Realized volatility in the futures markets

Abstract Using intraday returns on four futures contracts over a 5-year period, we calculate and analyze model-free measures of futures return volatility. We focus on the temporal characteristics and distributional properties of daily returns, return volatilities, (log of) standard deviations, standardized returns and pairwise correlations. The behavior of a number of tests for Gaussianity under long memory is explored via a simulation study. The simulation results indicate that tests of the “goodness-of-fit” variety are appropriate to use while the commonly employed Jarque–Bera test is severely oversized and its use is not recommended. We find that the standard deviations and the pairwise correlations exhibit long memory while the standardized returns are serially uncorrelated. We also find that the (unconditional) distributions of daily returns' volatility are leptokurtic and highly skewed to the right while the distributions of the standardized returns, the standard deviations and the pairwise correlations are statistically indistinguishable from the Gaussian distribution. Our results are consistent with that of Andersen et al. [Journal of the American Statistical Association 96 (2001a) 42; Journal of Financial Economics 61 (2001c) 43] on the time-series properties of realized volatility. The dynamic characteristics of the volatility series are modelled using fractionally integrated ARMA models.

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