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

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 nonvolatile market periods.

Automated summary

This paper examines the errors of the Bakshi et al. risk-neutral moment estimators and uses the Gram-Charlier density to specify skewness and excess kurtosis. The study finds that to obtain skewness with small errors, the range of strikes and step size need to meet certain conditions.