Semiparametric GARCH Models with Long Memory Applied to Value at Risk and Expected Shortfall

52 Pages Posted: 12 Apr 2021 Last revised: 9 Aug 2021

See all articles by Sebastian Letmathe

Sebastian Letmathe

Paderborn University

Yuanhua Feng

University of Paderborn

André Uhde

University of Paderborn - Faculty of Business Administration and Economics - Department of Taxation, Accounting & Finance

Date Written: April 10, 2021

Abstract

In this paper new semiparametric GARCH models with long memory are introduced. The estimation of the nonparametric scale function is carried out by an adapted version of the SEMIFAR algorithm (Beran et al., 2002). Recurring on the revised recommendations by the Basel Committee to measure market risk in the banks' trading books (Basel Committee on Banking Supervision, 2013), the semi- parametric GARCH models are applied to obtain rolling one-step ahead forecasts for the Value at Risk (VaR) and Expected Shortfall (ES) for market risk assets. In addition, standard regulatory traffic light tests (Basel Committee on Banking Supervision, 1996) and a newly introduced traffic light test for the ES are carried out for all models. The practical relevance of our proposal is demonstrated by a comparative study. Our results indicate that semiparametric long memory GARCH models are an attractive alternative to their conventional, parametric counterparts.

Keywords: semiparametric, long memory, GARCH models, forecasting, Value at Risk, Expected Shortfall, traffic light test, Basel Committee on Banking Supervision

JEL Classification: C14, C51, C52, G17, G32

Suggested Citation

Letmathe, Sebastian and Feng, Yuanhua and Uhde, André, Semiparametric GARCH Models with Long Memory Applied to Value at Risk and Expected Shortfall (April 10, 2021). Available at SSRN: https://ssrn.com/abstract=3823895 or http://dx.doi.org/10.2139/ssrn.3823895

Sebastian Letmathe (Contact Author)

Paderborn University ( email )

Warburger Str. 100
Paderborn, 33098
Germany

Yuanhua Feng

University of Paderborn ( email )

Warburger Str. 100
Paderborn, D-33098
Germany

André Uhde

University of Paderborn - Faculty of Business Administration and Economics - Department of Taxation, Accounting & Finance ( email )

Warburger Str. 100
D-33098 Paderborn
Germany

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