IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v8y2020i2p64-d369662.html
   My bibliography  Save this article

A Multi-State Approach to Modelling Intermediate Events and Multiple Mortgage Loan Outcomes

Author

Listed:
  • Richard Chamboko

    (NOVA IMS—Information Management School, New University of Lisbon, 1070-312 Lisbon, Portugal
    International Finance Corporation, World Bank Group, Washington, DC 20433, USA
    Institute for Intelligent Systems, University of Johannesburg, Johannesburg 2006, South Africa)

  • Jorge Miguel Bravo

    (NOVA IMS—Information Management School, New University of Lisbon, 1070-312 Lisbon, Portugal
    Department of Economics, Université Paris-Dauphine PSL, 75775 Paris, France)

Abstract

This paper proposes a novel system-wide multi-state framework to model state occupations and the transitions among current, delinquency, default, prepayment, repurchase, short sale and foreclosure on mortgage loans. The approach allows for the modelling of the progression of borrowers from one state to another to fully understand the risks of a cohort of borrowers over time. We use a multi-state Markov model to model the transitions to and from various states. The key factors affecting the transition into various loan outcomes are the ability to pay as measured by debt-to-income ratio, equity as marked by loan-to-value ratio, interest rates and the property type. Our findings have broader policy implications for better decision-making on granting loans and the design of debt relief and mortgage modification policies.

