INTERVAL ESTIMATION OF VALUE-AT-RISK FOR TAIWAN WEIGHTED STOCK INDEX BASED ON EXTREME VALUE THEORY

ABSTRACT

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].

Keywords:

• Value-at-Risk
• extreme value theory
• confidence interval