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.

中文翻译：

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方差风险溢价推断

目的

由于存在定价错误，作者考虑了基于期权价格和历史收益构建的方差风险溢价（VRP）和相关隐含方差的统计推断。

设计/方法/方法

作者提出了一种非参数核平滑方法，该方法消除了定价误差的不利影响，并导致了对隐含方差和VRP的一致估计。在期权数据和历史收益数据之间的相对样本大小的三种渐近体制下，提出了拟议的VRP估计量的渐近分布。

发现

这项研究表明，期权价格中的定价误差对现有的估计隐含方差的方法产生了不利影响，这导致VRP的估计量在统计上不一致。通过分析标准普尔500期权和收益数据，它表明，与其他隐式方差和VRP估计量相比，拟议的隐含方差和VRP估计量在解释超标普尔500收益率的变化时是更重要的变量，并且建议的VRP估算值最小样本外预测均方根误差。

研究局限/意义

这项研究有助于隐含方差和VRP的估计，并有助于预测未来实现的方差和股权溢价。

创意/价值

这项研究是第一个提出隐含方差和VRP且存在期权定价错误的一致估计方法的研究。