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Interpreting the volatility smile: an examination of the information content of option prices

  • Steven A. Weinberg
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    This paper evaluates how useful the information contained in options prices is for predicting future price movements of the underlying assets. We develop an improved semiparametric methodology for estimating risk-neutral probability density functions (PDFs), which allows for skewness and intertemporal variation in higher moments. We use this technique to estimate a daily time series of risk-neutral PDFs spanning the late 1980's through 1999, for S&P 500 futures, U.S. dollar/Japanese yen futures and U.S. dollar/deutsche mark futures, using options on these futures. For the foreign exchange futures, we find little discernable additional information contained in the estimated PDFs beyond the information derived from the Black-Scholes model, a fully parametric specification. For S&P 500 futures, we find that the risk-neutral distribution implied by the volatility smile better fits the realized returns than the Black-Scholes model, although this better overall fit is not exhibited in the second and third moments.

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    File URL: http://www.federalreserve.gov/pubs/ifdp/2001/706/default.htm
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    File URL: http://www.federalreserve.gov/pubs/ifdp/2001/706/ifdp706.pdf
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    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 706.

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    Date of creation: 2001
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    Handle: RePEc:fip:fedgif:706
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    1. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
    2. Hisashi Nakamura & Shigenori Shiratsuka, 1999. "Extracting market expectations from option prices: case studies in Japanese option markets," Working Paper Series WP-99-1, Federal Reserve Bank of Chicago.
    3. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Working Papers 99-15, Bank of Canada.
    4. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(01), pages 91-115, March.
    5. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
    6. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
    7. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
    8. JosÈ B. Campa & P.H. Kevin Chang & Robert L. Reider, 1997. "ERM bandwidths for EMU and after: evidence from foreign exchange options," Economic Policy, CEPR;CES;MSH, vol. 12(24), pages 53-89, 04.
    9. 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.
    10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    11. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
    12. 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.
    13. Bates, David S, 1991. " The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-44, July.
    14. Dilip B. Madan & Frank Milne, 1992. "Contingent Claims Valued and Hedged by Pricing and Investment in a Basis," Working Papers 868, Queen's University, Department of Economics.
    15. 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.
    16. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
    17. Corrado, Charles J & Su, Tie, 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 175-92, Summer.
    18. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
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