本篇論文的主要目的為利用Kernel迴歸模型來預測台灣抵押貸款違約率.過去大部分的文獻皆以有母數的統計方法做為實證的模型. LaCour-Little and Maxam (2001) 則以KR模型預測抵押貸款證券(MBS)的提前清償率,發現無母數的統計方法能有效的應用在違約模型.所以本篇參考LaCour-Little and Maxam (2001)的KR模型,資料是台灣北部某商業銀行提供,期間為2003年的12月到2006年6月的抵押貸款資料.我們發現(1)每月所得,LTV ratio,貸款額度,存款餘額,婚姻狀況以及教育程度對貸款者違約率有顯著性的影響.(2)在比較整體預測能力上,KR模型的預測能力皆比兩各有母數的統計模型(邏輯斯迴歸以及Probit 模型)來的好.(3)另外不管在Type I or Type II 誤差,KR模型的誤差率皆比輯斯迴歸以及Probit 模型來的低.

This paper is to estimate mortgage loan default probabilities in Taiwan’s mortgage market using a nonparametric kernel regression (KR) model. Many past studies utilize primarily the proportional hazard model or logistic regression (LR) as a technique for modeling and predicting default rates. LaCour-Little and Maxam (2001) use KR to estimate prepayment rates and find that the technique contributes to default modeling. Hence, we employ the kernel model to predict default rates using residential mortgage data between December 2003 and June 2006 from a financial holdings company in Taiwan. Our findings are as follows: (1) Income, Loan To Property Value ratio ( LTV ratio), Amount of Loan, Savings Deposit, Marital Status, and Education have significant impacts on the default of debtors, and LTV ratio, Marital Status, and Education are positively correlated with default rates, while Amount of Loan and Savings Deposit are negatively correlated with default rates; (2) The overall prediction accuracy of the KR default forecasting model, LR and Probit model are 81.96%, 66.99% and 66.94, respectively; (3) For either Type I or Type II errors, the nonparametric KR model provides a lower forecast error rates than the parametric LR and Probit model. We conclude that the nonparametric KR is shown to exhibit superior predictive ability compared with the LR model. Lenders can use all available data as the basis for early credit evaluation and employ the proposed nonparametric KR model to forecast default risks.

Ait-Sahalia, Y. and A. W. Lo. (1998). “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,” Journal of Finance 53(2), 499-547.
Ambrose, B. W., R. J. Buttimer, C. A. Capone. (1997). “Pricing Mortgage Default and Foreclosure Delay,” Journal of Money, Credit and Banking 29(3), 314-325.
Berkovec, J. A., G. B. Canner, S. A. Gabriel, and T. H. Hannan. (1994). “Race, Redlining, and Residential Mortgage Loan Performance,” Journal of Real Estate Finance and Economics 9(3), 263-294.
Berkson, J. (1944). “Application of the Logistic Function to Bio-Assay,” Journal of the American Statistical Association 39(227), 357-365.
Boudoukh, J., M. Richardson, R. Stanton, and R. F. Whitelaw. (1996). “Pricing Mortgage-Backed Securities in a Multifactor Interest Rate Environment: A Multivariate Density Estimation Approach,” Review of Financial Studies 10, 405.
Burkhard, J., E. De Giorgi. (2004). “An Intensity Based Non-Parametric Default Model for Residential Mortgage Portfolios,” National Centre of Competence in Research Financial Valuation and Risk Management Working Paper, Available at “http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=332927”.
Campbell, T., and J. Dietrich. (1983). “The Determinants of Default on Conventional Residential Mortgage,” Journal of Finance 38(5), 1569-1581.
Canner, G.B., S. A. Gabriel, and J. M. Woolley. (1991). “Race, Default Risk and Mortgage Lending: A Study of the FHA and Conventional Loan Markets,” Southern Economic Journal 58(1), 249-262.
Chou, Jian-Hsin, Hong-Fwu, Yu, and Jinn-Tsair Chen. (2004). “The Choice of Risk Valuation Factors of Mortgage Loan within the Banking Industry,” Web Journal of Chinese Management Review 7(2), 77-102.
Ciochetti, B. A., Y. Deng, G. Lee, J. D. Shilling, and R. Yao. (2003). “A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias,” Journal of Real Estate Finance and Economics 27(1), 5-23.
