Impact of Truncation on Model-Free Implied Moment Estimator

This study examines the impact of truncation, i.e., the unavailability of extremely deep-out-of-the-money option quotes, on the model-free implied moment estimators of Bakshi et al. (2003) and suggests how truncation should be controlled for implied higher moment estimation. We show that truncation has a significantly larger impact on the implied skewness and kurtosis estimators than on the implied volatility estimator and that the impact is not completely removed by linear extrapolation (LE) suggested by Jiang and Tian (2005) or domain symmetrization (DSym) proposed by Dennis and Mayhew (2002). As an alternative method, we suggest domain stabilization (DStab) which makes the truncation error less volatile