Bakshi, Kapadia, and Madan (2003) risk-neutral moment estimators: A Gram–Charlier density approach

Abstract

This paper is a sequel to Aschakulporn and Zhang (J Futures Mark 42(3):365–388, 2022). The errors of the Bakshi et al. (Rev Financ Stud 16(1):101–143, 2003) risk-neutral moment estimators is studied using the Gram–Charlier density—with the skewness and excess kurtosis specified. To obtain skewness with (absolute) errors less than 10^{-3}, the range of strikes (K_{min }, K_{max }) must contain at least 3/4 to 4/3 of the forward price and have a step size (Delta K) of no more than 0.1% of the forward price. The range of strikes and step size corresponds to truncation and discretization errors, respectively. This is consistent to Aschakulporn and Zhang (2022) for non-volatile market periods.