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Inference for variance risk premium

Shuang Zhang (Guanghua School of Management, Peking University, Beijing, China)
Song Xi Chen (Guanghua School of Management, Peking University, Beijing, China)
Lei Lu (Asper School of Business, University of Manitoba, Winnipeg, Canada)

China Finance Review International

ISSN: 2044-1398

Article publication date: 21 July 2020

Issue publication date: 26 January 2021

210

Abstract

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.

Keywords

Acknowledgements

Funding: This research is partially funded by China’s National Key Research Special Program Grant 2016YFC0207701, National Key Basic Research Program Grant 2015CB856000 and National Natural Science Foundation of China grants 71532001 and 71371016.The authors acknowledge support from LMEQF at Peking University.

Citation

Zhang, S., Chen, S.X. and Lu, L. (2021), "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

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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