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Confidence sets for asset correlations in portfolio credit risk

Listed author(s):
  • Carlos Castro


Abstract:Asset correlations are of critical importance in quantifying portfolio credit risk and economic capital in financial institutions. Estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration to the uncertainty around these point estimates. In this article we use Bayesian methods to estimate a dynamic factor model for default risk using rating data (McNeil et al., 2005; McNeil and Wendin, 2007).Bayesian methods allow us to formally incorporate human judgement in the estimation of assetcorrelation, through the prior distribution and fully characterize a confidence set for the correlations.Results indicate: i) a two factor model rather than the one factor model, as proposed bythe Basel II framework, better represents the historical default data. ii) importance of unobservedfactors in this type of models is reinforced and point out that the levels of the implied asset correlations critically depend on the latent state variable used to capture the dynamics of default,as well as other assumptions on the statistical model. iii) the posterior distributions of the assetcorrelations show that the Basel recommended bounds, for this parameter, undermine the levelof systemic risk.Resumen:Las correlaciones entre los activos de un portafolio crediticio, son parámetros de suma importanciapara la estimación del riesgo crediticio y capital económico de una institución financiera.La literatura especializada en la estimación de las correlaciones entre los activos, que utiliza información de migraciones entre las calificaciones de riesgo, se ha concentrado principalmenteen la estimación puntual de los parámetros, desconociendo la incertidumbre alrededor del estimadorpuntual. En este articulo utilizamos métodos bayesianos para estimar el modelo factorialdinámico para riesgo de quiebra utilizando datos de calificaciones de riesgo sobre un portafoliocrediticio (McNeil et al., 2005; McNeil andWendin, 2007). Los métodos bayesianos nos permiten:incorporar formalmente la información experta en el proceso de estimación de las correlacionesmediante la distribución a priori y obtener intervalos de confianza alrededor de los parámetrosde interés. Los resultados indican: i) un modelo de dos factores se ajusta mejor a la informaciónhistórica de quiebras, que el modelo de un factor (recomendado en Basilea II), ii) resalta la importancia de la introducción de factores no-observables en la especificación del modelo, en particular, las propiedades estadísticas de los factores no-observables puede tener un efecto importante sobre la magnitud de las correlaciones estimadas, iii) las distribuciones a posteriori de las correlaciones entre los activos indican que los intervalos sugeridos por el documento de Basileasubestiman el riesgo sistémico.

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Volume (Year): (2012)
Issue (Month): (June)

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Handle: RePEc:col:000151:009911
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  1. Koopman, Siem Jan & Kräussl, Roman & Lucas, André, 2006. "Credit cycles and macro fundamentals," CFS Working Paper Series 2006/33, Center for Financial Studies (CFS).
  2. Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
  3. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
  4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
  5. Koopman, Siem Jan & Lucas, André, 2008. "A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 510-525.
  6. Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
  7. McNeil, Alexander J. & Wendin, Jonathan P., 2007. "Bayesian inference for generalized linear mixed models of portfolio credit risk," Journal of Empirical Finance, Elsevier, vol. 14(2), pages 131-149, March.
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