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

60 Pages Posted: 18 Jul 2000 Last revised: 11 Aug 2022

See all articles by David S. Bates

David S. Bates

University of Iowa - Department of Finance; National Bureau of Economic Research (NBER)

Date Written: January 1997


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

Bates, David S., Post-'87 Crash Fears in S&P 500 Futures Options (January 1997). NBER Working Paper No. w5894, Available at SSRN:

David S. Bates (Contact Author)

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