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Estimating asset correlations from stock prices or default rates: which method is superior?

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Author Info
Düllmann, Klaus
Kunisch, Michael
Küll, Jonathan
Abstract

This paper sets out to help explain why estimates of asset correlations based on equity prices tend to be considerably higher than estimates based on default rates. Resolving this empirical puzzle is highly important because, firstly, asset correlations are a key driver of credit risk and, secondly, both data sources are widely used to calibrate risk models of financial institutions. By means of a simulation study, we explore the hypothesis that differences in the correlation estimates are due to a substantial downward bias characteristic of estimates based on default rates. Our results suggest that correlation estimates from equity returns are more efficient than those from default rates. This finding still holds if the model is misspecified such that asset correlations follow a Vasicek process which affects foremost the estimates from equity returns. The results lend support for the hypothesis that the downward bias of default-rate based estimates is an important although not the only factor to explain the differences in correlation estimates. Furthermore, our results help to quantify the estimation error of asset correlations dependent on the risk characteristics of the underlying data base. -- Abhängigkeiten zwischen den Ausfallereignissen von Kreditnehmern sind ein wesentlicher Treiber des Kreditrisikos in Kreditportfolien. Solche Abhängigkeiten werden gewöhnlich durch Asset-Korrelationen zwischen Firmenwertänderungen gemessen. Da Firmenwertänderungen nicht beobachtbar sind, werden diese Korrelationen oft aus Zeitreihen von Aktienrenditen oder aus historischen Ausfallraten geschätzt. Beide Ansätze haben in der Forschung zu erheblich unterschiedlichen Ergebnissen geführt. Da empirische Untersuchungen unterschiedliche Stichproben verwenden, ist es bisher nicht möglich gewesen, diese Unterschiede zu erklären. In diesem Arbeitspapier untersuchen wir die Hypothese, dass die beobachteten Unterschiede sich aus unterschiedlichen statistischen Eigenschaften der Schätzmethoden erklären, die jeweils bei der Schätzung aus Aktienrenditen und aus Ausfallraten verwendet werden. Eine Bestätigung der Hypothese kann Kreditrisikomanagern eine Hilfestellung geben bei der Auswahl der geeigneten Datenquelle für die Schätzung von Asset-Korrelationen. Um diese Hypothese zu bestätigen, verwenden wir eine umfassende Simulationsstudie mit einer Vielzahl von Risikoparametern und unterschiedlich großen Kreditportfolien. Wir beobachten, dass die statistischen Methoden eine wichtige Rolle bei der Erklärung der Unterschiede zwischen den Schätzwerten von Asset-Korrelationen basierend auf Aktienrenditen oder Ausfallraten spielen. Es ist grundsätzlich empfehlenswert, Aktienrenditen für die Schätzung zu verwenden, da die statistischen Fehler in diesem Fall geringer sind. Diese Beobachtung gilt auch, falls das Modell insofern fehlspezifiziert ist, als die Asset-Korrelationen nicht wie im Model unterstellt über die Zeit konstant sind, sondern einem stochastischen Prozess folgen.

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 2: Banking and Financial Studies with number 2008,04.

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Date of creation: 2008
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Handle: RePEc:zbw:bubdp2:7314

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Related research
Keywords: Asset correlation; single risk factor model; small sample properties; structural model; Basel II;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Mortgages

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    Other versions:
  5. Düllmann, Klaus & Scheicher, Martin & Schmieder, Christian, 2007. "Asset correlations and credit portfolio risk: an empirical analysis," Discussion Paper Series 2: Banking and Financial Studies 2007,13, Deutsche Bundesbank, Research Centre. [Downloadable!]
  6. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. " Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-25, July. [Downloadable!] (restricted)
  7. Michael B. Gordy, 2002. "A risk-factor model foundation for ratings-based bank capital rules," Finance and Economics Discussion Series 2002-55, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  9. 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. [Downloadable!] (restricted)
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  10. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December. [Downloadable!] (restricted)
  11. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management. [Downloadable!]
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  13. 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, vol. 28(4), pages 773-788, April. [Downloadable!] (restricted)
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