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Markov chain models for delinquency: Transition matrix estimation and forecasting

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  • Scott D. Grimshaw
  • William P. Alexander

Abstract

A Markov chain is a natural probability model for accounts receivable. For example, accounts that are ‘current’ this month have a probability of moving next month into ‘current’, ‘delinquent’ or ‘paid‐off’ states. If the transition matrix of the Markov chain were known, forecasts could be formed for future months for each state. This paper applies a Markov chain model to subprime loans that appear neither homogeneous nor stationary. Innovative estimation methods for the transition matrix are proposed. Bayes and empirical Bayes estimators are derived where the population is divided into segments or subpopulations whose transition matrices differ in some, but not all entries. Loan‐level models for key transition matrix entries can be constructed where loan‐level covariates capture the non‐stationarity of the transition matrix. Prediction is illustrated on a $7 billion portfolio of subprime fixed first mortgages and the forecasts show good agreement with actual balances in the delinquency states. Copyright © 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmbi:v:27:y:2011:i:3:p:267-279
    DOI: 10.1002/asmb.827
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    Citations

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    Cited by:

    1. Puneet Pasricha & Dharmaraja Selvamuthu & Guglielmo D’Amico & Raimondo Manca, 2020. "Portfolio optimization of credit risky bonds: a semi-Markov process approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-14, December.
    2. Gaffney, Edward & Kelly, Robert & McCann, Fergal, 2014. "A transitions-based framework for estimating expected credit losses," Research Technical Papers 16/RT/14, Central Bank of Ireland.
    3. Arno Botha & Conrad Beyers & Pieter de Villiers, 2020. "The loss optimisation of loan recovery decision times using forecast cash flows," Papers 2010.05601, arXiv.org.
    4. Pasanisi, Alberto & Fu, Shuai & Bousquet, Nicolas, 2012. "Estimating discrete Markov models from various incomplete data schemes," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2609-2625.
    5. Zhixin Liu & Ping He & Bo Chen, 2019. "A Markov decision model for consumer term-loan collections," Review of Quantitative Finance and Accounting, Springer, vol. 52(4), pages 1043-1064, May.
    6. 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.
    7. 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.
    8. 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.
    9. Johnson, Michael P. & Solak, Senay & Drew, Rachel Bogardus & Keisler, Jeffrey, 2013. "Property value impacts of foreclosed housing acquisitions under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 47(4), pages 292-308.
    10. Vilislav Boutchaktchiev, 2018. "A Markov Chain Model for the Cure Rate of Non-Performing Loans," Papers 1805.11804, arXiv.org, revised Jun 2018.
    11. He, Ping & Hua, Zhongsheng & Liu, Zhixin, 2015. "A quantification method for the collection effect on consumer term loans," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 17-26.

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