A Study on the Subadditivity of Value-at-Risk under Stable Distributions

穩定分配下風險值次加性之研究

10.30003/JRM.200711.0003

呂瑞秋(Richard Lu)；林蕙君(H. C. Lin)

Value-at-Risk ； Subadditivity ； Stable distribution ； Heavy tail ； Skewness

風險管理學報

9卷3期（2007 / 11 / 01）

245 - 254

英文

本研究以蒙地卡羅模擬方法探討在穩定分配下風險值是否違反次加性。穩定分配較常態分配一般化，常態分配其實只是穩定分配中的一個特例。在穩定分配下，分配的峰態與偏態可以彈性來調整。因此，適合用來檢查在不同的峰態與偏態下風險值的次加性是否違反。模擬結果顯示，只有在非常高的峰態下風險值是違反次加性，而目前常見的財務資料的分配並不具有如此高的峰態。另外，偏態的高低對於風險值是否違反次加性並沒有影響。

This paper is to examine the possibility for the subadditivity violations of the risk measure VaR under stable distributions by Monte Carlo simulations. Stable distributions are good candidates for this investigation because the normal distributions are special cases of the stable distributions, and it is flexible to set up varying degrees of skewness and kurtosis under the stable distributions. By increasing the kurtosis of stable distributions, the simulated results show that the violation becomes more serious. However, under the kurtosis range of current empirical financial studies, the violation does not exist. As to skewness, it is not as important as kurtosis in affecting subadditivity. Thus, in practice, using VaR for market risk measure may not be a serious flaw even it is subadditivity violated.

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