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

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Author Info
Andre Monteiro () (Vrije Universiteit Amsterdam)
Georgi V. Smirnov () (University of Porto)
Andre Lucas () (Vrije Universiteit Amsterdam)

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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.

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Publisher 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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Web page: http://www.tinbergen.nl/

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

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data
C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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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. [Downloadable!] (restricted)
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