IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v17y2015i4d10.1007_s11009-015-9437-8.html
   My bibliography  Save this article

Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings

Author

Listed:
  • Guglielmo D’Amico

    (Università G. d’Annunzio)

Abstract

In this paper we consider the problem of defining rate of occurrence of failures of higher orders for a system whose states form a finite state Markov jump process. Firstly, we derive an explicit formula for evaluating the rate of occurrence of failures of higher order for the system. Secondly, we propose a nonparametric statistical estimator of this function and we discuss its asymptotic properties. The covariance matrix and the asymptotic variance are computed by using the technology of multidimensional matrices. Finally, we provide applications to the modeling of financial credit ratings.

Suggested Citation

  • Guglielmo D’Amico, 2015. "Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 929-949, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-015-9437-8
    DOI: 10.1007/s11009-015-9437-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-015-9437-8
    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/s11009-015-9437-8?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. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    2. Valérie Girardin & André Sesboüé, 2009. "Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 181-200, June.
    3. Amparo Baíllo & José Luis Fernández, 2007. "A simple Markov chain structure for the evolution of credit ratings," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(6), pages 483-492, November.
    4. Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Schechtman, Ricardo, 2013. "Default matrices: A complete measurement of banks’ consumer credit delinquency," Journal of Financial Stability, Elsevier, vol. 9(4), pages 460-474.
    2. Trueck, Stefan & Rachev, Svetlozar T., 2008. "Rating Based Modeling of Credit Risk," Elsevier Monographs, Elsevier, edition 1, number 9780123736833.
    3. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    4. 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.
    5. Ángel Beade & Manuel Rodríguez & José Santos, 2024. "Multiperiod Bankruptcy Prediction Models with Interpretable Single Models," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1357-1390, September.
    6. Georges Dionne & Geneviève Gauthier & Khemais Hammami & Mathieu Maurice & Jean‐Guy Simonato, 2010. "Default Risk in Corporate Yield Spreads," Financial Management, Financial Management Association International, vol. 39(2), pages 707-731, June.
    7. Dannenberg, Henry, 2009. "Berücksichtigung von Schätzunsicherheit bei der Kreditrisikobewertung: Vergleich des Value at Risk der Verlustverteilung des Kreditrisikos bei Verwendung von Bootstrapping und einem asymptotischen Ans," IWH Discussion Papers 3/2009, Halle Institute for Economic Research (IWH).
    8. Arnaud_de_Servigny & Norbert_Jobst, 2005. "An Empirical Analysis of Equity Default Swaps (I): Univariate Insights," International Finance 0503007, University Library of Munich, Germany.
    9. Jones, Stewart & Johnstone, David & Wilson, Roy, 2015. "An empirical evaluation of the performance of binary classifiers in the prediction of credit ratings changes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 72-85.
    10. Custodio João, Igor & Lucas, André & Schaumburg, Julia & Schwaab, Bernd, 2023. "Dynamic clustering of multivariate panel data," Journal of Econometrics, Elsevier, vol. 237(2).
    11. I. Votsi & N. Limnios, 2015. "Estimation of the intensity of the hitting time for semi-Markov chains and hidden Markov renewal chains," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 149-166, June.
    12. François Coppens & Fernando Gonzáles & Gerhard Winkler, 2007. "The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations," Working Paper Research 118, National Bank of Belgium.
    13. 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.
    14. Anisa Caja & Frédéric Planchet, 2014. "Modeling Cycle Dependence in Credit Insurance," Risks, MDPI, vol. 2(1), pages 1-15, March.
    15. Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
    16. Mogens Bladt & Michael SØrensen, 2009. "Efficient estimation of transition rates between credit ratings from observations at discrete time points," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 147-160.
    17. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    18. Dimitris Gavalas & Theodore Syriopoulos, 2014. "Bank Credit Risk Management and Migration Analysis; Conditioning Transition Matrices on the Stage of the Business Cycle," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 20(2), pages 151-166, May.
    19. Rafael Weißbach & Wladislaw Poniatowski & Walter Krämer, 2013. "Nearest neighbor hazard estimation with left-truncated duration data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 33-47, January.
    20. 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.

    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:17:y:2015:i:4:d:10.1007_s11009-015-9437-8. 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.