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 $$10^{-3}$$10 - 3 , the range of strikes ( $$K_{\min }, K_{\max }$$K min , K max ) must contain at least 3/4 to 4/3 of the forward price and have a step size ( $$\Delta K$$Δ 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.

Since the S&P 100 Index underlies both American (OEX) and European (XEO) options, the value of the early exercise premium of American options can be directly observed. We find that the mid‐quote of an XEO option can be higher than that of an otherwise identical OEX option, and liquidity can explain this overpricing phenomenon of European options. Our results show that illiquid options are significantly overpriced in the S&P 100 Index options market. This finding indicates that an illiquid option can be overvalued with a higher market offer price, which is the requirement of market makers for compensation for providing liquidity.