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We examine stock market volatility before and after the introduction of equity index futures trading in twenty-five countries using various models that account for asynchronous data, conditional heteroskedasticity, asymmetric volatility responses, and the joint dynamics of each country's index with the world market portfolio. We find that futures trading is related to an increase in conditional volatility in the United States and Japan, but in nearly every other country, we find either no significant effect, or volatility-dampening effect. This result appears to be robust to model specification, and is corroborated by further analysis of the relationship between volatility, trading volume and open itnerest in stock index futures. We also document an increase in conditional covariance between country-specific and world returns at the time of futures listing.

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