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Nonparametric Estimation for Non-Homogeneous Semi-Markov Processes: An Application to Credit Risk

Author

Listed:
  • Andre Monteiro

    (Vrije Universiteit Amsterdam)

  • Georgi V. Smirnov

    (University of Porto)

  • Andre Lucas

    (Vrije Universiteit Amsterdam)

Abstract

We propose procedures for estimating the time-dependent transition matrices for the general class of finite nonhomogeneous continuous-time semi-Markov processes. We prove the existence and uniqueness of solutions for the system of Volterra integral equations defining the transition matrices, therefore showing that these empirical transition probabilities can be estimated from window censored event-history data. An implementation of the method is presented based on nonparametric estimators of the hazard rate functions in the general and separable cases. A Monte Carlo study is performed to assess the small sample behavior of the resulting estimators. We use these new estimators for dealing with a central issue in credit risk. We consider the problem of obtaining estimates of the historical corporate default and rating migration probabilities using a dataset on credit ratings from Standard & Poor's.

Suggested Citation

  • Andre Monteiro & Georgi V. Smirnov & Andre Lucas, 2006. "Nonparametric Estimation for Non-Homogeneous Semi-Markov Processes: An Application to Credit Risk," Tinbergen Institute Discussion Papers 06-024/2, Tinbergen Institute, revised 27 Mar 2006.
    • Handle: RePEc:tin:wpaper:20060024
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    References listed on IDEAS

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    1. Janssen, J. & de Dominicis, R., 1984. "Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 157-165, July.
    2. Brahim Ouhbi & Nikolaos Limnios, 1999. "Nonparametric Estimation for Semi-Markov Processes Based on its Hazard Rate Functions," Statistical Inference for Stochastic Processes, Springer, vol. 2(2), pages 151-173, May.
    3. Koopman, Siem Jan & Lucas, Andre & Monteiro, Andre, 2008. "The multi-state latent factor intensity model for credit rating transitions," Journal of Econometrics, Elsevier, vol. 142(1), pages 399-424, January.
    4. 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.
    5. 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.
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    Cited by:

    1. Koopman, Siem Jan & Lucas, Andre & Monteiro, Andre, 2008. "The multi-state latent factor intensity model for credit rating transitions," Journal of Econometrics, Elsevier, vol. 142(1), pages 399-424, January.
    2. Sabine Zinn, 2014. "The MicSim Package of R: An Entry-Level Toolkit for Continuous-Time Microsimulation," International Journal of Microsimulation, International Microsimulation Association, vol. 7(3), pages 3-32.
    3. Qi Cao & Erik Buskens & Talitha Feenstra & Tiny Jaarsma & Hans Hillege & Douwe Postmus, 2016. "Continuous-Time Semi-Markov Models in Health Economic Decision Making," Medical Decision Making, , vol. 36(1), pages 59-71, January.
    4. Monteiro, André A., 2009. "The econometrics of randomly spaced financial data: a survey," DES - Working Papers. Statistics and Econometrics. WS ws097924, Universidad Carlos III de Madrid. Departamento de Estadística.

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    More about this item

    Keywords

    Nonhomogeneous semi-Markov processes; transition matrix; Volterra integral equations; separability; credit risk;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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