Modelling and Forecasting Dynamic VaR Thresholds for Risk Management and Regulation

Abstract

The paper describes alternative methods of estimating Value-at-Risk (VaR) thresholds based on two calibrated models and three conditional volatility or GARCH models. The five models of volatility are used to estimate and forecast the VaR thresholds of an equally-weighted portfolio, comprising four financial stock indexes, namely S&P500, CAC40, FTSE100 a Swiss market index (SMI). On the basis of the number of (non-)violations of the Basel Accord thresholds, the best performing model is PS-GARCH, followed closely by VARMA-AGARCH, neither of which would lead to the imposition of any penalties. The next best performing threshold forecasts are given by the Portfolio-GARCH and RiskmetricsTM-EWMA models, both of which would have a penalty of 0.5. Not surprisingly, the worst forecasts are obtained from the standard normal method based on historical variances.