跨品种期货套利交易最优保证金比率设计——基于Copula函数及极值理论的研究

The Optimal Margin Ratio Design of Across Varieties Futures Arbitrage Trading

文章主要研究期货交易中最优风险保证金的比率设定问题,通过考虑变动保证金的设定来弥补目前固定保证金不足的问题。在期货套利交易保证金问题上,文章给出了商品期货套利交易保证金的测定理论。在测定的过程中,引入了收益率的非对称Laplace分布和GARCH-T函数分布,在Gumbel Copula函数的基础上,应用蒙特卡洛模拟算法对两种商品的套利交易的保证金问题给出了测定,并以豆油和豆粕期货为例,选取时间序列进行了实证研究,得出结论:套利交易的保证金水平在理论上小于非套利交易下两单独品种保证金的收取之和。此外再结合极值理论,在改进VAR的基础上,得出在极端情况下的套利交易的最优保证金比率设计。

This paper mainly studies the setting problem of the optimal risk trading margin ratio in futures trading, by changing the variation margin setting to make up the insufficient of the fixed deposit. As for the futures arbitrage trading margin issue , this paper first presents the determination theory of commodity futures arbitrage trading margin. In the process of determination, the yield of asymmetric Laplace distribution and GARCH-T function distribution are introduced. On the base of the Gumbel Copulas function, the margin ratio determination of the two goods by the Monte Carlo Simulation Algorithm is provided. The paper takes soybean oil and soybean meal futures as an example and does empirical research on the time series of them and draws the conclusion： in theory, the arbitrage trading margin level is less than the sum of two separate varieties deposit charge in the carry trade. In addition, the paper applies the extreme value theory and concludes that in extreme cases of arbitrage, the optimal margin ratio design on the basis of the improvement of VAR.