Improving accuracy and precision of value-at-risk forecasts

Value-at-risk (VaR) models are intended to measure the relationships among many uncertainties. This paper focuses on ways to improve accuracy and precision of VaR forecasts. Unlike most previous studies that are only concerned with the tail behavior of predicted returns, this paper proposes a new methodology to incorporate a number of sources of resampling uncertainty in VaR forecasts. The study illustrates the methodology using the filtered historical simulation model. This new approach employs both the bootstrap and its close alternative, the jackknife method. In particular, the delete-d jackknife is adopted as it is specifically designed for non-smooth statistics such as the quantile. The delete-d jackknife has the attraction of producing unbiased statistics since it resamples from the original distribution rather than from the empirical distribution as in the bootstrap. Applied to five return series, the proposed technique is shown to provide more accurate VaR forecasts than the other eight models in terms of statistical loss measures. In addition, they provide reasonable improvement over the other eight models in terms of statistical and regulatory tests. In particular, considerable improvement is achieved in terms of forecast precision.

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