Interval Estimation of Value-At-Risk for Taiwan Weighted Stock Index Based on Extreme Value Theory

應用極值理論於台股指數風險值區間估計

10.29977/JCIIE.200801.0004

周建新(Jian-Hsin Chou)；于鴻福(Hong-Fwu Yu)；陳振宇(Zhen-Yu Chen)

風險值 ； 極值理論 ； 信賴區間 ； Value-at-Risk ； extreme value theory ； confidence interval

工業工程學刊

25卷1期（2008 / 01 / 01）

31 - 42

英文

風險值為一衡量市場風險的方法，廣受金融機構所採用。在有關風險值之相關文獻上，雖有許多的論文探討風險值的估計，不過卻多集中在風險值之點估計上。然而，點估計本身亦會產生估計誤差，具有不確定性，且可能會導致錯誤之估計結果。信賴區間為一量化指標，可以有效地用來描述來自抽樣誤差的不確定性；在實際應用上，區間估計較點估計更受喜愛。本文之目的即在應用極值理論，來估計台股指數之風險值，並建構風險值之信賴區間。此外，為了驗證本文模型之估計效率，特與張揖平等[9]所提之方法作一比較。實證結果顯示，使用極值理論所計算出之信賴區間的寬度較小；此意謂應用極值理論來估計台股指數之風險值的信賴區間，較張揖平等[9]所提之方法更有效率。

Value-at-Risk (VaR) is a tool widely used by financial institutions to report and measure market risk. There have been a great number of studies in estimating VaR. Most of which are focused on the point estimation of VaR. However, in estimating a quantity, a point estimate can be misleading, because it may or may not be close to the quantity being estimated. So we cannot know the accuracy of estimating the quantity. Confidence interval (CI) is one of the most useful manners of quantifying uncertain due to ”sampling error”. Besides, the mathematics of interval estimation and hypotheses testing are closely re-lated. Hence, in practical situations, the interval estimation is more preferred than the point estimation. This paper is aimed at applying the extreme value theory (EVT) to evaluate CIs of the VaR of Taiwan weighted stock index. To assess the efficiency of the proposed method in this paper, comparisons with the methods studied in Chang et al. [9] are also made. The empirical results show that the widths of the CIs obtained by the EVT model are narrower than those obtained by Chang et al. [9]. This indicates that the EVT model is more efficient in estimating the VaR of Taiwan weighted stock index than those in Chang et al. [9].

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