Forecasting VaR using analytic higher moments for GARCH processes

a r t i c l e i n f o JEL classification: C53 G17 Keywords: GARCH Higher conditional moments Approximate predictive distributions Value-at-Risk S&P 500 Treasury bill rate Euro–US dollar exchange rate It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish– Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets , for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.