在本篇文章中，我們採用長期記憶模型來估計S&P500、Nasdaq100和Dow Jones Industrial Index三個股票指數期貨的日收盤價的風險值。為了更準確地計算風險值，本文採用常態分配、t分配以及偏斜t分配來做模型估計以及風險值之計算。有鑒於大多數探討風險值的文獻只考慮買入部位的風險，本研究除了估計買入部位的風險值，也估計放空部位的風險值，以期更能全面性地估算風險。實證結果顯示，ARFIMA-FIGARCH模型配合偏斜t分配較其他兩種分配更能精確地估算樣本內的風險值。基於ARFIMA-FIGARCH模型配合偏斜t分配在樣本內風險值計算的優異表現，我們利用此模型搭配來實際求算樣本外風險值。結果如同樣本內風險值一般，ARFIMA-FIGARCH模型配合偏斜t分配在樣本外也有相當好的風險預測能力。

In this thesis, we estimate Value-at-Risk (VaR) for daily closing price of three stock index futures contracts, S&P500, Nasdaq100, and Dow Jones, using the double long memory models. Due to the existence of a long-term persistence characterized in our data, the ARFIMA-FIGARCH models are used to compute the VaR. In order to investigate better, three kinds of density distributions, normal, Student-t, and skewed Student-t distributions, are used for estimating models and computing the VaR. In addition to the VaR for the long trading positions which most researches focus on to date, the VaR for the short trading positions are calculated as well in this study. From the empirical results we show that for the three stock index futures, the ARFIMA-FIGARCH models with skewed Student-t distribution perform better in computing in-sample VaR both in long and short trading positions than symmetric models and has a quite excellent performance in forecasting out-of-sample VaR as well.

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