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


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  • Andre Monteiro

    (Vrije Universiteit Amsterdam)

  • Georgi V. Smirnov

    (University of Porto)

  • Andre Lucas

    (Vrije Universiteit Amsterdam)


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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-024/2.

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Date of creation: 08 Mar 2006
Date of revision: 27 Mar 2006
Handle: RePEc:dgr:uvatin:20060024

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Keywords: Nonhomogeneous semi-Markov processes; transition matrix; Volterra integral equations; separability; credit risk;

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  1. 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.
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Cited by:
  1. Siem Jan Koopman & André Lucas & André Monteiro, 2005. "The Multi-State Latent Factor Intensity Model for Credit Rating Transitions," Tinbergen Institute Discussion Papers 05-071/4, Tinbergen Institute, revised 04 Jul 2005.
  2. Andre A. Monteiro, 2009. "The econometrics of randomly spaced financial data: a survey," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws097924, Universidad Carlos III, Departamento de Estadística y Econometría.


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