Linear extrapolation and model-free option implied moments

Abstract

This study proposes an approach for assessing the effectiveness of linear extrapolation (LE) for the implied moment estimators even in cases in which the true values of implied moments are unknown. To this end, we develop truncation sensitivity functions for simulation and empirical analyses. LE proves effective for implied volatility, skewness, and kurtosis estimators. However, higher moment (i.e., implied skewness and kurtosis) estimators exhibit sensitivity to truncation, that is, the absence of option prices in the outermost region of the strike price domain, regardless of the use of LE to address truncation.