A note on skewness and kurtosis adjusted option pricing models under the Martingale restriction

• Published in: Quantitative finance 2004-10, Vol.4 (5), p.479-488
• Main Authors: Negrea, Bogdan, Jurczenko, Emmanuel, Maillet, Bertrand
• Format: Article
• Language: English
• Subjects: Economic models; Kurtosis; Options markets; Options trading; Prices; Securities prices; Skewness; Studies
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697680400000032

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 significant. However, their formula contains a typographic error that can be significant. Brown and Robinson (2002) correct their pricing formula and provide and example of economic significance 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 sCorrado and Su (19ssss96) and Brown and Robinson (2002), and market data from the French options market. We show that differences between the original, corrected and our modified versions of the Corrado and Su (1996) original model are minor on the whole sample, but could be economically significant in specific cases, namely for the maturity and far-from-the-money options when markets are turbulent.