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
Date Written: May 5, 2011
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: Suggested Citation