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

Authors: Emmanuel Jurczenko abc;  Bertrand Maillet bcd; Bogdan Negrea d
Affiliations:   a ESCP-EAP European School of Management, Finance Dept., Paris cedex 13
b A.A. Advisors/QCG (ABN Amro Group), Paris cedex 13
c Variances, Paris cedex 13
d TEAM/CNRS - University of Paris-1, Paris cedex 13
DOI: 10.1080/14697680400020309
Publication Frequency: 8 issues per year
Published in: journal Quantitative Finance, Volume 4, Issue 5 October 2004 , pages 479 - 488
Number of References: 21
Formats available: HTML (English) : PDF (English)
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Abstract

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. Brown and Robinson (2002) correct their pricing formula and provide an 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 Corrado and Su (1996) 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 long maturity and far-from-the-money options when markets are turbulent.
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