Explaining Pre- and Post-1987 Crash Asset Prices Within a Unified General Equilibrium Framework

47 Pages Posted: 5 Feb 2007 Last revised: 1 Jul 2011

See all articles by Luca Benzoni

Luca Benzoni

Federal Reserve Bank of Chicago - Research Department

Pierre Collin-Dufresne

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute; National Bureau of Economic Research (NBER)

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management; National Bureau of Economic Research (NBER)

Date Written: October 18, 2007

Abstract

The 1987 stock market crash occurred with minimal impact on observable economic variables (e.g., consumption), yet dramatically and permanently changed the shape of the implied volatility curve for equity index options. Here, we propose a general equilibrium model that captures many salient features of the U.S. equity and options markets before, during, and after the crash. The representative agent is endowed with Epstein-Zin preferences and the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. In reaction to a market crash, the agent updates her beliefs about the distribution of the jump component. We identify a realistic calibration of the model that matches the prices of short-maturity at-the-money and deep out-of-the-money S&P 500 put options, as well as the prices of individual stock options. Further, the model generates a steep shift in the implied volatility 'smirk' for S&P 500 options after the 1987 crash. This 'regime shift' occurs in spite of a minimal impact on observable macroeconomic fundamentals. Finally, the model's implications are consistent with the empirical properties of dividends, the equity premium, as well as the level and standard deviation of the risk-free rate. Overall, our findings show that it is possible to reconcile the stylized properties of the equity and option markets in the framework of rational expectations, consistent with the notion that these two markets are integrated.

Keywords: Volatility Smile, Volatility Smirk, Implied Volatility, Option Pricing, Portfolio Insurance, Market Risk, Individual Stock Options

JEL Classification: G12, G13

Suggested Citation

Benzoni, Luca and Collin-Dufresne, Pierre and Goldstein, Robert S., Explaining Pre- and Post-1987 Crash Asset Prices Within a Unified General Equilibrium Framework (October 18, 2007). Available at SSRN: https://ssrn.com/abstract=960982 or http://dx.doi.org/10.2139/ssrn.960982

Luca Benzoni (Contact Author)

Federal Reserve Bank of Chicago - Research Department ( email )

230 South LaSalle Street
Chicago, IL 60604
United States
312-322-8499 (Phone)

HOME PAGE: http://lbenzoni.frbchi.googlepages.com/

Pierre Collin-Dufresne

Ecole Polytechnique Fédérale de Lausanne ( email )

Quartier UNIL-Dorigny, Bâtiment Extranef, # 211
40, Bd du Pont-d'Arve
CH-1015 Lausanne, CH-6900
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management ( email )

19th Avenue South
Minneapolis, MN 55455
United States
612-624-8581 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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