Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL

ICMA Centre Discussion Papers in Finance DP 2011-08

28 Pages Posted: 13 May 2011

See all articles by Carol Alexander

Carol Alexander

University of Sussex Business School

Emese Lazar

University of Reading - ICMA Centre

Silvia Stanescu

University of Kent - Kent Business School

Date Written: May 5, 2011

Abstract

It is widely accepted that some of the most accurate predictions of aggregated asset returns are based on an appropriately specified GARCH process. As the forecast horizon is greater than the frequency of the GARCH model, such predictions either require time-consuming simulations or they can be approximated using a recent development in the GARCH literature, viz. analytic conditional moment formulae for GARCH aggregated returns. We demonstrate that this methodology yields robust and rapid calculations of the Value-at-Risk (VaR) generated by a GARCH process. Our extensive empirical study applies Edgeworth and Cornish-Fisher expansions and Johnson SU distributions, combined with normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets; it validates the accuracy of the analytic approximations to GARCH aggregated returns and derives GARCH VaR estimates that are shown to be highly accurate over multiple horizons and significance levels.

Keywords: GARCH, higher conditional moments, approximate predictive distributions, Value-at-Risk, Conditional VaR, Expected tail loss, Expected shortfall

JEL Classification: C53, G17

Suggested Citation

Alexander, Carol and Lazar, Emese and Stanescu, Silvia, Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL (May 5, 2011). ICMA Centre Discussion Papers in Finance DP 2011-08. Available at SSRN: https://ssrn.com/abstract=1832386 or http://dx.doi.org/10.2139/ssrn.1832386

Carol Alexander (Contact Author)

University of Sussex Business School ( email )

Falmer, Brighton BN1 9SL
United Kingdom

HOME PAGE: http://www.carolalexander.org

Emese Lazar

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom
+44 (0)1183 786675 (Phone)
+44 (0)1189 314741 (Fax)

Silvia Stanescu

University of Kent - Kent Business School ( email )

Canterbury, Kent CT2 7PE
United Kingdom

Register to save articles to
your library

Register

Paper statistics

Downloads
119
Abstract Views
801
rank
231,456
PlumX Metrics