“已实现”双幂次变差与多幂次变差的有效性分析

Analysis of the efficiency of realized bipower variation and realized multipower variation

近年来,基于金融高频数据的波动率研究成为金融学研究领域的热点,而有效性是衡量波动率估计量优劣的重要标准,本文对波动率估计量的新方法“已实现”双幂次变差和“已实现”多幂次变差的有效性进行了研究,得出“已实现”双幂次变差在一般条件下比“已实现”波动更有效的结论,并且证明了在一定条件下,“已实现”多幂次变差的幂次个数越多,该波动率估计量的有效性越高.这一结论为“已实现”多幂次变差的幂次个数选取提供了原则.

Recently the study of volatility of high frequency financial data became a focus in financial study. The efficiency of volatility is an important criterion. In this paper, through studying the efficiency of the realized bipower variation and the realized muhipower variation, which are new methods of volatility estimator, conclusion is draw that in general the realized bipower variation is more efficient than the realized volatility. We also give a theorem that under some condition the more the power of realized muhipower variation is, the more efficient the realized muhipower variation is. The result of the theorem provides a principle of how to select the power of the realized multipower variation.