probability has not often been addressed in past mortgage loan data mining studies. The LGD has rarely been used to assess the comprehensive credit risk for a portfolio of mortgage loans. The location of a mortgaged property is strongly correlated with the price of that property as well as providing social, demographic, and economic information which inherently characterizes the mortgage loan population. Thus, to make an accurate assessment of the credit risk associated with the loan portfolio, one requires a specific data mining technique capable of determining the heterogeneity of the portfolio across regions. The sample utilized in this study consists of data on two thousand foreclosed mortgages in Kaohsiung City. We first test the homogeneity between the different city districts; second, we estimate the magnitude of the heterogeneity, including the spatial heterogeneity; third, a prior distribution for the heterogeneity is formulated using data mining methods; finally, the overall LGD, showing the credit risk for a given default probability is calculated.

Data mining is a technique for extracting knowledge from information. It can be applied to determine the various social, medical, demographic, financial and economic factors, and collect information (Bayam et al., 2005, Cho and Kim, 2004, Chun and Kim, 2004, Chun and Park, 2005, Chun and Park, 2006, Coussement and Van den Poel, 2008, Ha and Park, 1998, Hsu and Chen, 2007, Hwang et al., 2008, Kuo and Chen, 2001 and Prinzie and Van den Poel, 2005). There are many factors that could have an influence on the default behavior of residential mortgages, such as the present value of the mortgage payments, characteristics of the family, loan to value (LTV) ratio, home equity, unemployment rate, and divorce rate (Ciochetti et al., 2001, Deng et al., 1996, Deng et al., 2000, Deng, 1997, Lambrecht et al., 2003 and Marrison, 2002). In their study of the effects of counseling on mortgage default behavior, Hartarska and Gonzalez-Vega, 2005 and Hartarska and Gonzalez-Vega, 2006 concluded that counseled borrowers were less likely to default on their mortgage than non-counseled borrowers, and that this also affected the optimal exercise. Ambrose, Capone, and Deng (2001) decomposed the boundary conditions for optimal default exercise to look at the economic dynamics leading to optimal default timing for mortgage foreclosure. Ong, Neo, and Tu (2007) showed that price expectations, volatility and equity losses are influential factors for individual households, with past price movement being the most important of these. However, there has been little research on how these factors influence mortgages prior to foreclosure or how they are correlated with location. Thus, in this study, we test homogeneity in different city districts. The remaining part of this paper is organized as follows. In Section 2 we discuss our motivation for adopting a nonlinear mixed model. In Section 3 we present an empirical analysis of random effects and in Section 4 some conclusions are offered.

Many factors, such as the upset price (X1), price of average square footage (X2), square footage (X3), number of bids (X5), total stories (X9), MRT station distance (X11), and unemployment rate (X14), have a significant impact on successful bids for foreclosed mortgages. A nonlinear mixed model can be used to classify the foreclosed mortgages into two groups, with a bidder and without a bidder. In this study, we discuss some methods for exploring the adequacy of the systematic part of the model, and the diagnostic methods for determining the overdispersion and random effects. We obtain following analytical results: (1) Analysis of the maximum likelihood estimates shows that the upset price, total stories, MRT station distance and economic growth rate have positively significant effects on successful bids for foreclosed mortgages. The price of average square footage, number of bids, width of road, and unemployment rate are significantly negatively related to successful bids. (2) The goodness-of-fit of the model is examined using both deviance and Pearson χ2 tests. The deviance and Pearson χ2 are larger than the degrees of freedom; the P-values for deviance χ2 is smaller than 0.05 (<.0001). The test results indicate that this model seems to have an overdispersion for the data. (3) We test H0: σ = 0 and H1: σ ≠ 0 for the model. The P-value is smaller than 0.05 and thus indicates that the model has random effects. (4) The predicted random effects are less varied than the sample proportions.