In this article, we study the market of the Chicago Board Options Exchange S&P 500 three-month variance futures that were listed on May 18, 2004. By using a simple mean-reverting stochastic volatility model for the S&P 500 index, we present a linear relation between the price of fixed time-to-maturity variance futures and the VIX 2 . The model prediction is supported by empirical tests. We find that a model with a fixed mean-reverting speed of 1.2929 and a daily-calibrated floating long-term mean level has a good fit to the market data between May 18, 2004, and August 17, 2007. The market price of volatility risk estimated from the 30-day realized variance and VIX 2 has a mean value of Ϫ19.1184.
In this paper, we study the market of the CBOE S&P 500 three-month variance futures that were listed on May 18, 2004. By using a simple mean-reverting stochastic volatility model for the S&P 500 index, we present a linear relation between the price of fixed time-to-maturity variance futures and the V IX 2 . The model prediction is supported by empirical tests. We find that a model with a fixed mean-reverting speed of 1.2929 and a daily-calibrated floating long-term mean level has a good fit to the market data between
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