Value-at-Risk Performance of Stochastic and ARCH Type Volatility Models: New Evidence

This paper evaluates the effectiveness of selected volatility models in forecasting Value-at-Risk (VaR) for 1-day and 10-day horizons. The latter is the actual reporting horizon required by the Basel Committee on Banking Supervision, but not considered in existing studies. The autoregressive stochastic volatility (Taylor, 1982) is found to be less effective than simpler ARCH type models such as the RiskMetrics and GARCH models. 10-day VaR forecasting is shown to be a difficult task by construction. Various schemes to construct this forecast are proposed and evaluated. In particular, a scheme that uses return time series of 10-day intervals transforms the 10-day VaR forecasting into 1-step-ahead forecasting and shows considerable improvement in accuracy although the result might be due to inclusion of the 1987 crash in training the models. ∗Department of Accounting and Finance, Monash University, Australia