On the application of Filtering Historical Simulation to the HAR-RV for VaR forecasting

Abstract

We propose a Filtered Historical Simulation method, applied to the Heterogeneous AutoRegressive - Realized Volatility (measured on tick-by-tick data) model, to predict one-day-ahead Value at Risk. A great number of ticks are available during the trading day, but they are not present overnight. On a similar research, Realized Volatility has been re-scaled to take into account overnight returns and related volatility. We want to apply a different procedure, in order to test whether the specification of a dynamic model to the overnight returns, in particular, a GARCH model, could improve the Volatility forecasts to the aim of VaR computations. We find that the two approaches lead to similar results, but the model for 1% VaR with the GARCH specification on overnight returns allows for lower failures and performs better on the Dynamic Quantile test and Conditional Coverage test. We tested the versions of FHS-HAR-RV model on Standard and Poor’s 500 Index Futures, from January 2, 1996, to December 14, 2011 of tick-by-tick data and daily returns.