The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models

This paper extends the solution proposed by Aït-Sahalia, Fan, and Li (2013) for the leverage effect puzzle, which refers to a fact that empirical correlation between daily asset returns and the changes of daily volatility estimated from high frequency data is nearly zero. Complementing the analysis in Aït-Sahalia, Fan, and Li (2013) via the Heston model, we work with a generic semi-nonparametric stochastic volatility model via an operator-based expansion method. Under such a general setup, we identify a new source of bias due to the flexibility of variance dynamics, distinguishing the leverage effect parameter from the instantaneous correlation parameter. For estimating the leverage effect parameter, we show that the main results on analyzing the various sources of biases as well as the resulting statistical procedures for biases correction in Aït-Sahalia, Fan, and Li (2013) hold true and are thus indeed theoretically robust. For estimating the instantaneous correlation parameter, we developed a new nonparametric estimation method.

本文拓展了Aït-Sahalia、Fan与Li（2013）针对杠杆效应（leverage effect）之谜提出的解决方案。所谓杠杆效应之谜，指的是通过高频数据估计得到的日度资产收益率与日度波动率变化之间的经验相关性近乎为零这一现象。本文通过算子展开方法构建通用半非参数随机波动率模型，以此补充Aït-Sahalia、Fan与Li（2013）借助赫斯特模型（Heston model）所完成的分析。在这一一般性框架下，本文识别出由方差动态过程的灵活性所带来的新偏误来源，并将杠杆效应参数与瞬时相关参数加以区分。针对杠杆效应参数的估计，本文证明了Aït-Sahalia、Fan与Li（2013）中关于各类偏误来源的分析结果以及由此衍生的偏误修正统计流程均成立，因此该研究确实具备理论稳健性。针对瞬时相关参数的估计，本文提出了一种全新的非参数估计方法。