The Role of Model Risk in Extreme Value Theory for Capital Adequacy

Journal of Risk 18(6), 2016, 39-70

Posted: 28 Feb 2018

See all articles by Ralf Kellner

Ralf Kellner

Saarland University

Daniel Roesch

University of Regensburg

Harald (Harry) Scheule

University of Technology Sydney (UTS) - School of Finance and Economics; Financial Research Network

Multiple version iconThere are 2 versions of this paper

Date Written: 2016

Abstract

In the recent literature, methods from extreme value theory (EVT) have frequently been applied for the estimation of tail risk measures. While previous analyses show that EVT methods often lead to accurate estimates for risk measures, a potential drawback lies in high standard errors of point estimates of these methods as only a fraction of the data set is used. Thus, the aim of this paper is to comprehensively study the impact of model risk on EVT methods when determining the Value-at-Risk and Expected Shortfall. We distinguish between misspecification, estimation and prediction risk and show that methods from extreme value theory are less prone to misspecification and estimation risk, however, they exhibit a higher sensitivity towards prediction risk. We find that this can lead to more severe Value-at-Risk and Expected Shortfall underestimations than for traditional estimation methods in extreme cases. Hence, we show how sources of model risk should be taken into account for the quantification of capital requirements, in order to provide sufficient capital levels in the presence of model risk.

Keywords: Extreme Value Theory, Model Risk, Capital Requirements, Value-at-Risk, Expected Shortfall

Suggested Citation

Kellner, Ralf and Roesch, Daniel and Scheule, Harald, The Role of Model Risk in Extreme Value Theory for Capital Adequacy (2016). Journal of Risk 18(6), 2016, 39-70, Available at SSRN: https://ssrn.com/abstract=3126282

Ralf Kellner (Contact Author)

Saarland University ( email )

Stadtwald
Saarbrucken, Saarland D-66123
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/

Harald Scheule

University of Technology Sydney (UTS) - School of Finance and Economics ( email )

P.O. Box 123
Broadway, NSW 2007
Australia

HOME PAGE: http://https://www.uts.edu.au/staff/harald.scheule

Financial Research Network ( email )

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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