Forecasting conditional volatility of returns by using the relationship among returns, trading volume, and open interest in commodity futures markets

Sang-Hak Lee, Purdue University


The current evidence on the empirical relationship between asset returns, trading volume, and open interest in futures markets is largely inconclusive, and the literature on the theoretical and empirical links between return volatility and volume and open interest are even more limited. The purpose of this study is to examine these relationships for 59 futures contracts traded on US and UK exchanges. The bivariate LARCH model of returns and trading volume, the bivariate LARCH model of returns and open interest, and the trivariate LARCH model (returns, volume and open interest) are estimated to examine the statistical relationship among the variables and to compare volatility forecast performance. The univariate LARCH and EGARCH models serve as reference models. The relationship between returns per se and volume is inconclusive, but the relationship between absolute returns and volume is stable and consistently positive. These findings are consistent with the results reported in the literature. Further, returns and volume exhibit a more consistently positive and significant relationship than returns and open interest, but the results suggest that open interest contains distinct information relative to trading volume. Two forecast performance measures are used to compare the volatility forecasts from alternative low-order univariate and multivariate LARCH models. The univariate LARCH model exhibits the smallest prediction error, the univariate EGARCH model has second-smallest prediction error for returns per se, and the bivariate GARCH model with volume has the second-smallest prediction error model for absolute returns. Overall, the results suggest that the univariate GARCH models that do not incorporate volume or open interest information perform well in forecasting return volatilities. However, the differences in the magnitudes of the forecast performance measures are small, and the performance rankings are not uniform across different performance measures or different benchmark criteria. Consequently, a general conclusion on the overall forecasting performance of the competing models cannot be drawn, and the findings suggest that forecast performance may depend on contract-specific factors. Although the multivariate GARCH models may provide improved return volatility forecasts, the gains are largely dependent on context and may be small relative to the univariate GARCH models.




Foster, Purdue University.

Subject Area

Agricultural economics

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