Stock Index Futures Margin Level Settings by Hill Estimation and Empirical Analysis

Abstract

The article does empirical research on the margin level setting of Shanghai and Shenzhen 300 index futures. First of all, through the trend comparison chart of index and simulation index futures in 100 trading days, we obtain the conclusion that index data can instead of index futures. Then, 482 full samples' daily returns is to descriptive statistical analysis and test of normality, we obtain that it doesn't obey normal distribution, furthermore, it has a "peak and fat-tail", the left tail down the possibility of large, up the possibility of the right tail is large, To the tail, left tail has down possibility while right tail has up possibility, right tail has more risk than left. Secondly, we use extreme value theory which good at researching tail's distribution characteristics and the Hill estimation method to solve the tail index estimates of full samples, left and right tail, and we obtain the margin level is 3.5717%. Thirdly, after the estimated margin level and actual historical price volatility (the absolute value of index returns) for comparison tests, we find that under the assumption of 0.01default rates, the margin level cannot cover 99% of price fluctuations, the result is low. Finally, we solve margin level's coverage under different default rates and obtain that when default rate is equal to 0.03, the margin level can cover 97% of price fluctuations.