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通过期望效用函数的三阶Taylor展开度量了偏度对投资者目标函数的影响,建立了考虑偏度的最优对冲模型.根据模型推导了最优对冲比率的解析公式,该解析公式在偏度为零时可以退化为均值方差最优对冲比率,因此可以看作传统均值方差对冲模型的推广.以恒生指数期货和现货数据为例对模型进行了验证,结果表明:考虑偏度的最优对冲模型的效果要优于传统的均值方差对冲模型.
The third-order Taylor expansion of expected utility function is used to measure the influence of skewness on the investor’s objective function, and the optimal hedging model with skewness is established. The analytical formula of optimal hedge ratio is deduced according to the model. It can be degenerated into the optimal hedge ratio of mean variance when it is zero, so it can be regarded as the generalization of the traditional mean variance hedging model.The model is verified by the example of Hang Seng Index Futures and spot data.The results show that the optimal hedging The effect of the model is better than the traditional mean-variance hedging model.