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Recovering Probability Distributions from Option Prices


  • Jackwerth, Jens Carsten
  • Rubinstein, Mark


This article derives underlying asset risk-neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices. Alternative optimization specifications produce approximately the same implied distributions. A new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed. Since the crash, the risk-neutral probability of a three (four) standard deviation decline in the index (about -36 percent (-46 percent) over a year) is about 10 (100) times more likely than under the assumption of lognormality. Copyright 1996 by American Finance Association.

Suggested Citation

  • Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
  • Handle: RePEc:bla:jfinan:v:51:y:1996:i:5:p:1611-32

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    References listed on IDEAS

    1. Campbell, John Y & Hamao, Yasushi, 1992. " Predictable Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration," Journal of Finance, American Finance Association, vol. 47(1), pages 43-69, March.
    2. Campbell, John Y & Ammer, John, 1993. " What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns," Journal of Finance, American Finance Association, vol. 48(1), pages 3-37, March.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    5. Blanchard, Olivier J, 1981. "Output, the Stock Market, and Interest Rates," American Economic Review, American Economic Association, vol. 71(1), pages 132-143, March.
    6. Campbell, John Y, 1991. "A Variance Decomposition for Stock Returns," Economic Journal, Royal Economic Society, vol. 101(405), pages 157-179, March.
    7. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    8. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    9. Feldstein, Martin & Horioka, Charles, 1980. "Domestic Saving and International Capital Flows," Economic Journal, Royal Economic Society, vol. 90(358), pages 314-329, June.
    10. Gultekin, Mustafa N & Gultekin, N Bulent & Penati, Alessandro, 1989. " Capital Controls and International Capital Market Segmentation: The Evidence from the Japanese and American Stock Markets," Journal of Finance, American Finance Association, vol. 44(4), pages 849-869, September.
    11. Bekaert, Geert & Hodrick, Robert J, 1992. " Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," Journal of Finance, American Finance Association, vol. 47(2), pages 467-509, June.
    12. Gultekin, Mustafa N. & Gultekin, N. Bulent, 1983. "Stock market seasonality : International Evidence," Journal of Financial Economics, Elsevier, vol. 12(4), pages 469-481, December.
    13. Phillips, Kerk L., 1991. "A two-country model of stochastic output with changes in regime," Journal of International Economics, Elsevier, vol. 31(1-2), pages 121-142, August.
    14. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
    15. Fama, Eugene F, 1990. " Stock Returns, Expected Returns, and Real Activity," Journal of Finance, American Finance Association, vol. 45(4), pages 1089-1108, September.
    16. Connor, Gregory & Korajczyk, Robert A., 1988. "Risk and return in an equilibrium APT : Application of a new test methodology," Journal of Financial Economics, Elsevier, vol. 21(2), pages 255-289, September.
    17. Robert J. Hodrick, 1991. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Interference and Measurement," NBER Technical Working Papers 0108, National Bureau of Economic Research, Inc.
    18. Chen, Nai-Fu, 1991. " Financial Investment Opportunities and the Macroeconomy," Journal of Finance, American Finance Association, vol. 46(2), pages 529-554, June.
    19. Wheatley, Simon, 1988. "Some tests of international equity integration," Journal of Financial Economics, Elsevier, vol. 21(2), pages 177-212, September.
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