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本文从上证50ETF期权价格中提取无模型隐含波动率并检验其信息含量，基于随机折现因子理论推导波动率风险的系统性与正负性判定公式，从波动率风险溢酬和相关性两方面验证波动率是否为系统性风险，进而基于A股市场的个股数据检验波动率风险在股票截面收益上的定价能力。研究结果表明：无模型隐含波动率包含BS隐含波动率中的所有信息和历史波动率中的大部分信息，是未来已实现波动率的有效估计；市场波动率为系统性风险因子且存在显著为负的风险溢酬；组合分析表明，对市场波动率暴露较大的股票组合在未来的收益较低，且暴露最大与最小股票组合的收益率之差显著为负，该结论在控制经典风险因子和改变交易策略之后依然稳健；Fama-MacBeth两步法结果表明波动率风险被定价且风险价格显著为负。
Abstract：This paper extracts the model-free implied volatility from the SSE 50 ETF option prices and verifies its information content. Based on the stochastic discount factor theory, we derive the formula to judge whether the volatility is a positive or negative systematic risk, and verify it from the aspects of volatility risk premium and correlation. Furthermore, we examine the pricing power of volatility in the cross-section stock returns in A-share market. The results show that: The model-free implied volatility subsumes all information contained in the BS implied volatility and most of the information contained in the historical volatility, thus is a more efficient predictor for future realized volatility; The volatility is a systematic risk factor, and there is a significant negative volatility risk premium; The portfolio analysis indicates that the stocks with high sensitivities to market volatility have lower returns in the future, the high-minus-low hedge portfolio returns are negative, and this negative relationship remains significant after controlling classical risk factors and changing the trading strategy; The Fama-MacBeth two-step method shows that the volatility risk is priced with a significantly negative value.
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①陈蓉等（2019）的研究结论认为，虽然我国市场的波动率风险是非系统性风险，但期权隐含的波动率风险溢酬却显著为负，这与美国情形不同，也不符合金融学原理。文中指出产生这一问题的可能原因是样本区间太短且2015年的股市极不稳定。
②本文提取与iVIX在以下几方面有显著区别：理论基础方面，是基于Bakshi等（2003）的定理1，而iVIX是基于Britten-Jones和Neuberger(2000）的命题1；方差定义方面，是基于二次合约，而iVIX是基于二次变差；基础资产方面，是基于现货资产，而iVIX是基于远期资产。
③因篇幅所限，详细推导过程以附录A展示，见《统计研究》网站所列附件。下同。
①因篇幅所限，波动率序列的描述性统计结果以附表1展示。
①因篇幅所限，波动率序列的相关系数以附表2展示。
①分别控制ln HV、ln MFIV，以及同时控制ln HV和ln MFIV后，ln BSV的系数显著性逐步下降直至不显著。
②因篇幅所限，MFIV的信息含量检验以附表3展示。
③因篇幅所限，HAR-RV模型的样本外预测能力以附表4展示。
④在经典跨期消费投资决策中，随机折现因子也被称为定价核，实际上是跨期消费的边际替代率。
①风险中性密度在Arrow-Dereu经济中被称为状态价格密度，在无套利均衡定价模型中被称为等价鞅测度。
②需要说明的是，在检验波动率信息含量时，本文是基于上证50ETF期权及其标的进行，因为期权价格隐含其标的资产的信息。当讨论系统性风险时，本应该讨论上证50指数期权与上证50指数之间的关系，但是遗憾的是我国目前还没有上市交易上证50指数期权，而上证50ETF跟踪上证50指数，本文依据陈蓉等（2019）的做法，假设上证50ETF期权隐含信息也适用于上证50指数。因此，本文讨论上证50ETF期权隐含的波动率与上证50指数波动率之间的关系，以及波动率是否为系统性风险因子。
①Liu等（2019）认为构建因子收益率应该保持市值中性，因此需要根据市值分组，以控制市值影响。
②因篇幅所限，因子收益率的均值，标准差和相关系数以附表5展示。
③对每只股票而言，β都具有时变性，使用月度窗口的日数据是平衡时变性与精确性的结果，Pástor和Stambaugh(2003),Ang等（2006）都曾采用每月的日收益率数据来进行研究。
①此处个股特征变量与前文因子收益率既有区别又有联系，因子收益率是根据特征变量和排序法构建出来的收益率时间序列，而个股特征变量是同时具有时间维度和个股维度的面板数据。
①因篇幅所限，详细结果以附表6~10展示。
②本文还考虑换手率、PS指标（Pástor和Stambaugh,2003）和隐含交易成本（IRC,Dick-Nielsen等，2012）等流动性指标。控制不同流动性指标后的结果一致，因篇幅所限，结果以附表10展示。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2024.03.009
中图分类号:F224;F832.5
引用信息:
[1]黄金波,王天娇.无模型隐含波动率的信息含量与定价能力——基于上证50ETF期权的实证研究[J].统计研究,2024,41(03):115-128.DOI:10.19343/j.cnki.11-1302/c.2024.03.009.
基金信息:
国家自然科学基金面上项目“基于资产价格隐含信息的最优资产配置与风险管理”（71971068）和“期权价格隐含的尾部风险及其信息含量研究”(72371079); 广东省自然科学基金杰出青年项目“基于前瞻信息的下方风险测度及其应用”（2023B1515020045）; 深圳大学2035卓越研究计划哲学社会科学项目“中国特色的前瞻性金融风险指标体系构建：理论与应用”（ZYZD2302）
2024-03-11
2024-03-11
2024-03-11