Cunningham, D., and C. Capone. (1990). “The Relative Termination Experience of Adjustable to Fixed-Rate Mortgages,” The Journal of Finance 45(5), 1687-1703.
Deng, Y. (1997). “Mortgage Termination: An Empirical Hazard Model with Stochastic Term Structure,” Journal of Real Estate Finance and Economics 14(3), 309-331.
Deng, Y., J. M. Quigley, and R. Van Order. (1996). “Mortgage Default and Low Downpayment Loans: The Costs of Public Subsidy,” Regional Science and Urban Economics 26, 263-285.
Deng, Y., J. M. Quigley, and R. Van Order. (2000). “Mortgage Terminations, Heterogeneity and The Exercise of Mortgage Options,” Econometrica 68(2), 275-307.
Epley, D. R., T. P. Cronan and L. Perry. (1985). “A Research Note on Discrimination in Mortgage Lending,” AREUEA Journal 13(4), 446-451.
Epley, D. R., K. Liano and R. Haney. (1996). “Borrower Risk Signaling Using Loan-to-Value Ratios,” The Journal of Real Estate Research 11(1), 71-86.
Follain, J. R., J. Ondrich, and G. Sinha. (1997). “Ruthless Prepayment? Evidence from Multifamily Mortgages,” Journal of Urban Economics 41(1), 78-101.
Foster, C., and R. Van Order. (1984). “An Option Based Model of Mortgage Default,” Housing Finance Review 3(4), 351-372.
Green, J., and J. B. Shoven. (1986), “The Effects of Interest Rates on Mortgage Prepayment,” Journal of Money, Credit and Banking 18(1), 41-59.
Herzog, J. P., and J. S. Earley. (1970). “Home Mortgage Delinquency and Foreclosure,” New York: National Bureau of Economic Research.
Hilliard, J. E., A. L. Schwartz, and A. L. Tucker. (1996). “Bivariate Binomial Options Pricing with Generalized Interest Rate Processes,” Journal of Financial Research 19(4), 585-602.
Hilliard, J. E., J. B. Kau, and V. C. Slawson. (1996). “Valuing Prepayment and Default in A Fixed Rate Mortgage: A Bivariate Binomial Pricing Technique,” University of Georgia working paper.
Hilliard, J. E., J. B. Kau, and V. C. Slawson. (1998). “Valuing Prepayment and Default in A Fixed-Rate Mortgage: A Bivariate Binomial Options Pricing Technique,” Real Estate Economics 26(3), 431-468.
Hsieh, Yung-Ming, Chia-Hsing Huang, Tsung-Je Liou. (2005). “A Comparative Study of Predictive Models for Mortgage Loan Default,” Soochow Journal of Economics and Business 48, 103-125.
Hutchinson, J. M., A. W. Lo, and T. Poggio. (1994). “A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks,” Journal of Finance 49(3), 851-889.
Kau, J. B. and D. C. Keenan. (1999). “Patterns of Rational Default,” Regional Science and Urban Economics 29(6), 765-785.
Kim, J. S., G. K. Tokuhata, and J. R. Bratz. (1985). “Comparison of Multivariate Regression Analysis between Logistic Model and the Least Square Model Using SAS Software,” SAS Users Group International Conference Proceedings, 1109-1112.
Kordas, G. (2002). “Credit Scoring Using Binary Quantile Regression,” University of Pennsylvania Working Paper, Available at “http://www.econ.upenn.edu/~kordas/.”.
LaCour-Little, M., and C. Maxam. (2001). “Applied Nonparametric Regression Techniques: Estimating Prepayments on Fixed-Rate Mortgage-Backed Securities,” Journal of Real Estate Finance and Economics 23(2), 139-160.
LaCour-Little, M., M. Marshoun, and C. Maxam. (2002). “Improving Parametric Mortgage Prepayment Models with Non-parametric Kernel Regression,” Journal of Real Estate Research 24(3), 299-327.
Lawrence, E. C., L. D. Smith, and M. Rhoades. (1992). “An Analysis of Default Risk in Mobile Home Credit,” Journal of Banking and Finance 16(2), 299-312.
