Prepayment and Default Risks of Mortgage-Backed Security Collateral Pools

Yıl 2024, Cilt: 24 Sayı: 1, 21 - 42, 03.02.2024

Tuğba Güneş Ayşen Apaydın

https://doi.org/10.21121/eab.1289964

Öz

Mortgage-backed securities (MBS) are structured financial products that are produced via securitization of mortgage loans. Due to the nature of securitization, all risks of mortgage loans are transferred from originators to MBS investors. Prepayment and default risks of mortgages lead to uncertainty in MBS cash flows and create a complex problem for valuation of these instruments. Therefore, estimating these mortgage termination risks has become the focus of valuation of MBS collateral pools. This study explores two questions by using a publicly open dataset provided by Fannie Mae. First, two machine learning algorithms (Random Forest and Multinomial Logit Regression) are used for classification to predict whether a mortgage loan is likely to be prepaid, defaulted or current. Afterwards, Competing Risks Cox Regression Analysis is performed to see determinants of when mortgage termination risks are likely to happen. It is found that not all mortgage borrowers behave optimally in their prepayment and default decisions. Therefore, in addition to refinancing incentive and negative equity which depend on variations in prevailing mortgage interest rates and housing prices, heterogeneity in mortgage borrowers’ behaviors and loan characteristics, and also local economic factors are significantly important in estimating mortgage termination risks. It is worth noting that prominence role of mortgage payment delinquencies in particularly predicting defaults emphasizes the essential need of monitoring payments by servicers to keep safety of MBS investors and financial markets.

Anahtar Kelimeler

mortgage risks, mortgage-backed securities, valuation of MBS collateral pools, real estate finance, machine learning

