Skewness and kurtosis implied by option prices: a second comment

Several authors have proposed series expansion methods to price options when the risk-neutral density is asymmetric and leptokurtic. Among these, Corrado and Su (1996) provide an intuitive pricing formula based on a Gram-Charlier Type A series expansion. However, their formula contains a typographic error that can be signi…cant. Brown and Robinson (2002) correct their pricing formula and provide an example of economic signi…cance under plausible market conditions. The purpose of this comment is to slightly modify their pricing formula to provide consistency with a martingale restriction. We also compare the sensitivities of option prices to shifts in skewness and kurtosis using parameter values from Corrado- Su (1996) and Brown-Robinson (2002), and market data from the French options market. We show that di¤erences between the original, corrected, and our modi…ed versions of the Corrado-Su (1996) original model are minor on the whole sample, but could be economically significant in speci…c cases, namely for long maturity and far-from-the-money options when markets are turbulent.