State-of-the-art methodologies such as the semi-parametric spline interpolation Footnote 1 of Figlewski ( 2008) or the three-dimensional kernel regression of OptionMetrics ( 2016) produce surprisingly large differences in standard option-implied quantities. Our findings hold more generally for any quantity that is extracted from the aggregation of option prices along the strike range. We document in this paper that the method for constructing the volatility surface affects these standard option-implied quantities. Many popular option-implied metrics such as risk-neutral variance, skewness and the variance risk premium are calculated based on an estimate of the option-implied volatility surface. Based on 14 years of end-of-day and intraday S&P 500 and Euro Stoxx 50 option data we conclude that the proposed one-dimensional kernel regression represents option market information more accurately than existing approaches of the literature. We assess its statistical accuracy relative to existing state-of-the-art parametric, semi- and non-parametric volatility surfaces by means of leave-one-out cross-validation, including the volatility surface of OptionMetrics. To overcome this problem, we propose a volatility surface that is built with a one-dimensional kernel regression. The variations are even larger for risk-neutral skewness. Estimates for risk-neutral variance differ across volatility surfaces by more than 10% on average, leading to variance risk premium estimates that differ by 60% on average. For some state-of-the-art volatility surfaces, the differences are economically surprisingly large and lead to systematic biases, especially for out-of-the-money put options. We find that option-implied information such as forward-looking variance, skewness and the variance risk premium are sensitive to the way the volatility surface is constructed.
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