本研究選取台灣加權指數、日本Nikkei225指數、美國S&P500指數、美國道瓊工業指數、德國DAX指數、法國CAC指數、英國FTSE100指數、香港恆生HSI指數等8個股票市場加權指數做為研究標的，使用三種常見的波動度估計方法( SMA、EWMA和GARCH )搭配不同機率分配假設，比較2000年~2017年不同股市時期的風險值(VaR, value at risk)穿透率(violation rate)，探討不同股市時期應採取何種波動度估計方法和機率分配假設組合，才能提升風險值穿透率之準確性(accuracy)。研究結果顯示高信心水準下，採用EWMA搭配Laplace分配以及normal-Laplace混和分配，皆能提升風險值穿透率準確性，實證高信心水準下，使用高狹的(leptokurtic)機率分配假設能減輕「極端風險」(tail risk)。

This study proposes to use three common volatility estimation methods ( SMA, EWMA and GARCH ) ,in combination with different assumptions of probability distributions for financial asset return to estimate VaR (Value-at-Risk). We choose eight stock market index data including Taiex, Nikkei225, S&P500, Dow Jones index, DAX, CAC, FTSE and Heng Seng as research targets. The violation rate of VaR is compared in each stock market index from 2000~2017, and what kind of combination can increase the accuracy of violation rate in different stock market periods is discussed in this study. Under high confidence level, using EWMA conbined with Laplace distribution and EWMA conbined with normal-Laplace distribution can outperform the accuracy of violation rate in most of stock market periods. We demonstrate that using leptokurtic probability distribution assumption for financial asset return can alleviate tail risk espeacially when α is high confidence level.

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