A Hausman Test for Partially Linear Models with an Application to Implied Volatility Surface

Yixiao Jiang
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Yixiao Jiang: Department of Economics, Christopher Newport University, Newport News, VA 23606, USA
Authors registered in the RePEc Author Service: Yixiao Jiang and Yixiao Jiang

JRFM, 2020, vol. 13, issue 11, 1-12

Abstract: This paper develops a test that helps assess whether the term structure of option implied volatility is constant across different levels of moneyness. The test is based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. Distribution of the proposed test statistic is investigated in a general semiparametric setting via the multivariate Delta method. Using recent S&P 500 index traded options data from September 2009 to December 2018, we find that a partially linear model permitting a flexible “volatility smile” and an additive quadratic time effect is a statistically adequate depiction of the implied volatility data for most years. The constancy of implied volatility term structure, in turn, implies that option traders shall feel confident and execute volatility-based strategies using at-the-money options for its high liquidity.

Keywords: implied volatility; option data; semiparametric index model (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2020
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