Nonparametric Estimation for Non-Homogeneous Semi-Markov Processes: An Application to Credit Risk
AbstractWe 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 InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-024/2.
Date of creation: 08 Mar 2006
Date of revision: 27 Mar 2006
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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 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-04-22 (All new papers)
- NEP-ECM-2006-04-22 (Econometrics)
- NEP-FIN-2006-04-22 (Finance)
- NEP-RMG-2006-04-22 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- Andre A. Monteiro, 2009. "The econometrics of randomly spaced financial data: a survey," Statistics and Econometrics Working Papers ws097924, Universidad Carlos III, Departamento de Estadística y Econometría.
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