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

32 Pages Posted: 8 Jul 2016

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: July 1, 2016

Abstract

In the recent literature, methods from extreme value theory (EVT) have frequently been applied to 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 large standard errors of the point estimates in these methods, as only a fraction of the data set is used. Thus, we comprehensively study the impact of model risk on EVT methods when determining the value-at-risk and expected shortfall. We distinguish between first-order effects of model risk, which consist of misspecification and estimation risk, and second-order effects of model risk, which refer to the dispersion of risk measure estimates, and show that EVT methods are less prone to first-order effects. However, they show a greater sensitivity toward second order effects. We find that this can lead to severe value-at-risk and expected shortfall underestimations and should be reflected in regulatory capital models.

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 (July 1, 2016). Journal of Risk, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2804937

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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