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Post-'87 Crash Fears in S&P 500 Futures Options

  • David S. Bates
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    This paper shows that post-crash implicit distributions have been strongly negatively skewed, and examines two competing explanations: stochastic volatility models with negative correlations between market levels and volatilities, and negative-mean jump models with time-varying jump frequencies. The two models are nested using a Fourier inversion European option pricing methodology, and fitted to S&P 500 futures options data over 1988-1993 using a nonlinear generalized least squares/Kalman filtration methodology. While volatility and level shocks are substantially negatively correlated, the stochastic volatility model can explain the implicit negative skewness only under extreme parameters (e.g., high volatility of volatility) that are implausible given the time series properties of option prices. By contrast, the stochastic volatility/jump-diffusion model generates substantially more plausible parameter" estimates. Evidence is also presented against the hypothesis that volatility follows a diffusion.

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    File URL: http://www.nber.org/papers/w5894.pdf
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    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5894.

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    Date of creation: Jan 1997
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    Publication status: published as Journal of Econometrics, Vol. 94, nos. 1/2 (2000): 181-238.
    Handle: RePEc:nbr:nberwo:5894
    Note: AP
    Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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    Web page: http://www.nber.org
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    1. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
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    3. Grossman, Sanford J & Zhou, Zhongquan, 1996. " Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
    4. 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.
    5. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," NBER Working Papers 5500, National Bureau of Economic Research, Inc.
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    8. Franks, Julian R & Schwartz, Eduardo S, 1991. "The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options," Economic Journal, Royal Economic Society, vol. 101(409), pages 1460-75, November.
    9. 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.
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    11. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    12. George, Thomas J. & Longstaff, Francis A., 1993. "Bid-Ask Spreads and Trading Activity in the S&P 100 Index Options Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(03), pages 381-397, September.
    13. 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.
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    15. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    16. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    17. Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 57-74, March.
    18. Stein, Jeremy, 1989. " Overreactions in the Options Market," Journal of Finance, American Finance Association, vol. 44(4), pages 1011-23, September.
    19. Mohammed M. Chaudhury & Jason Wei, 1994. "Upper bounds for american futures options: A note," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 14(1), pages 111-116, 02.
    20. Dumas, Bernard J & Fleming, Jeff & Whaley, Robert E, 1996. "Implied Volatility Functions: Empirical Tests," CEPR Discussion Papers 1369, C.E.P.R. Discussion Papers.
    21. Schmalensee, Richard & Trippi, Robert R, 1978. "Common Stock Volatility Expectations Implied by Option Premia," Journal of Finance, American Finance Association, vol. 33(1), pages 129-47, March.
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