Analytic Approximations To VaR In a GARCH Framework

The forecasting ability of GARCH models has been the subject of numerous research

papers. However, most papers consider only point variance forecasts. This paper shows how

approximate predictive distributions for future cumulative returns can be constructed using

the first four conditional moments of the returns generated by a GARCH process. An

important application of these distributions is for Value-at-Risk (VaR) calculations. In fact

simulations are not needed to evaluate the VaR of a portfolio with GARCH process returns

over any time horizon. Our analytic formulae for the moments of cumulative returns

distributions may be used instead. The empirical performance of this quasi-analytical method

of computing VaR is assessed.