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A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk

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  • Siem Jan Koopman

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • André Lucas

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Robert Daniels

    ()
    (De Nederlandsche Bank, Amsterdam)

Abstract

We model 1981–2002 annual US default frequencies for a panel of firms in different rating and age classes. The data is decomposed into a systematic and firm-specific risk component, where the systematic component reflects the general economic conditions and default climate. We have to cope with (i) the shared exposure of each age cohort and rating class to the same systematic risk factor; (ii) strongly non-Gaussian features of the individual time series; (iii) possible dynamics of an unobserved common risk factor; (iv) changing default probabilities over the age of the rating, and (v) missing observations. We propose a non-Gaussian multivariate state space model that deals with all of this issues simultaneously. The model is estimated using importance sampling techniques that have been modified in a multivariate setting. This multivariate approach has significant advantages in terms of parameter stability and convergence of the importance sampler.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-060/4.

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Date of creation: 13 Jun 2005
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Handle: RePEc:dgr:uvatin:20050060

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

Related research

Keywords: credit risk; multivariate unobserved component models; importance sampling; non-Gaussian state space models;

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References

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  1. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  2. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  3. Altman, Edward I, 1989. " Measuring Corporate Bond Mortality and Performance," Journal of Finance, American Finance Association, American Finance Association, vol. 44(4), pages 909-22, September.
  4. Koopman, Siem Jan & Lucas, Andre & Klaassen, Pieter, 2005. "Empirical credit cycles and capital buffer formation," Journal of Banking & Finance, Elsevier, Elsevier, vol. 29(12), pages 3159-3179, December.
  5. Anil Bangia & Francis X. Diebold & Til Schuermann, 2000. "Ratings Migration and the Business Cycle, With Application to Credit Portfolio Stress Testing," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 00-26, Wharton School Center for Financial Institutions, University of Pennsylvania.
  6. Siem Jan Koopman & Andr� Lucas, 2003. "Business and Default Cycles for Credit Risk," Tinbergen Institute Discussion Papers, Tinbergen Institute 03-062/2, Tinbergen Institute, revised 09 Jan 2003.
  7. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
  8. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  9. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198523543, October.
  10. Linda Allen & Anthony Saunders, 2003. "A survey of cyclical effects in credit risk measurement model," BIS Working Papers 126, Bank for International Settlements.
  11. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 1-19, January.
  12. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1317-39, November.
  13. Altman, Edward I. & Suggitt, Heather J., 2000. "Default rates in the syndicated bank loan market: A mortality analysis," Journal of Banking & Finance, Elsevier, Elsevier, vol. 24(1-2), pages 229-253, January.
  14. Dietsch, Michel & Petey, Joel, 2004. "Should SME exposures be treated as retail or corporate exposures? A comparative analysis of default probabilities and asset correlations in French and German SMEs," Journal of Banking & Finance, Elsevier, Elsevier, vol. 28(4), pages 773-788, April.
  15. Cowan, Adrian M. & Cowan, Charles D., 2004. "Default correlation: An empirical investigation of a subprime lender," Journal of Banking & Finance, Elsevier, Elsevier, vol. 28(4), pages 753-771, April.
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