風險價值(VaR)，它被定義為一個給定的時間範圍內利潤和
損失分佈的條件分位數。雖然蒙地卡羅模擬是評估投資組合
風險價值最有效的方法，這種方法主要的缺點在於需要大量的
計算需求。所以在本文中，我們考慮在因子模型之下的重要性
採樣。此外，我們對風險因子建模在多元常態分配和多元t分
配。在此假設之下，引用upper bound 和optimal tilting 兩
種方法來尋找新測度的最佳解。最後，比較重要性採樣和蒙地
卡羅的相對效率。我們可以看出重要性採樣顯著地比蒙地卡羅
來的更好。

Value-at-Risk (VaR), which is defined as the conditional quantile of the profit-and-loss distribution for a given time horizon. Although the Monte Carlo simulation is the most powerful method to evaluate portfolio VaR, a major drawback of this method is that it is computationally demanding. So in this paper, we consider the efficient importance sampling method under factor model. Furthermore, we model the risk factors with multivariate normal
distribution and multivariate t distribution. Among this assumptions, we introduce upper bound method and optimal tilting method to find the alternative measure Q. In the end, we give the relative efficiency of importance sampling method and Monte Carlo method. We show that the importance sampling method is significantly better than Monte Carlo method.

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