Tail behavior of stock index futures and margin setting

• Main Authors: Tzu-chuan Kao, 高子荃
• Other Authors: Chu-hsiung Lin
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/04752998671207820695

博士 === 國立高雄第一科技大學 === 管理研究所 === 94 === Abstract To capture the variation in the tail behavior of financial returns distributions, firstly, this study provides a multiple structural changes model for detecting multiple structural changes in the tails of financial returns distributions. The proposed approach possesses two advantages: (a) It can directly determine the number of structural breaks in a time series of tail indexes regardless of whether the true tail index series is increasing or decreasing (b) It can allow for different dynamic tail behavior among different regimes such that the mean tail-index levels of returns distribution can exhibit different values in different regimes. Empirical applications are based on daily data for six stock index futures returns: the DJIA, Nasdaq100, FTSE100, DAX, Nikkei225 and TX. The empirical results demonstrate that: (a) The existence of one break point in the left and right tails of the Nikkei225 futures returns distribution during the sample period, and the likelihood of extreme price movements displays an increasing trend in the left and right tails. The existence of one break point in the left tails of the DJIA futures returns distribution during the sample period, and the likelihood of extreme price movements displays a decreasing trend in the left tails. Furthermore, there exists one break point in the right tail of the TX futures returns distribution, and the likelihood of extreme price movements displays an increasing trend in the right tails. (b) For DJIA, Nikkei225 and TX contracts, the estimated breaks dates in the left and right tail behaviors are differences. (c) For Nasdaq100, FTSE and DAX contracts, there are no break points in the left and right tails of the futures returns. Additionally, this study applies the recursive and rolling tests proposed by Quintos, Fan and Phillips (2001) to test the null hypothesis that the tail indexes of futures returns distribution is constancy over time. The empirical results show that the null hypothesis of constant tail behavior is rejected for all stock iv index futures contracts. To summarize above empirical results, it reflects the different extreme risk information available to long and short investors, therefore, creating differences in risk management between long and short investors in futures markets. Secondly, this study provides an approach, the VaR-x method that incorporates a modification of the Hill estimator based on extreme value theory (EVT) into a Student-t distribution, for setting the unconditional and conditional margin levels. The conditional and unconditional VaR-x approaches are especially appealing because the modified Hill estimator can avoid small sample bias and does not condition its tail observations as does the Hill estimator. The empirical results demonstrate that given lower probabilities of margin violation, the VaR-x approach to setting unconditional margin levels is more accurate than either the normal approach or the Hill non-parametric approach proposed by Cotter (2001). Additionally, this study demonstrates that using the conditional VaR-x approach to setting margin levels can better capture extreme events, thus ensuring adequate prudence, something that is particularly crucial in periods of strong fluctuation. Finally, this study specifies the unconditional VaR-x approach in a structural change framework to give Margin committees some information on how to adjust margin levels as necessary given structural change in market conditions. The empirical results demonstrate that using the unconditional VaR-x approach in a structural change framework to setting margins levels is better than the unconditional VaR-x approach. This empirical evidence suggests that the margin requirements and the number of adjustments on long and short positions should differ according to the differences in the behavior of left and right tails.