Multiple-period market risk prediction under long memory: when VaR is higher than expected

The paper aims to model multiple-period market risk forecasts under long memory persistence in market volatility.

The paper proposes volatility forecasts based on a combination of the GARCH(1,1)-model with potentially fat-tailed and skewed innovations and a long memory specification of the slowly declining influence of past volatility shocks. As the square-root-of-time rule is known to be mis-specified, the GARCH setting of Drost and Nijman is used as benchmark model. The empirical study of equity market risk is based on daily returns during the period January 1975 to December 2010. The out-of-sample accuracy of VaR predictions is studied for 5, 10, 20 and 60 trading days.

The long memory scaling approach remarkably improves VaR forecasts for the longer horizons. This result is only in part due to higher predicted risk levels. Ex post calibration to equal unconditional VaR levels illustrates that the approach also enhances efficiency in allocating VaR capital through time.

The improved VaR forecasts show that one should account for long memory when calibrating risk models.

The paper models single-period returns rather than choosing the simpler approach of modeling lower-frequency multiple-period returns for long-run volatility forecasting. The approach considers long memory in volatility and has two main advantages: it yields a consistent set of volatility predictions for various horizons and VaR forecasting accuracy is improved.