Value-at-Risk approach is being increasingly used in the risk management industry. And the EWMA(exponentially weighted moving average) model and the historical simulation are most widely used to estimate VaR due to the simplicity of implementing. But these two approaches have some critical problems. The EWMA model does not well account for the fat tails and non-linearity due to its normality assumption. The historical simulation does not allow for the time varying volatility because it applies the same weight to every historical return.
So the new VaR methods such as the Hull & White model and the hybrid approach are proposed recently. These two methods are designed to overcome the shortcomings of the EWMA and historical simulation by combining two approaches.
In this paper four different VaR approaches, the EWMA, the historical simulation, the Hull and White model and the hybrid approach is back-tested on six portfolios invested over five years. Empirical test shows that the combined methods, the Hull and White and the hybrid, make a little improvement in the precision of VaR forecast. But these two methods still have the problem that estimate VaR inaccurately in the extreme event. So it is necessary to use the supplementary techniques such as the stress testing and the scenario analysis for the proper risk management.
