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A Markov regenerative process with recurrence time and its application

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  • Puneet Pasricha

    (Indian Institute of Technology Delhi)

  • Dharmaraja Selvamuthu

    (Indian Institute of Technology Delhi)

Abstract

This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times, in particular, forward and backward recurrence processes. We obtain the transient solution of the process in the form of a generalized Markov renewal equation. A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model. To model the credit rating dynamics to demonstrate its applicability, we apply the proposed stochastic process to Standard and Poor’s rating agency’s data. Further, statistical tests confirm that the proposed model captures the rating dynamics better than the existing models, and the inclusion of recurrence times significantly impacts the transition probabilities.

Suggested Citation

  • Puneet Pasricha & Dharmaraja Selvamuthu, 2021. "A Markov regenerative process with recurrence time and its application," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-22, December.
    • Handle: RePEc:spr:fininn:v:7:y:2021:i:1:d:10.1186_s40854-021-00255-z
    DOI: 10.1186/s40854-021-00255-z
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    References listed on IDEAS

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    1. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
    2. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    3. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.
    4. Haomin Wang & Gang Kou & Yi Peng, 2021. "Multi-class misclassification cost matrix for credit ratings in peer-to-peer lending," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(4), pages 923-934, March.
    5. Puneet Pasricha & Dharmaraja Selvamuthu & Viswanathan Arunachalam, 2017. "Markov regenerative credit rating model," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 18(3), pages 311-325, May.
    6. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2016. "Downward migration credit risk problem: a non-homogeneous backward semi-Markov reliability approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 393-401, March.
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    8. Christensen, Jens H.E. & Hansen, Ernst & Lando, David, 2004. "Confidence sets for continuous-time rating transition probabilities," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2575-2602, November.
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    Cited by:

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