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Skewness and kurtosis implied by option prices: a second comment

Author

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  • Jurczenko, Emmanuel
  • Maillet, Bertrand
  • Negrea, Bogdan
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 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.

Suggested Citation

  • Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Skewness and kurtosis implied by option prices: a second comment," LSE Research Online Documents on Economics 24938, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24938
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    1. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    2. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, September.
    3. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Do Call Prices and the Underlying Stock Always Move in the Same Direction?," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 549-584.
    6. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    7. Longstaff, Francis A, 1995. "Option Pricing and the Martingale Restriction," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1091-1124.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    10. Capelle-Blancard, Gunther & Jurczenko, Emmanuel & Maillet, Bertrand, 2001. "The approximate option pricing model: performances and dynamic properties," Journal of Multinational Financial Management, Elsevier, vol. 11(4-5), pages 427-443, December.
    11. Menachem Brenner & Young Ho Eom, 1997. "No-Arbitrage Option Pricing: New Evidence on the Validity of the Martingale Property," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-009, New York University, Leonard N. Stern School of Business-.
    12. Christine A. Brown & David M. Robinson, 2002. "Skewness and Kurtosis Implied by Option Prices: A Correction," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 25(2), pages 279-282, June.
    13. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
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    Cited by:

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    2. Ovidiu TURCOANE, 2012. "Option Price Estimations and Speculative Trading In Knowledge Society," Informatica Economica, Academy of Economic Studies - Bucharest, Romania, vol. 16(4), pages 131-141.
    3. Hosam Ki & Byungwook Choi & Kook‐Hyun Chang & Miyoung Lee, 2005. "Option pricing under extended normal distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(9), pages 845-871, September.
    4. Chateau, John-Peter D., 2009. "Marking-to-model credit and operational risks of loan commitments: A Basel-2 advanced internal ratings-based approach," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 260-270, December.
    5. Chateau, John-Peter D., 2007. "Beyond Basel-2 simplified standardized approach: Credit risk valuation of short-term loan commitments," International Review of Financial Analysis, Elsevier, vol. 16(5), pages 412-433.

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    More about this item

    Keywords

    option pricing models; skewness; Kurtosis;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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