Suggested Citation

  • Richard Chamboko & Jorge Miguel Bravo, 2020. "A Multi-State Approach to Modelling Intermediate Events and Multiple Mortgage Loan Outcomes," Risks, MDPI, vol. 8(2), pages 1-29, June.
  • Handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:64-:d:369662
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/8/2/64/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-9091/8/2/64/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Erwin Charlier & Arjan Van Bussel, 2003. "Prepayment Behavior of Dutch Mortgagors: An Empirical Analysis," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(2), pages 165-204, June.
    2. Chao Tian & Roberto Quercia & Sarah Riley, 2016. "Unemployment as an Adverse Trigger Event for Mortgage Default," The Journal of Real Estate Finance and Economics, Springer, vol. 52(1), pages 28-49, January.
    3. Tracy, Joseph & Wright, Joshua, 2016. "Payment changes and default risk: The impact of refinancing on expected credit losses," Journal of Urban Economics, Elsevier, vol. 93(C), pages 60-70.
    4. Castro, Vítor, 2013. "Macroeconomic determinants of the credit risk in the banking system: The case of the GIPSI," Economic Modelling, Elsevier, vol. 31(C), pages 672-683.
    5. Aron, Janine & Muellbauer, John, 2016. "“Modelling and forecasting mortgage delinquency and foreclosure in the UK.”," Journal of Urban Economics, Elsevier, vol. 94(C), pages 32-53.
    6. Ventura Bravo, Jorge Miguel & Pereira da Silva, Carlos Manuel, 2006. "Immunization using a stochastic-process independent multi-factor model: The Portuguese experience," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 133-156, January.
    7. D. J. Hand & W. E. Henley, 1997. "Statistical Classification Methods in Consumer Credit Scoring: a Review," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 523-541, September.
    8. Atif Mian & Amir Sufi & Francesco Trebbi, 2015. "Foreclosures, House Prices, and the Real Economy," Journal of Finance, American Finance Association, vol. 70(6), pages 2587-2634, December.
    9. Kristopher Gerardi & Adam Hale Shapiro & Paul S. Willen, 2007. "Subprime outcomes: risky mortgages, homeownership experiences, and foreclosures," Working Papers 07-15, Federal Reserve Bank of Boston.
    10. Janine Aron & John Muellbauer, 2010. "Modelling and Forecasting UK Mortgage Arrears and Possessions," Economics Series Working Papers 499, University of Oxford, Department of Economics.
    11. John Y. Campbell, 2013. "Mortgage Market Design," Review of Finance, European Finance Association, vol. 17(1), pages 1-33.
    12. Luigi Guiso & Paola Sapienza & Luigi Zingales, 2009. "Moral and Social Constraints to Strategic Default on Mortgages," Economics Working Papers ECO2009/27, European University Institute.
    13. Nystrom, Kaj & Skoglund, Jimmy, 2006. "A credit risk model for large dimensional portfolios with application to economic capital," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2163-2197, August.
    14. Edward I. Altman, 1968. "The Prediction Of Corporate Bankruptcy: A Discriminant Analysis," Journal of Finance, American Finance Association, vol. 23(1), pages 193-194, March.
    15. Piskorski, Tomasz & Seru, Amit & Vig, Vikrant, 2010. "Securitization and distressed loan renegotiation: Evidence from the subprime mortgage crisis," Journal of Financial Economics, Elsevier, vol. 97(3), pages 369-397, September.
    16. Eduardo S. Schwartz & Walter N. Torous, 1993. "Mortgage Prepayment and Default Decisions: A Poisson Regression Approach," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(4), pages 431-449, December.
    17. Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-299, August.
    18. Adam M. Guren & Arvind Krishnamurthy & Timothy J. Mcquade, 2021. "Mortgage Design in an Equilibrium Model of the Housing Market," Journal of Finance, American Finance Association, vol. 76(1), pages 113-168, February.
    19. Whelan, Karl, 2014. "Ireland’s Economic Crisis: The Good, the Bad and the Ugly," Journal of Macroeconomics, Elsevier, vol. 39(PB), pages 424-440.
    20. Juan Carranza & Dairo Estrada, 2013. "Identifying the determinants of mortgage default in Colombia between 1997 and 2004," Annals of Finance, Springer, vol. 9(3), pages 501-518, August.
    21. Foote, Christopher L. & Gerardi, Kristopher & Willen, Paul S., 2008. "Negative equity and foreclosure: Theory and evidence," Journal of Urban Economics, Elsevier, vol. 64(2), pages 234-245, September.
    22. Sumit Agarwal & Gene Amromin & Itzhak Ben-David & Souphala Chomsisengphet & Tomasz Piskorski & Amit Seru, 2017. "Policy Intervention in Debt Renegotiation: Evidence from the Home Affordable Modification Program," Journal of Political Economy, University of Chicago Press, vol. 125(3), pages 654-712.
    23. Kerry D. Vandell & Walter Barnes & David Hartzell & Dennis Kraft & William Wendt, 1993. "Commercial Mortgage Defaults: Proportional Hazards Estimation Using Individual Loan Histories," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(4), pages 451-480, December.
    24. Christopher Mayer & Edward Morrison & Tomasz Piskorski & Arpit Gupta, 2014. "Mortgage Modification and Strategic Behavior: Evidence from a Legal Settlement with Countrywide," American Economic Review, American Economic Association, vol. 104(9), pages 2830-2857, September.
    25. Lessmann, Stefan & Baesens, Bart & Seow, Hsin-Vonn & Thomas, Lyn C., 2015. "Benchmarking state-of-the-art classification algorithms for credit scoring: An update of research," European Journal of Operational Research, Elsevier, vol. 247(1), pages 124-136.
