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Confidence sets for asset correlations in portfolio credit risk

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  • Carlos Castro

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    Abstract

    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 asset correlation, 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 by the Basel II framework, better represents the historical default data. ii) importance of unobserved factors 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 asset correlations show that the Basel recommended bounds, for this parameter, undermine the level of systemic risk. Resumen: Las correlaciones entre los activos de un portafolio crediticio, son parámetros de suma importancia para 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 principalmente en la estimación puntual de los parámetros, desconociendo la incertidumbre alrededor del estimador puntual. En este articulo utilizamos métodos bayesianos para estimar el modelo factorial dinámico para riesgo de quiebra utilizando datos de calificaciones de riesgo sobre un portafolio crediticio (McNeil et al., 2005; McNeil andWendin, 2007). Los métodos bayesianos nos permiten: incorporar formalmente la información experta en el proceso de estimación de las correlaciones mediante la distribución a priori y obtener intervalos de confianza alrededor de los parámetros de interés. Los resultados indican: i) un modelo de dos factores se ajusta mejor a la información histórica 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 Basilea subestiman el riesgo sistémico.

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    Article provided by UNIVERSIDAD DEL ROSARIO in its journal REVISTA DE ECONOMÍA DEL ROSARIO.

    Volume (Year): (2012)
    Issue (Month): ()
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    Handle: RePEc:col:000151:009911

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    1. 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.
    2. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
    3. 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 449-70, May.
    4. redakce, 2012. "n/a," Ekonomika a Management, University of Economics, Prague, vol. 2012(1), pages 72-73.
    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. Koopman, Siem Jan & Kräussl, Roman & Lucas, André & Monteiro, André B., 2009. "Credit cycles and macro fundamentals," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 42-54, January.
    7. 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.
    8. 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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