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

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  • David S. Bates
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    Abstract

    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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    Bibliographic Info

    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

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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. 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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    5. 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.
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    7. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
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    9. Stein, Jeremy, 1989. " Overreactions in the Options Market," Journal of Finance, American Finance Association, vol. 44(4), pages 1011-23, September.
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    11. Dumas, Bernard J & Fleming, Jeff & Whaley, Robert E, 1996. "Implied Volatility Functions: Empirical Tests," CEPR Discussion Papers 1369, C.E.P.R. Discussion Papers.
    12. 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.
    13. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," NBER Working Papers 5500, National Bureau of Economic Research, Inc.
    14. 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.
    15. 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.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    17. 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.
    18. Grossman, Sanford J & Zhou, Zhongquan, 1996. " Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
    19. 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.
    20. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
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    Citations

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    Cited by:
    1. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Centre de Recherche en Economie et Statistique.
    2. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    3. Eduardo Walker, 2002. "The Chilean Experience in Completing Markets with Financial Indexation," Central Banking, Analysis, and Economic Policies Book Series, in: Fernando Lefort & Klaus Schmidt-Hebbel & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Serie (ed.), Indexation, Inflation and Monetary Policy, edition 1, volume 2, chapter 9, pages 259-294 Central Bank of Chile.
    4. 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.
    5. David Bates & Roger Craine, 1998. "Valuing the Futures Market Clearinghouse's Default Exposure During the 1987 Crash," NBER Working Papers 6505, National Bureau of Economic Research, Inc.
    6. Harrison Hong & Jeremy C. Stein, 1999. "Differences of Opinion, Rational Arbitrage and Market Crashes," NBER Working Papers 7376, National Bureau of Economic Research, Inc.
    7. Liu, Jun, 2001. "Dynamic Choice and Risk Aversion," University of California at Los Angeles, Anderson Graduate School of Management qt36v1d9zg, Anderson Graduate School of Management, UCLA.
    8. Joseph Chen & Harrison Hong & Jeremy C. Stein, 2000. "Forecasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Prices," NBER Working Papers 7687, National Bureau of Economic Research, Inc.
    9. Marie Briere, 2006. "Market Reactions to Central Bank Communication Policies :Reading Interest Rate Options Smiles," Working Papers CEB 38, ULB -- Universite Libre de Bruxelles.

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