Parameter Estimation, Bias Correction and Uncertainty Quantification in the Vasicek Credit Portfolio Model

29 Pages Posted: 8 Aug 2019

See all articles by Marius Pfeuffer

Marius Pfeuffer

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg

Maximilian Nagl

University of Regensburg

Matthias Fischer

Friedrich-Alexander-Universität Erlangen-Nürnberg

Daniel Roesch

University of Regensburg

Date Written: August 7, 2019

Abstract

This paper is devoted to the parameterization of correlations in the Vasicek credit portfolio model. First, we analytically approximate standard errors for value-at-risk and expected shortfall based on the standard errors of intra-cohort correlations. Second, we introduce a novel copula-based maximum likelihood estimator for inter-cohort correlations and derive an analytical expression of the standard errors. Our new approach enhances current methods in terms of both computing time and, most importantly, direct uncertainty quantification. Both contributions can be used to quantify a margin of conservatism, which is required by regulators. Third, we illustrate powerful procedures that reduce the well-known bias of current estimators, showing their favorable properties. Further, an open-source implementation of all estimators in the novel R package AssetCorr is provided and selected estimators are applied to Moody’s Default & Recovery Database.

Keywords: asset correlation, Vasicek model, delta method, copula, bias correction, margin of conservatism

Suggested Citation

Pfeuffer, Marius and Nagl, Maximilian and Fischer, Matthias and Roesch, Daniel, Parameter Estimation, Bias Correction and Uncertainty Quantification in the Vasicek Credit Portfolio Model (August 7, 2019). Journal of Risk 22(4), 1–29, 2020, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3433211

Marius Pfeuffer

University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg ( email )

Fachbereich Rechtswissenschaft
Schillerstr. 1
Erlangen, DE 91054
Germany

Maximilian Nagl (Contact Author)

University of Regensburg ( email )

93040 Regensburg
D-93040 Regensburg, 93053
Germany

Matthias Fischer

Friedrich-Alexander-Universität Erlangen-Nürnberg ( email )

Erlangen-Nürnberg
Lange Gasse 20,
Nurnberg
Germany

Daniel Roesch

University of Regensburg ( email )

Chair of Statistics and Risk Management
Faculty of Business, Economics and BIS
Regensburg, 93040
Germany

HOME PAGE: http://www-risk.ur.de/

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