佳作分享|Inference for variance risk premium
Inference for variance risk premium
Authors：
Shuang Zhang
Guanghua School of Management, Peking University, Beijing, China, and
Song Xi Chen
Guanghua School of Management, Peking University, Beijing, China, and
Lei Lu
Asper School of Business, University of Manitoba, Winnipeg, Canada
Citation:
Zhang, S., Chen, S.X. and Lu, L. (2020), "Inference for variance risk premium", China Finance Review International, Vol. 11 No. 1, pp. 26-52. https://doi.org/10.1108/CFRI-04-2020-0044
关
键
词
Implied variance, Variance risk premium, Pricing errors, Kernel estimation
摘
要
Purpose
With the presence of pricing errors, the authors consider statistical inference on the variance risk premium (VRP) and the associated implied variance, constructed from the option prices and the historic returns.
Design/methodology/approach
The authors propose a nonparametric kernel smoothing approach that removes the adverse effects of pricing errors and leads to consistent estimation for both the implied variance and the VRP. The asymptotic distributions of the proposed VRP estimator are developed under three asymptotic regimes regarding the relative sample sizes between the option data and historic return data.
Findings
This study reveals that existing methods for estimating the implied variance are adversely affected by pricing errors in the option prices, which causes the estimators for VRP statistically inconsistent. By analyzing the S&P 500 option and return data, it demonstrates that, compared with other implied variance and VRP estimators, the proposed implied variance and VRP estimators are more significant variables in explaining variations in the excess S&P 500 returns, and the proposed VRP estimates have the smallest out-of-sample forecasting root mean squared error.
Research limitations/implications
This study contributes to the estimation of the implied variance and the VRP and helps in the predictions of future realized variance and equity premium.
Originality/value
This study is the first to propose consistent estimations for the implied variance and the VRP with the presence of option pricing errors.
结
构
Introduction
Implied variance and existing estimators
Effects of pricing errors
Error-corrected IV estimator
Variance risk premium
Simulation studies
Empirical results
Conclusion
成
果
The kernel density estimates for the density of the moneyness of the SPX call options traded in 2006 and 2007, with the Gaussian kernel and the smooth bandwidth hm1＝0.073 and hm2＝0.015, respectively.
Average biases of the estimated option prices and the estimated integrands at T＝1/12. Based on 2000 simulations.
Plot with different data frequency and against the horizon [T-t,t] and[t,t+T], with fixing t=0 respectively.
The bias, the standard deviation (SD) and the root mean squared error (RMSE) for the estimates with the underlying asset pricing process (23) and T＝1/12.
Bias and standard deviation (SD) of the two components of CBOE's IV estimator.
The bias, the standard deviation (SD) and the root mean squared error (RMSE) for the estimates with the underlying asset pricing process (23) and T＝1/4.
Ordinary least square estimates of the regression Models (27).
The time series of the three VRP estimators from January 2009 to December 2015 based on S&P 500 option data.
Summary statistics of different variance risk premium estimates for S&P 500 from January 2009 to December 2015.
Regression results of Model (29) with three different VRP estimates.
Out-of-sample predictions based on univariate regressions and selected models.
结
论
We have proposed a consistent estimation approach for the IV and the VRP, which can remove the adverse effects of the pricing errors in the option prices, by first conducting nonparametric regression estimation of the option price function. This is an improvement over the existing estimators for both IV and VRP proposed by Jiang and Tian (2005) and CBOE (2003). Our theoretical study and numerical simulations show that in the presence of option pricing errors, Jiang and Tian (2005) and CBOE’s IV estimators and subsequently the VRP estimators are adversely affected by the observational errors in the option prices. We also present an asymptotic analysis on the proposed VRP estimation under three asymptotic regimes regarding the relative order of sample sizes in the option data for IV estimation to the historic return data for estimating the RV.
In the empirical study of the S&P 500 data, we found that the IV was a more significant predictor for the subsequent RV than the Black-Scholes IV and the lagged RV, which was consistent with the findings in Jiang and Tian (2005). Besides, the proposed consistent estimators for the IV and VRP provide more accurate fitting and forecasting performance than the other IV and VRP estimates, as well as the BS IV and the lagged RV. In the forecasting of S&P 500 returns, we verified that the VRP as a predictor is more efficient than other commonly used predictors, such as the price-earnings ratio and the stochastically detrend risk-free rate. And our proposed estimation for the VRP contains more information of the stock market returns, as compared to the existing model-free approaches.
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作者简介
路磊，加拿大曼尼托巴大学阿斯博商学院金融学教授，Bryce Douglas讲席教授，博士生导师, 金融学研究生项目负责人。他于2007年毕业于加拿大麦吉尔大学，获得金融学博士学位。2007-2011年任教于上海财经大学金融学院， 2011-2016年任教于北京大学光华管理学院。他的研究方向包括资产定价，行为金融和国际金融。他的研究成果发表在Journal of Financial and Quantitative Analysis，Management Science, Journal of Corporate Finance, Journal of Economic Dynamics and Control, Journal of Futures Markets, Economic Theory, Economics Letters, and China Finance Review International等英文期刊；他的研究也发表在《管理科学学报》和《金融研究》等中文期刊。他曾经主持过国家自然科学基金面上项目，上海市浦江人才计划项目，以及中国金融期货交易所的研究项目。他目前担任China Finance Review International 和Accounting and Finance杂志副主编。
陈松蹊，国家特聘专家，北京大学讲席教授，商务统计与经济计量系联合系主任、北京大学统计科学中心联席主任。1993年澳大利亚国立大学统计学博士。2017年全职北大之前是美国Iowa State University统计学终身教授，加盟北大后主要致力于商务统计与经济计量学学科建设及北大统计学研究队伍的建设工作。
数理统计学会(Institute of Mathematical Statistics) 资深会员（fellow)，美国统计学会会士（fellow），国际统计学会 (International Statistics Institute) 当选会员 （elected member），数理统计学会 (IMS) 理事会常务理事( Council member)。The Annals of Statistics(统计年鉴) 编委， 自2010年；Journal of the American Statistical Association (美国统计学会会刊）编委， 自2018年；Journal of Business and Economic Statistics 编委， 自2013年；Environmentrics, Associate Editor, 自2018年。曾任Statistics and Its Interface 的联席主编（2010-2013）。
张爽，经济学博士，研究方向：金融计量。
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