IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v12y2010i2d10.1007_s11009-009-9142-6.html
   My bibliography  Save this article

Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models

Author

Listed:
  • Guglielmo D’Amico

    (Universitá “G. D’Annunzio”)

  • Jacques Janssen

    (Université de Bretagne Occidentale)

  • Raimondo Manca

    (Universitá “La Sapienza” di Roma)

Abstract

In this paper we show how it is possible to construct an efficient Migration models in the study of credit risk problems presented in Jarrow et al. (Rev Financ Stud 10:481–523, 1997) with Markov environment. Recently it was introduced the semi-Markov process in the migration models (D’Amico et al. Decis Econ Finan 28:79–93, 2005a). The introduction of semi-Markov processes permits to overtake some of the Markov constraints given by the dependence of transition probabilities on the duration into a rating category. In this paper, it is shown how it is possible to take into account simultaneously backward and forward processes at beginning and at the end of the time in which the credit risk model is observed. With such a generalization, it is possible to consider what happens inside the time after the first transition and before the last transition where the problem is studied. This paper generalizes other papers presented before. The model is presented in a discrete time environment.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9142-6
    DOI: 10.1007/s11009-009-9142-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-009-9142-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-009-9142-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guglielmo D'Amico & Jacques Janssen & Raimondo Manca, 2009. "The Dynamic Behaviour of Non-Homogeneous Single-Unireducible Markov and Semi-Markov Chains," Lecture Notes in Economics and Mathematical Systems, in: Ahmad K. Naimzada & Silvana Stefani & Anna Torriero (ed.), Networks, Topology and Dynamics, pages 195-211, Springer.
    2. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
    3. 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..
    4. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
    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. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2011. "Discrete Time Non-Homogeneous Semi-Markov Reliability Transition Credit Risk Models and the Default Distribution Functions," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 465-481, November.
    2. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2011. "Bivariate Semi-Markov Process for Counterparty Credit Risk," Papers 1112.0226, arXiv.org, revised Oct 2012.
    3. Brecht Verbeken & Marie-Anne Guerry, 2021. "Discrete Time Hybrid Semi-Markov Models in Manpower Planning," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    4. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2011. "A customer’s utility measure based on the reliability of multi-state systems," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(1), pages 1-20, May.
    5. Hunt, Julien & Devolder, Pierre, 2011. "Semi Markov regime switching interest rate models and minimal entropy measure," LIDAM Discussion Papers ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Guglielmo D’Amico & Thomas Gkelsinis, 2024. "On a Mixed Transient–Asymptotic Result for the Sequential Interval Reliability for Semi-Markov Chains," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    8. Vlad Stefan Barbu & Guglielmo D’Amico & Thomas Gkelsinis, 2021. "Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    9. Guglielmo D’Amico & Montserrat Guillen & Raimondo Manca, 2012. "Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance," Working Papers XREAP2012-05, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2012.
    10. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.
    11. Hunt, Julien & Devolder, Pierre, 2011. "Semi-Markov regime switching interest rate models and minimal entropy measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3767-3781.
    12. P.-C.G. Vassiliou, 2020. "Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    13. Guglielmo D’Amico, 2013. "A semi-Markov approach to the stock valuation problem," Annals of Finance, Springer, vol. 9(4), pages 589-610, November.
    14. 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.

    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. Trueck, Stefan & Rachev, Svetlozar T., 2008. "Rating Based Modeling of Credit Risk," Elsevier Monographs, Elsevier, edition 1, number 9780123736833.
    2. Figlewski, Stephen & Frydman, Halina & Liang, Weijian, 2012. "Modeling the effect of macroeconomic factors on corporate default and credit rating transitions," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 87-105.
    3. Valerio Vacca, 2011. "An unexpected crisis? Looking at pricing effectiveness of different banks," Temi di discussione (Economic working papers) 814, Bank of Italy, Economic Research and International Relations Area.
    4. Wozabal, David & Hochreiter, Ronald, 2012. "A coupled Markov chain approach to credit risk modeling," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 403-415.
    5. Jeffrey R. Stokes, 2023. "A nonlinear inversion procedure for modeling the effects of economic factors on credit risk migration," Review of Quantitative Finance and Accounting, Springer, vol. 61(3), pages 855-878, October.
    6. Areski Cousin & Jérôme Lelong & Tom Picard, 2023. "Rating transitions forecasting: a filtering approach," Post-Print hal-03347521, HAL.
    7. Xing, Haipeng & Sun, Ning & Chen, Ying, 2012. "Credit rating dynamics in the presence of unknown structural breaks," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 78-89.
    8. Fuertes, Ana-Maria & Kalotychou, Elena, 2007. "On sovereign credit migration: A study of alternative estimators and rating dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3448-3469, April.
    9. Michael Kalkbrener & Natalie Packham, 2024. "A Markov approach to credit rating migration conditional on economic states," Papers 2403.14868, arXiv.org.
    10. Areski Cousin & J'er^ome Lelong & Tom Picard, 2021. "Rating transitions forecasting: a filtering approach," Papers 2109.10567, arXiv.org, revised Jun 2023.
    11. Jafry, Yusuf & Schuermann, Til, 2004. "Measurement, estimation and comparison of credit migration matrices," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2603-2639, November.
    12. Biase di Giuseppe & Guglielmo D'Amico & Jacques Janssen & Raimondo Manca, 2014. "A Duration Dependent Rating Migration Model: Real Data Application and Cost of Capital Estimation," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 64(3), pages 233-245, June.
    13. Valerio Vacca, 2017. "An Unexpected Crisis? Looking at Pricing Effectiveness of Heterogeneous Banks," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 46(2), pages 171-206, July.
    14. 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.
    15. Lapshin, Viktor & Anton, Markov, 2022. "MCMC-based credit rating aggregation algorithm to tackle data insufficiency," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 68, pages 50-72.
    16. Narcisa Kadlcakova & Joerg Keplinger, 2004. "Credit Risk and Bank Lending in the Czech Republic," Working Papers 2004/06, Czech National Bank.
    17. Brian BARNARD, 2017. "Rating Migration and Bond Valuation: Decomposing Rating Migration Matrices from Market Data via Default Probability Term Structures," Expert Journal of Finance, Sprint Investify, vol. 5(1), pages 49-72.
    18. Livingston, Miles & Naranjo, Andy & Zhou, Lei, 2008. "Split bond ratings and rating migration," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1613-1624, August.
    19. Til Schuermann & Yusuf Jafry, 2003. "Measurement and Estimation of Credit Migration Matrices," Center for Financial Institutions Working Papers 03-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
    20. Brian BARNARD, 2018. "Rating Migration and Bond Valuation: Ahistorical Interest Rate and Default Probability Term Structures," Expert Journal of Finance, Sprint Investify, vol. 6(1), pages 16-30.

    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:spr:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9142-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.