| Summary: | 碩士 === 國立高雄第一科技大學 === 財務管理所 === 92 === This study considers extreme value theory base to discuss how to set futures margins under price limits.First, we observe the issue in not taking the truncated distribution into account. In this part, we apply the extreme value theory to estimate the appropriate margin levels of the futures market in Taiwan. The weighted stock, financial sector stock and electronic sector stock index futures have been chosen and analyzed in this study. Methodologically, the Gauss-Newton method is utilized to estimate the parameters in the nonlinear regression. The findings of this part include: the electronic sector and the financial sector index futures have the largest and smallest volatility, respectively. Under the same probability of default, the margin level of electronic sector index futures should be larger than financial sector index futures. In fact, these findings are quite consistent with the observations in the market. Furthermore, due to the limitations of 7% price variation, the method proposed by Brossard (2001), which is based on different probabilities of default and different percentages of price limitation has been borrowed to find the appropriate futures margin level. The conclusion is that the estimated futures margin level with price limitation should be set lower than the one without limitation.
Finally, we take the truncated distribution into account and apply the extreme value theory and Quasi- Newton method which is often used to calculate parameters in the likelihood functions to estimate the appropriate margin of the futures market in CBOT. Because this situation is that price limits lead to price distribution truncated, we introduce censored technology to overcome the difficulty in price limits. To financial field , it is a state-of-the-art method and the first research to solve the truncated distribution. The findings in the last part are compose of the fact that the margins of corn futures in CBOT is not enough to prevent all occurrences of default. Besides, the findings also show that price limits are indeed able to cold down price changes and directly support the overreaction hypothesis.
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