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Is it possible to forecast VaR on oil using GARCHs models ?

Energy products volatility involves specialists into the estimations of Value-at-Risk. Various models, derived from the GARCH model, are used independently, or not: The Exponential GARCH (EGARCH), Skewed Asymmetric Power ARCH (APARCH), Hyperbolic GARCH (HYGARCH) and Fractionally integrated GARCH (FIAPARCH). Our analysis focuses on the performance of a market yield estimation and the Value-at-Risk projection. This latter is evaluated compared to the closing prices observations from 1987 and December 2019, related to the WTI and to the Brent.

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Firstly, the following concepts are determined in order to establish the analysis methodology:

The ARCH, GARCH, APARCH, FIAPARCH, HYGARCH models and the Value-at-Risk; the statistical precision test on the Value-at-Risk projections (Kupiec, de Eugle et Manganelli) and the long memory tests of the volatility (Geweke and Porter-Hudak log-periodogram regression, Robison semi-parametric Gaussian and the Lo & MacKinlay Variance relation). Then, a descriptive data study on the whole observations highlights a non-Gaussian distribution regarding the closing prices, the absence of white noise and the auto-correlated squares. The stationary test of the time series is positive while the unit root hypothesis is rebutted. The R/S Lo test highlights a long-term memory, confirmed by the GPH and GDP test at 95%. Following the different GARCH models in the sample, the t-student asymmetric distribution seems more productive.Moreover, the tests of FIGARCH, FIAPARCH, HYGARCH models using the Student distribution, the asymmetric Student law and the GARCH model with Gaussian distribution led in the sample highlights the t-Student asymmetric distribution performance, comparatively to the classic distribution. Furthermore, intra and extra-sample, the FIAPARCH model proves to be the closest to the Value-at-Risk.

When certain existing models proved to be truly performant on a given day (APARCH), or only took consideration of some parameters (like the distribution model), our analysis demonstrates an experimental performance of the FIARPARCH using the asymmetric distribution of the t-Student law, considering the thick distribution tail and the long-term memory, for a high horizon (above 10 days). These results are in adequacy with the financial institutions requirements.

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