| Summary: | 碩士 === 國立雲林科技大學 === 財務金融系碩士班 === 95 === The value at risk（VaR）is that we use simple and definitely number to quantify the risk in the complex financial market. The result of the estimation of the value at risk most depends on those extreme events, especially those events which have low probability and bring great affection when they occur. That is extreme value. Therefore, we hope that we can estimate the quantile of the tail distribution in each financial market, and find an appropriate VaR model. Extreme value theory（EVT） focus on the tail distribution, and studies the affection of infrequent events on value at risk. In financial area, extreme value theory is a parametric method. When we lack the data of the tail, and we can apply extreme value theory to estimate value at risk, and it is appropriately in high confidence level.
The thesis that we adopt Taiwan exchange index（TAIEX）and Taiwan futures index（TX）in 2000/1/4 to 2006/12/31 as sample. We use historical simulate method, montecarlo method, and the Peak-over-threshold Model（POT model）of the extreme value theory to estimate value at risk. We can obtain that montecarlo method is appropriate to estimate value at risk. Historical simulate method underestimates the value at risk in low confidence level. Extreme value theory estimates high value at risk in low confidence level, and it seems that extreme value theory can catch the risk of the extreme value, and let us know the high probability of the risk will occur. But when we use likelihood ratio test（LR test）to examine the result, we can obtain that the extreme value theory overestimates value at risk in low confidence level. In high confidence level, extreme value theory can estimate larger value at risk that it tells us that exreme value theory can catch better the risk of the extreme value. In the thesis, we also obtain to estimate value at risk appropriately in high confidence level. We obtain to estimate of the risk appropriately in 99.9% confidence level of the Taiwan exchange index and 99% confidence level of the Taiwan futures index.
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