Abstract
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. 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. 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. The variations are even larger for risk-neutral skewness. To overcome this problem, we propose a volatility surface that is built with a one-dimensional kernel regression. 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. 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.
Highlights
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
The aggregated root mean squared errors (RMSEs) for the end-of-day, data-rich, environment are summarized in Table 5, the respective mean absolute error (MAE) error figures can be found in Table 9 in “Appendix E”
For S&P 500 options we find that the volatility surface from the one-dimensional kernel regression produces the lowest RMSE (0.0092) and MAE (0.0019)
Summary
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. We document in this paper that the method for constructing the volatility surface affects these standard option-implied quantities. State-of-the-art methodologies such as the semi-parametric spline interpolation of Figlewski (2008) or the three-dimensional kernel regression of OptionMetrics (2016) produce surprisingly large differences in standard option-implied quantities. In our sample for S&P 500 options (2004–2017), Bakshi et al (2003) risk-neutral variance for medium-term maturities, computed with exactly the same procedure, but based on the volatility surface from the interpolation scheme of Figlewski (2008) or OptionMetrics (2016), differs in relative terms by more than 10% on average. The 1-month-ahead variance risk premium varies across both volatility surfaces by a relative margin of on average 60%. Differences are even more troublesome for risk-neutral skewness, where we document relative differences in the order of 200% and more
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