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Option Pricing and Distribution Characteristics

  • David J. Mauler


    (Department of Economics, Brigham Young University)

  • James B. McDonald


    (Department of Economics, Brigham Young University)

A number of flexible distributions (generalized beta of the second kind, inverse hyperbolic sine, g-and-h, Weibull, Burr-3, Burr-12, generalized gamma) are examined in the setting of option-pricing to explore potential improvements over the standard assumption of lognormal returns. Price formulas are presented specific to each assumed distributional form. The IHS option price formula has not previously been presented in the literature. An empirical application follows where implied risk-neutral density functions for each distribution are estimated from options on the S&P 500 Index. The distributions' performance relative to one another is then evaluated, with the GB2 appearing to be the most attractive choice.

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Paper provided by Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory in its series BYU Macroeconomics and Computational Laboratory Working Paper Series with number 2012-08.

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Length: 19 pages
Date of creation: Nov 2012
Date of revision:
Publication status: Forthcoming in Computational Economics
Handle: RePEc:byu:byumcl:201208
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  1. 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.
  2. Charles J. Corrado, 2001. "Option pricing based on the generalized lambda distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(3), pages 213-236, 03.
  3. McDonald, James B. & Turley, Patrick, 2011. "Distributional Characteristics: Just a Few More Moments," The American Statistician, American Statistical Association, vol. 65(2), pages 96-103.
  4. Bruce J. Sherrick & Philip Garcia & Viswanath Tirupattur, 1996. "Recovering probabilistic information from option markets: Tests of distributional assumptions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(5), pages 545-560, 08.
  5. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
  6. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  7. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
  8. James B. Mcdonald & Jeff Sorensen & Patrick A. Turley, 2013. "Skewness And Kurtosis Properties Of Income Distribution Models," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(2), pages 360-374, 06.
  9. Frank Fabozzi & Radu Tunaru & George Albota, 2009. "Estimating risk-neutral density with parametric models in interest rate markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 55-70.
  10. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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