Lawrence, E. C. and N. Arshadi. (1995). “A Multinomial Logit Analysis of Problem Loan Resolution Choices in Banking,” Journal of Money, Credit and Banking 27(1), 202-216.
Lee, Shin-Ping. (2000). “An Analysis of Default Risk on Residential Mortgage Loans,” Web Journal of Chinese Management Review 3(3), 111-126.
Mills, E. S., and Luan, Sende Lubuele. (1994). “Performance of Residential Mortgages in Low and Moderate-Income Neighborhoods,” Journal of Real Estate Finance and Economics 9(3), 245-260.
Morton, T. G. (1975). “A Discriminant Function Analysis of Residential Mortgage Delinquency and Foreclosure,” AREUEA Journal 3(1), 73-90.
Nadaraya, E. A. (1964). “On Estimating Regression,” Theory of Probability and Its Application 10, 186-190.
Nelson, D. and K. Ramaswamy. (1990) “Simple Binomial Processes as Diffusion Approximations in Financial Models,” Review of Financial Studies 3(3), 393-430.
Ohlson, J. A. (1980). “Financial Ratios and the Probabilistic Prediction of Bankruptcy,” Journal of Accounting Research 18(1), 109-131.
Quercia, R. G., and M. A. Stegman. (1992). “Residential Mortgage Default: A Review of the Literature,” Journal of Housing Research 3(2), 341-379.
Quigley, J. M., and R. Van Order. (1991). “Defaults on Mortgage Obligations and Capital Requirements for U. S. Savings Institutions: A Policy Perspective,” Journal of Public Economics 44(1), 353-369.
Rosenblatt, M. (1956). “Remarks on Some Non-Parametric Estimates of A Density Function,” Ann. Math. Statist 27, 832-837.
Sandor, R., and H. Sosin. (1975). “The Determinations of Mortgage Risk Premiums: A Case Study of the Portfolio of A Savings and Loan Association,” The Journal of Business 48(1), 27-38.
Schwartz, E. S., and W. N. Torous. (1993). “Mortgage Prepayment and Default Decisions: A Poisson Regression Approach,” AREUEA Journal 21(4), 431-449.
Scott, D. (1992). Multivariate Density Estimation: Theory Practice and Visualization. New York: Wiley
Smith, L., S. Sanchez, and E. Lawrence. (1996). “A Comprehensive Model for Managing Credit Risk on Home Mortgage Portfolios,” Decision Sciences 27(2), 291–317.
Steenackers, A. and M. J. Goovaerts. (1989). “A Credit Scoring Model for Personal Loans,” Journal of Insurance Mathematics Economics, 31-34.
Van Order, R. (1990). “The Hazards of Default,” Secondary Mortgage Markets Fall, 29-31.
Vandell, K. D. (1978). “Default Risk under Alternative Mortgage Instruments,” Journal of Finance 33(5), 1279-1296.
Vandell, K. D., and T. Thibodeau. (1985). “Estimation of Mortgage Defaults Using Disaggregate Loan History Data,” AREUEA Journal 13(3), 292-316.
von Furstenberg, G. M. (1969). “Default Risk on FHA-Insured Home Mortgages As A Function of the Terms of Financing: A Quantitative Analysis,” Journal of Finance 24(3), 459-477.
_____, G. M. (1970a). “Interstate Differences in Mortgage Lending Risks: An Analysis of Causes,” Journal of Financial and Quantitative Analysis 5, 249-242.
_____, G. M. (1970b). “The Investment Quality of Home Mortgages,” Journal of Risk and Insurance 37(3), 437-445.
von Furstenberg, G. M. and R. J. Green. (1974). “Home Mortgage Delinquencies: A Cohort Analysis,” Journal of Finance 29(5), 1545-1548.
Watson, G. S. (1964). “Smooth Regression Analysis,” Sankhya, Series A: 26, 359-372.
Williams, A. O., W. Beranek, and J. Kenkel. (1974). “Default Risk in Urban Mortgages: A Pittsburgh Prototype Analysis,” AREUEA Journal 2(2), 101-102.
Zorn, P. M., and M. J. Lea. (1989). “Mortgage Borrower Repayment Behavior: A Microeconomic Analysis with Canadian Adjustable Rate Mortgage Data,” AREUEA Journal 17(1), 118-136.