Gram-Charlier展开在动态金融高阶矩建模中的近似误差

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

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 conditional 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.