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

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  • David S. Bates

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.

Suggested Citation

  • David S. Bates, 1997. "Post-'87 Crash Fears in S&P 500 Futures Options," NBER Working Papers 5894, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:5894
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    1. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
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    Citations

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    Cited by:

    1. 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.
    2. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    3. Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2001. "Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices," Journal of Financial Economics, Elsevier, vol. 61(3), pages 345-381, September.
    4. 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.
    5. Marie Briere, 2006. "Market Reactions to Central Bank Communication Policies :Reading Interest Rate Options Smiles," Working Papers CEB 38, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. 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.
    8. 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.
    9. Harrison Hong & Jeremy C. Stein, 1999. "Differences of Opinion, Rational Arbitrage and Market Crashes," NBER Working Papers 7376, National Bureau of Economic Research, Inc.

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