    26. Patrick Bajari & Chenghuan Sean Chu & Minjung Park, 2008. "An Empirical Model of Subprime Mortgage Default From 2000 to 2007," NBER Working Papers 14625, National Bureau of Economic Research, Inc.
    27. du Jardin, Philippe & Séverin, Eric, 2011. "Predicting corporate bankruptcy using a self-organizing map: An empirical study to improve the forecasting horizon of a financial failure model," MPRA Paper 44262, University Library of Munich, Germany.
    28. Yongheng Deng & John M. Quigley & Robert Van Order, 2000. "Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options," Econometrica, Econometric Society, vol. 68(2), pages 275-308, March.
    29. Gülçin Özkan & Ms. Filiz D Unsal, 2012. "Global Financial Crisis, Financial Contagion, and Emerging Markets," IMF Working Papers 2012/293, International Monetary Fund.
    30. Crook, Jonathan N. & Edelman, David B. & Thomas, Lyn C., 2007. "Recent developments in consumer credit risk assessment," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1447-1465, December.
    31. Marco Di Maggio & Amir Kermani & Benjamin J. Keys & Tomasz Piskorski & Rodney Ramcharan & Amit Seru & Vincent Yao, 2017. "Interest Rate Pass-Through: Mortgage Rates, Household Consumption, and Voluntary Deleveraging," American Economic Review, American Economic Association, vol. 107(11), pages 3550-3588, November.
    32. Andreas Fuster & Paul S. Willen, 2017. "Payment Size, Negative Equity, and Mortgage Default," American Economic Journal: Economic Policy, American Economic Association, vol. 9(4), pages 167-191, November.
    33. Patrick J. Heagerty & Thomas Lumley & Margaret S. Pepe, 2000. "Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker," Biometrics, The International Biometric Society, vol. 56(2), pages 337-344, June.
    34. Michelle A. Danis & Anthony Pennington-Cross, 2005. "A dynamic look at subprime loan performance," Working Papers 2005-029, Federal Reserve Bank of St. Louis.
    35. Kelly, Robert & O’Malley, Terence, 2016. "The good, the bad and the impaired: A credit risk model of the Irish mortgage market," Journal of Financial Stability, Elsevier, vol. 22(C), pages 1-9.
    36. Butaru, Florentin & Chen, Qingqing & Clark, Brian & Das, Sanmay & Lo, Andrew W. & Siddique, Akhtar, 2016. "Risk and risk management in the credit card industry," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 218-239.
    37. B Baesens & T Van Gestel & S Viaene & M Stepanova & J Suykens & J Vanthienen, 2003. "Benchmarking state-of-the-art classification algorithms for credit scoring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 627-635, June.
    38. Timothy Jones & Dean Gatzlaff & G. Stacy Sirmans, 2016. "Housing Market Dynamics: Disequilibrium, Mortgage Default, and Reverse Mortgages," The Journal of Real Estate Finance and Economics, Springer, vol. 53(3), pages 269-281, October.
    39. Richard Chamboko & Jorge M. Bravo, 2016. "On the modelling of prognosis from delinquency to normal performance on retail consumer loans," Risk Management, Palgrave Macmillan, vol. 18(4), pages 264-287, December.
    40. Sewin Chan & Claudia Sharygin & Vicki Been & Andrew Haughwout, 2014. "Pathways After Default: What Happens to Distressed Mortgage Borrowers and Their Homes?," The Journal of Real Estate Finance and Economics, Springer, vol. 48(2), pages 342-379, February.
    41. Edward I. Altman, 1968. "Financial Ratios, Discriminant Analysis And The Prediction Of Corporate Bankruptcy," Journal of Finance, American Finance Association, vol. 23(4), pages 589-609, September.
    42. Tomasz Piskorski & Amit Seru, 2018. "Mortgage Market Design: Lessons from the Great Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 49(1 (Spring), pages 429-513.
    43. Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn C., 2012. "Mixture cure models in credit scoring: If and when borrowers default," European Journal of Operational Research, Elsevier, vol. 218(1), pages 132-139.
    44. Christopher Mayer & Karen Pence & Shane M. Sherlund, 2009. "The Rise in Mortgage Defaults," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 27-50, Winter.
    45. Neil Bhutta & Jane Dokko & Hui Shan, 2017. "Consumer Ruthlessness and Mortgage Default during the 2007 to 2009 Housing Bust," Journal of Finance, American Finance Association, vol. 72(6), pages 2433-2466, December.
    46. James B. Kau & Donald C. Keenan & Taewon Kim, 1993. "Transaction Costs, Suboptimal Termination and Default Probabilities," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(3), pages 247-263, September.
    47. Patrick Bajari & Chenghuan Sean Chu & Denis Nekipelov & Minjung Park, 2013. "A Dynamic Model of Subprime Mortgage Default: Estimation and Policy Implications," NBER Working Papers 18850, National Bureau of Economic Research, Inc.
    48. repec:bin:bpeajo:v:49:y:2019:i:2018-01:p:429-513 is not listed on IDEAS
    49. Patrick J. Heagerty & Yingye Zheng, 2005. "Survival Model Predictive Accuracy and ROC Curves," Biometrics, The International Biometric Society, vol. 61(1), pages 92-105, March.
    50. Deng, Yongheng & Quigley, John M. & Van Order, Robert & Mac, Freddie, 1996. "Mortgage default and low downpayment loans: The costs of public subsidy," Regional Science and Urban Economics, Elsevier, vol. 26(3-4), pages 263-285, June.
    51. Maria Stepanova & Lyn Thomas, 2002. "Survival Analysis Methods for Personal Loan Data," Operations Research, INFORMS, vol. 50(2), pages 277-289, April.