Kaynakça

• Agarwal , S., Ambrose, B. W., & Yildirim, Y. (2015). The subprime virus. Real Estate Economics, 43(4), 891- 915.
• Ahlawat, S. (2019). Evaluation of Mortgage Default Characteristics Using Fannie Mae’s Loan Performance Data. The Journal of Real Estate Finance and Economics, 59(4), 589-616.
• Alpaydin, E. (2020). Introduction to machine learning: MIT press.
• An, X., Deng, Y., & Gabriel, S. A. (2021). Default option exercise over the financial crisis and beyond. Review of Finance, 25(1), 153-187.
• Barbaglia, L., Manzan, S., & Tosetti, E. (2023). Forecasting loan default in Europe with machine learning. Journal of Financial Econometrics, 21(2), 569-596.
• Bennett, P., Peach, R., & Peristiani, S. (2001). How much mortgage pool information do investors need? The Journal of Fixed Income, 11(1), 8-15.
• Bergstra, J., & Bengio, Y. (2012). Random search for hyperparameter optimization. Journal of machine learning research, 13(2).
• Berliner, B., Quinones, A., & Bhattacharya, A. (2016). Mortgage Loans to Mortgage-Backed Securities. In F. J. Fabozzi (Ed.), The Handbook of Mortgage-Backed Securities (Seventh Edition ed., pp. 3-29). Oxford, United Kingdom: Oxford Univeristy Press.
• Berrar, D. (2018). Cross Validation. In S. Ranganathan, K. Nakai, & C. Schonbach (Eds.), Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics (Vol. 1, pp. 542-545): Elsevier.
• Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654.
• Blumenstock, G., Lessmann, S., & Seow, H.-V. (2022). Deep learning for survival and competing risk modelling. Journal of the Operational Research Society, 73(1), 26-38.
• Breiman, L. (2001). Random forests. Machine learning, 45(1), 5-32.
• Chen, J., Xiang, J., & Yang, T. T. (2018). Re-Default Risk of Modified Mortgages. International Real Estate Review, 21(1).
• Cooper, M. J. (2018). A Deep Learning Prediction Model for Mortgage Default. Master of Engineering Thesis, University of Bristol, England.
• Cowden, C., Fabozzi, F. J., & Nazemi, A. (2019). Default prediction of commercial real estate properties using machine learning techniques. The Journal of Portfolio Management, 45(7), 55-67.
• Cox, D. R. (1972). Regression models and life‐tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187-202.
• Danis, M. A., & Pennington-Cross, A. (2008). The delinquency of subprime mortgages. Journal of Economics and Business, 60(1-2), 67-90.
• Davidson, A. S., Herskovitz, M. D., & Van Drunen, L. D. (1988). The refinancing threshold pricing model: An economic approach to valuing MBS. The Journal of Real Estate Finance and Economics, 1(2), 117-130.
• Davis, R., Lo, A. W., Mishra, S., Nourian, A., Singh, M., Wu, N., & Zhang, R. (2022). Explainable machine learning models of consumer credit risk. Available at SSRN 4006840.
• Demiroglu, C., Dudley, E., & James, C. M. (2014). State foreclosure laws and the incidence of mortgage default. The Journal of Law and Economics, 57(1), 225-280.
• Demyanyk, Y. (2017). The impact of missed payments and foreclosures on credit scores. The Quarterly Review of Economics and Finance, 64, 108-119.
• Deng, Y., Pavlov, A. D., & Yang, L. (2005). Spatial heterogeneity in mortgage terminations by refinance, sale and default. Real Estate Economics, 33(4), 739-764.
• Downing, C., Stanton, R., & Wallace, N. (2005). An empirical test of a two‐factor mortgage valuation model: how much do house prices matter? Real Estate Economics, 33(4), 681-710.
• Drummond, C., & Holte, R. C. (2003). Class Imbalance, and Cost Sensitivity: Why Under Sampling beats Over-Sampling. Paper presented at the Workshop on Learning from Imbalanced Datasets II, ICML, Washington DC.
• Dunn, K. B., & McConnell, J. J. (1981). Valuation of GNMA mortgage‐backed securities. The Journal of Finance, 36(3), 599-616.
• Fabozzi, F. J., Bhattacharya, A. K., & Berliner, W. S. (2007). Mortgage-Backed Securities: Products, Structuring, and Analytical Techniques. Hoboken (Vol. 200): John Wiley & Sons.
• Fannie Mae. (2019). Fannie Mae Single-Family Loan Performance Data, USA. Retrieved from https:// capitalmarkets.fanniemae.com/credit-risk-transfer/ single-family-credit-risk-transfer/fannie-mae-singlefamily-loan-performance-data
• FHFA. (2021). House Price Index Datasets, USA. Retrieved from https://www.fhfa.gov/DataTools/Downloads/Pages/House-Price-Index-Datasets.aspx#qpo
• Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American statistical association, 94(446), 496-509.
• Foote, C. L., & Willen, P. S. (2018). Mortgage-default research and the recent foreclosure crisis. Annual Review of Financial Economics, 10, 59-100.
• Fout, H., Li, G., Palim, M., & Pan, Y. (2020). Credit risk of low income mortgages. Regional Science and Urban Economics, 80, 103390.
• Freddie Mac. (2020). Mortgage Rates - Historical Data, . Retrieved from http://www.freddiemac.com/pmms/ pmms_archives.html
• Freddie Mac. (2021). Quarterly Refinance Statistics Archive, USA. Retrieved from http://www.freddiemac.com/research/datasets/refinance-stats/archive.page#archive
• Gerardi, K., Herkenhoff, K. F., Ohanian, L. E., & Willen, P. S. (2018). Can’t pay or won’t pay? unemployment, negative equity, and strategic default. The Review of Financial Studies, 31(3), 1098-1131.
