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

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  • Steven A. Weinberg
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    Abstract

    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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    Bibliographic Info

    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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    Keywords: Risk management ; Asset-liability management;

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    References

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    1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
    2. 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.
    3. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
    4. 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.
    5. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Working Papers 99-15, Bank of Canada.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
    11. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    12. Nakamura, Hisashi & Shiratsuka, Shigenori, 1999. "Extracting Market Expectations from Option Prices: Case Studies in Japanese Option Markets," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 17(1), pages 1-43, May.
    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. 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.
    15. 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.
    16. 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.
    17. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
    18. 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.
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    Cited by:
    1. Francisco Alonso & Roberto Blanco & Gonzalo Rubio, 2005. "Testing the forecasting performace of IBEX 35 option implied risk neutral densities," Banco de Espa�a Working Papers 0504, Banco de Espa�a.
    2. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.

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