    52. Bo Liu & Tien Foo Sing, 2018. "“Cure” Effects and Mortgage Default: A Split Population Survival Time Model," The Journal of Real Estate Finance and Economics, Springer, vol. 56(2), pages 217-251, February.
    53. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    54. Bellotti, Tony & Crook, Jonathan, 2013. "Forecasting and stress testing credit card default using dynamic models," International Journal of Forecasting, Elsevier, vol. 29(4), pages 563-574.
    55. Scott D. Grimshaw & William P. Alexander, 2011. "Markov chain models for delinquency: Transition matrix estimation and forecasting," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(3), pages 267-279, May.
    56. Sumit Agarwal & Gene Amromin & Souphala Chomsisengphet & Tim Landvoigt & Tomasz Piskorski & Amit Seru & Vincent Yao, 2015. "Mortgage Refinancing, Consumer Spending, and Competition: Evidence from the Home Affordable Refinancing Program," NBER Working Papers 21512, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Richard Chamboko, 2024. "Digital financial services adoption: a retrospective time-to-event analysis approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-27, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alin Marius Andries & Anca Copaciu & Radu Popa & Razvan Vlahu, 2021. "Recourse and (strategic) mortgage defaults: Evidence from changes in housing market laws," Working Papers 727, DNB.
    2. Piskorski, Tomasz & Seru, Amit, 2021. "Debt relief and slow recovery: A decade after Lehman," Journal of Financial Economics, Elsevier, vol. 141(3), pages 1036-1059.
    3. Richard Chamboko & Jorge M. Bravo, 2016. "On the modelling of prognosis from delinquency to normal performance on retail consumer loans," Risk Management, Palgrave Macmillan, vol. 18(4), pages 264-287, December.
    4. Kristopher Gerardi & Kyle F. Herkenhoff & Lee E. Ohanian & Paul S. Willen, 2018. "Can’t Pay or Won’t Pay? Unemployment, Negative Equity, and Strategic Default," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 1098-1131.
    5. Adam M. Guren & Arvind Krishnamurthy & Timothy J. Mcquade, 2021. "Mortgage Design in an Equilibrium Model of the Housing Market," Journal of Finance, American Finance Association, vol. 76(1), pages 113-168, February.
    6. John Y. Campbell, 2013. "Mortgage Market Design," Review of Finance, European Finance Association, vol. 17(1), pages 1-33.
    7. Gene Amromin & Jennifer Huang & Clemens Sialm & Edward Zhong, 2018. "Complex Mortgages [Why don’t lenders renegotiate more home mortgages? Redefaults, self-cures, and securitization]," Review of Finance, European Finance Association, vol. 22(6), pages 1975-2007.
    8. O’Toole, Conor & Slaymaker, Rachel, 2021. "Repayment capacity, debt service ratios and mortgage default: An exploration in crisis and non-crisis periods," Journal of Banking & Finance, Elsevier, vol. 133(C).
    9. Khandani, Amir E. & Lo, Andrew W. & Merton, Robert C., 2013. "Systemic risk and the refinancing ratchet effect," Journal of Financial Economics, Elsevier, vol. 108(1), pages 29-45.
    10. Sumit Agarwal & Slava Mikhed & Barry Scholnick & Man Zhang, 2022. "Reducing Strategic Default in a Financial Crisis," Working Papers 21-36, Federal Reserve Bank of Philadelphia.
    11. Chen L. Miller, 2018. "Comparison of Two Affordable Housing Finance Channels," International Real Estate Review, Global Social Science Institute, vol. 21(2), pages 227-250.
    12. Kelly, Robert & O’Malley, Terence, 2016. "The good, the bad and the impaired: A credit risk model of the Irish mortgage market," Journal of Financial Stability, Elsevier, vol. 22(C), pages 1-9.
    13. Kelly, Robert & O'Malley, Terence, 2014. "A Transitions-Based Model of Default for Irish Mortgages," Research Technical Papers 17/RT/14, Central Bank of Ireland.
    14. Stephanie Moulton & Yung Chun & Stephanie Casey Pierce & Roberto Quercia & Sarah Riley & Holly Holtzen, 2022. "Does Temporary Mortgage Assistance for Unemployed Homeowners Reduce Longer‐Term Mortgage Default? An Analysis of the Hardest Hit Fund Program," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 41(2), pages 515-551, March.
    15. Goodstein, Ryan & Hanouna, Paul & Ramirez, Carlos D. & Stahel, Christof W., 2017. "Contagion effects in strategic mortgage defaults," Journal of Financial Intermediation, Elsevier, vol. 30(C), pages 50-60.
    16. Hanming Fang & You Suk Kim & Wenli Li, 2015. "The Dynamics of Adjustable-Rate Subprime Mortgage Default: A Structural Estimation," Finance and Economics Discussion Series 2015-114, Board of Governors of the Federal Reserve System (U.S.).
    17. Andreas Fuster & David Lucca & James Vickery, 2023. "Mortgage-backed securities," Chapters, in: Refet S. Gürkaynak & Jonathan H. Wright (ed.), Research Handbook of Financial Markets, chapter 15, pages 331-357, Edward Elgar Publishing.
    18. Kelly, Robert & McCann, Fergal, 2016. "Some defaults are deeper than others: Understanding long-term mortgage arrears," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 15-27.
    19. Alexei Tchistyi, 2018. "An Equilibrium Model of Housing and Mortgage Markets with State-Contingent Lending Contracts," 2018 Meeting Papers 244, Society for Economic Dynamics.
    20. Benjamin J. Keys & Tomasz Piskorski & Amit Seru & Vincent Yao, 2014. "Mortgage Rates, Household Balance Sheets, and the Real Economy," NBER Working Papers 20561, National Bureau of Economic Research, Inc.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:64-:d:369662. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.