• Groot, J. D. (2016). Credit risk modeling using a weighted support vector machine, Master Thesis, Universiteit Utrecht.
• Hayre, L., & Young, R. (2004). Guide to mortgage-backed securities. Citigroup White Paper.
• Hertzmann, A., & Fleet, D. (2012). Machine Learning And Data Mining Lecture Notes. Computer Science Department, University of Toronto.
• Huh, Y., & Kim, Y. S. (2019). The Real Effects of Secondary Market Trading Structure: Evidence from the Mortgage Market. Available at SSRN 3373949.
• Johnston, E., & Van Drunen, L. (1988). Pricing mortgage pools with heterogeneous mortgagors: Empirical evidence. Unpublished manuscript, University ofUtah.
• Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data (Vol. 360): John Wiley & Sons.
• Kalotay, A., Yang, D., & Fabozzi, F. J. (2004). An optiontheoretic prepayment model for mortgages and mortgage-backed securities. International Journal of Theoretical and Applied Finance, 7(08), 949-978.
• Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282), 457-481.
• Kau, J. B., Keenan, D. C., & Li, X. (2011). An analysis of mortgage termination risks: a shared frailty approach with MSA-level random effects. The Journal of Real Estate Finance and Economics, 42(1), 51-67.
• Kau, J. B., Keenan, D. C., & Smurov, A. A. (2006). Reduced form mortgage pricing as an alternative to optionpricing models. The Journal of Real Estate Finance and Economics, 33(3), 183-196.
• Keys, B. J., Pope, D. G., & Pope, J. C. (2016). Failure to refinance. Journal of Financial Economics, 122(3), 482-499.
• Kok, N., Koponen, E.-L., & Martínez-Barbosa, C. A. (2017). Big data in real estate? From manual appraisal to automated valuation. The Journal of Portfolio Management, 43(6), 202-211.
• LaCour-Little, M. (2008). Mortgage termination risk: a review of the recent literature. Journal of Real Estate Literature, 16(3), 295-326.
• Link, W. A. (1989). A model for informative censoring. Journal of the American statistical association, 84(407), 749-752.
• López, A. L., López, E., & Ponce, H. (2022). Credit Risk Models in the Mexican Context Using Machine Learning. Paper presented at the Mexican International Conference on Artificial Intelligence.
• Lowell, L., & Corsi, M. (2006). Mortgage Pass-Through Securities. In F. J. Fabozzi (Ed.), The Handbook of Prepayment and Default Risks of Mortgage-Backed Security Collateral Pools 41 Mortgage-Backed Securities (Sixth Edition ed., pp. 45-79). US: McGraw-Hill.
• Mamonov, S., & Benbunan-Fich, R. (2017). What can we learn from past mistakes? Lessons from data mining the Fannie Mae mortgage portfolio. Journal of Real Estate Research, 39(2), 235-262.
• McConnell, J. J., & Buser, S. A. (2011). The origins and evolution of the market for mortgage-backed securities. Annu. Rev. Financ. Econ., 3(1), 173-192.
• Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. The Journal of Finance, 29(2), 449-470.
• Patrabansh, S. (2015). The Marginal Effect of FirstTime Homebuyer Status on Mortgage Default and Prepayment, FHFA Working Paper 15-2, USA. Pennington-Cross, A. (2010). The duration of foreclosures in the subprime mortgage market: a competing risks model with mixing. The Journal of Real Estate Finance and Economics, 40(2), 109-129.
• Prentice, R. L., Kalbfleisch, J. D., Peterson Jr, A. V., Flournoy, N., Farewell, V. T., & Breslow, N. E. (1978). The analysis of failure times in the presence of competing risks. Biometrics, 541-554. Quigley, J. M., & Van Order, R. (1991). Defaults on mortgage obligations and capital requirements for US savings institutions: A policy perspective. Journal of Public Economics, 44(3), 353-369.
• Rajashri, P. J., Davis, T., & McCoy, B. (2016). Valuation of Mortgage-Backed Securities. In F. J. Fabozzi (Ed.), The Handbook of Mortgage-Backed Securities: 7th Edition: Oxford University Press.
• Richard, S. F., & Roll, R. (1989). Prepayments of fixed-rate mortgage-backed securities. Journal of Portfolio Management, 15(3), 73.
• Schelkle, T. (2018). Mortgage default during the US mortgage crisis. Journal of money, credit and banking, 50(6), 1101-1137.
• Schwartz, E. S., & Torous, W. N. (1989). Prepayment and the valuation of mortgage‐backed securities. The Journal of Finance, 44(2), 375-392.
• Sirignano, J., Sadhwani, A., & Giesecke, K. (2016). Deep learning for mortgage risk. arXiv preprint arXiv:1607.02470.
• Spahr, R. W., & Sunderman, M. A. (1992). The effect of prepayment modeling in pricing mortgage-backed securities. Journal of housing research, 381-400.
• Timmis, G. (1985). Valuation of GNMA mortgage-backed securities with transaction costs, heterogeneous households and endogenously generated prepayment rates. Carnegie-Mellon University.
• Weiner, J. (2016). Modeling Prepayments and Defaults for MBS Valuation. In F. J. Fabozzi (Ed.), The Handbook of Mortgage-Backed Securities (Seventh Edition ed., pp. 531-559). Oxford, United Kingdom: Oxford Univeristy Press.
• Zhu, X., Chu, Q., Song, X., Hu, P., & Peng, L. (2023). Explainable prediction of loan default based on machine learning models. Data Science and Management.