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Option Prices and the Underlying Asset's Return Distribution

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  • Grundy, Bruce D

Abstract

This work examines the relation between option prices and the true, as opposed to risk-neutral, distribution of the underlying asset. If the underlying asset follows a diffusion with an instantaneous expected return at least as large as the instantaneous risk-free rate, observed option prices can be used to place bounds on the moments of the true distribution. An illustration of the paper's results is provided by the analysis of the information concerning the mean and standard deviation of market returns contained in the prices of S&P 100 Index Options. Copyright 1991 by American Finance Association.

Suggested Citation

  • Grundy, Bruce D, 1991. "Option Prices and the Underlying Asset's Return Distribution," Journal of Finance, American Finance Association, vol. 46(3), pages 1045-1069, July.
    • Handle: RePEc:bla:jfinan:v:46:y:1991:i:3:p:1045-69
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    Cited by:

    1. Yu, Xisheng & Xie, Xiaoke, 2015. "Pricing American options: RNMs-constrained entropic least-squares approach," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 155-173.
    2. Luis F. Zuluaga & Javier F. Peña, 2005. "A Conic Programming Approach to Generalized Tchebycheff Inequalities," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 369-388, May.
    3. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    4. Roy H. Kwon & Jonathan Y. Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    5. Lo, Andrew W & Wang, Jiang, 1995. "Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March.
    6. Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
    7. Donald Brown & Rustam Ibragimov & Johan Walden, 2015. "Bounds for path-dependent options," Annals of Finance, Springer, vol. 11(3), pages 433-451, November.
    8. Martin Cincibuch, 2002. "Distributions Implied by Exchange Traded Options: A Ghost’s Smile?," CERGE-EI Working Papers wp200, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    9. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
    10. Jose M. Campa & P.H. Kevin Chang & Robert L. Reider, 1997. "Implied Exchange Rate Distributions: Evidence from OTC Option Markets," NBER Working Papers 6179, National Bureau of Economic Research, Inc.
    11. Wilkens, Sascha & Roder, Klaus, 2006. "The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market," Global Finance Journal, Elsevier, vol. 17(1), pages 50-74, September.
    12. José Manuel Campa & P.H. Kevin Chang & James F. Refalo, 1999. "An Options-Based Analysis of Emerging Market Exchange Rate Expectations: Brazil's Real Plan, 1994-1997," Working Papers 99-08, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Roy Kwon & Jonathan Li, 2016. "A stochastic semidefinite programming approach for bounds on option pricing under regime switching," Annals of Operations Research, Springer, vol. 237(1), pages 41-75, February.
    14. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    15. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
    16. Hsuan-Chu Lin & Ren-Raw Chen & Oded Palmon, 2012. "Non-parametric method for European option bounds," Review of Quantitative Finance and Accounting, Springer, vol. 38(1), pages 109-129, January.
    17. Jose Manuel Campa & P.H. Kevin Chang, 1996. "Options-based evidence of the credibility of the peseta in the ERM," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 3-22, January.
    18. repec:dau:papers:123456789/30 is not listed on IDEAS
    19. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    20. Wong, Man Hong & Zhang, Shuzhong, 2014. "On distributional robust probability functions and their computations," European Journal of Operational Research, Elsevier, vol. 233(1), pages 23-33.
    21. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    22. Tianyang Wang & James Dyer & Warren Hahn, 2015. "A copula-based approach for generating lattices," Review of Derivatives Research, Springer, vol. 18(3), pages 263-289, October.
    23. Paolo Guasoni & Lóránt Nagy & Miklós Rásonyi, 2021. "Young, timid, and risk takers," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1332-1356, October.

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