波动率合格代理变量的必要条件及其非参数检验

A Necessary Condition for a Qualified Proxy of Volatility and Its Test

在较弱的假设下导出合格波动率代理变量的必要条件,并借助重抽样技术构建了检验该必要条件的非参数方法。用其进行中外股指高频数据的实证研究表明:对于中国股指的数据,采用"已实现波动率"作为代理变量违背了上述必要条件而有不适合作为合格代理变量之虞;但欧美股市的数据却未检测出上述问题。最后,根据实证结果对"已实现波动率"进行适当改造,使其成为能避免上述偏差的改进代理变量。

In view of the importance of volatility proxy for model evaluation,we propose a necessary condition to be qualified proxies of volatility.A robust approach is given to check the condition in order to investigate the justification of realized volatilities as proxies of volatility.This approach works through comparing the performance of proxies in each sub-sample and whole sample respectively.Applying the approach to stock index,we found that there are some evidences which strongly suggest that realized volatilities are not qualified proxies of volatility for Shanghai stock market data,while the evidences that realized volatilities fail to meet the necessary condition were not detected for Europe and America stock market data.Finally,based on the empirical results,this paper further propose a simple method to revise those proxies and a revised volatility proxy is given as well.