Gram-Charlier展开在动态金融高阶矩建模中的近似误差  

The Approximation Bias of Gram-Charlier Expansion in Dynamic Higher Moments Modelling

作　　者：王天一[1] 李超 黄卓[3] 

机构地区：[1]对外经济贸易大学金融学院,北京100029 [2]摩根大通北京量化研究中心,北京100033 [3]北京大学国家发展研究院,北京100871

出　　处：《数理统计与管理》2017年第5期919-929,共11页Journal of Applied Statistics and Management

基　　金：教育部人文社会科学青年基金项目(12YJC790073;13YJC790146);国家自然科学基金青年基金项目(71201001;71301027);对外经济贸易大学中央高校基本科研业务经费(14YQ05)

摘　　要：Gram-Charlier展开(GCE)在动态条件高阶矩GARCH模型中得到了广泛应用。相比于常见的分布,GCE的高阶矩形式更加直观,能更直接地刻画条件高阶矩的动态特征。此展开函数并不非负,在实际应用时需要平方并归一化,但已有文献大多忽略此处理后高阶矩所发生的变化。本文研究了平方处理方法对展开函数高阶矩的影响,推导了正确的高阶矩形式。实证研究表明,用原始参数作为近似高阶矩会产生显著偏误,在VaR预测时会严重低估风险。The Gram-Charlier Expansion （GCE） of the Gaussian density under GARCH framework has been widely used to model the conditional dynamic higher moments. Compared with other generalized distributions, GARCH-GCE models describe the dynamic equations of conditionad skewness and kurtosis in a more direct way. While GCE function is not always positive, it is often squared and normalized in empirical studies. However, little attention has been paid to the fact that the higher moments of squared-GCE function are different from the parameters of original GCE function. This paper derives the correct skewness and kurtosis of the squared-GCE function, and examines the approximation bias. Empirical results suggest a significant bias when distribution parameters are used instead of the correct skewness and kurtosis, which will result in severe underestimate of the VaR.

关 键 词：高阶矩 GARCH Gram—Charlier展开 Cornish—Fisher展开 

分 类 号：F830[经济管理—金融学] O212[理学—概率论与数理统计]