Effectiveness of Linear Extrapolation in Model-Free Implied Moment Estimation

Abstract

This study proposes a new methodology with which the effectiveness of linear extrapolation (LE) of Jiang and Tian (2005) for the implied moment estimators of Bakshi et al. (2003) can be evaluated, even when the true moments are unknown. Using S&P 500 index options data and truncation sensitivity functions, this study suggests that although LE is effective for all three estimators, the implied skewness and kurtosis estimators can remain sensitive to truncation, i.e., the complete unavailability of option prices for a part of deep-out-of-the-money or deep-in-the-money region of strike price domain, even when LE is employed to mitigate truncation.

Keywords: Linear extrapolation, truncation error, model-free implied moment estimators, skewness, kurtosis

JEL Classification: C14, C58, G13