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Option traders use (very) sophisticated heuristics, never the Black-Scholes-Merton formula

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  • Haug, Espen Gaarder
  • Taleb, Nassim Nicholas
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    Abstract

    Option traders use a heuristically derived pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called "Black-Scholes-Merton" owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contradiction with it). However, we have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the "risk" parameter through "dynamic hedging", (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter using put-call parity, (3) option traders did not use the Black-Scholes-Merton formula or similar formulas after 1973 but continued their bottom-up heuristics more robust to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop using the wrong designation for option pricing.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

    Volume (Year): 77 (2011)
    Issue (Month): 2 (February)
    Pages: 97-106

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    Handle: RePEc:eee:jeborg:v:77:y:2011:i:2:p:97-106

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    Web page: http://www.elsevier.com/locate/jebo

    Related research

    Keywords: Options Option hedging Delta hedging Put-call parity Derivatives;

    References

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    1. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    2. Nicolae Garleanu & Lasse Heje Pedersen & Allen M. Poteshman, 2009. "Demand-Based Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 4259-4299, October.
    3. Zimmermann, Heinz & Hafner, Wolfgang, 2007. "Amazing discovery: Vincenz Bronzin's option pricing models," Journal of Banking & Finance, Elsevier, vol. 31(2), pages 531-546, February.
    4. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
    5. J-P. Bouchaud & M. Potters, 2001. "Welcome to a non-Black-Scholes world," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 482-483.
    6. Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-24, December.
    7. Mixon, Scott, 2009. "Option markets and implied volatility: Past versus present," Journal of Financial Economics, Elsevier, vol. 94(2), pages 171-191, November.
    8. Kairys, Joseph P, Jr & Valerio, Nicholas, III, 1997. " The Market for Equity Options in the 1870s," Journal of Finance, American Finance Association, vol. 52(4), pages 1707-23, September.
    9. 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 637-54, May-June.
    10. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    11. A. James Boness, 1964. "Elements of a Theory of Stock-Option Value," Journal of Political Economy, University of Chicago Press, vol. 72, pages 163.
    12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    13. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Plerou, V, 2000. "Scale invariance and universality of economic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 31-41.
    14. Gigerenzer, Gerd & Todd, Peter M. & ABC Research Group,, 2000. "Simple Heuristics That Make Us Smart," OUP Catalogue, Oxford University Press, number 9780195143812, October.
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    Cited by:
    1. Godfrey Charles-Cadogan & John A. Cole, 2013. "Bankruptcy Risk Induced by Career Concerns of Regulators," Papers 1312.7346, arXiv.org.
    2. Nassim N. Taleb & Raphael Douady, 2012. "Mathematical Definition, Mapping, and Detection of (Anti)Fragility," Papers 1208.1189, arXiv.org.
    3. Timothy C. Johnson, 2013. "Reciprocity as the foundation of Financial Economics," Papers 1310.2798, arXiv.org.
    4. Turner, John D., 2014. "Financial history and financial economics," QUCEH Working Paper Series 14-03, Queen's University Centre for Economic History, Queen's University Belfast.

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