Estimation and Comparison of "Value atRisk" of crude oil prices using HistoricalSimulation, GARCH and GPD methods

Abstract

My results indicate that conditional Extreme Value Theory and Filtered Historical Simulation procedures offer a major improvement over the traditional methods (non-parametric and parametric). Such models produce a VaR which reacts to the change of volatility dynamics. The general observation would be that for the 95% VaR measures the EVT-based models and the others traditional models produce equally good VaR estimates (except for theNormal method at the 95% confidence level). As expected, the unconditional normal distribution performs poorly and is rejected for all confidence levels. This model underestimates the true VaR and is not appropriate for extreme quantiles estimation. The conditional normal approach can not be rejected for the 95% confidence level but its performance deteriorates at higher quantiles. This approach, while it responds to changing volatility, tends to be violated rather more often, because it fails to fully account to the leptokurtosis of the residuals. This model tends to underestimate the true risk. Such result constitutes an alarm to any market participants that use the models based on normality assumption. Conditional GPD model yields abetter VaR estimation than provided by the GDP. The number of days when VaR is higher than actual price change is close to the excepted one. Furthermore, Conditional GPD methodology provides a more flexible VaR quantification, which accounts of volatility dynamics. Further-more, The GARCH-GED/sGED model may give equally good result for left tail, as well as thetwo combined approach. Finally my results confirm the importance of filtering process for thes uccess of standard approaches such as EVT and Historical Simulation.