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Do S&P 500 index options violate the martingale restriction?

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  • Norman Strong
  • Xinzhong Xu

Abstract

The study tests Longstaff's martingale restriction on S&P 500 index options over the period 1990–1994. Assuming the S&P index follows a lognormal distribution results in systematic violations of the martingale restriction, the implied index value from options consistently overestimating the market value. Adopting a generalized distribution, allowing for nonnormal third and fourth moments, produces economically insignificant rejections of the martingale restriction. A simulation analysis supports the empirical results from the lognormal model in the presence of nonnormal skewness and kurtosis. Overall, the results support the conclusion that the no‐arbitrage assumption coupled with the generalized distribution offers a good working model for S&P index options over the period studied. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 499–521, 1999

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  • Norman Strong & Xinzhong Xu, 1999. "Do S&P 500 index options violate the martingale restriction?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(5), pages 499-521, August.
    • Handle: RePEc:wly:jfutmk:v:19:y:1999:i:5:p:499-521
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    Cited by:

    1. Ching-Ping Wang & Hung-Hsi Huang & Chien-Chia Hung, 2011. "Implied Index And Option Pricing Errors: Evidence From The Taiwan Option Market," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 5(2), pages 115-125.

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