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A Joint Model for Returns and Realized Measures of Volatility: Considering Dependencies among Innovations

H. Qu, X.D. Li


Returns and volatilities of financial assets are critical considerations for investment and risk management. Most of the current research models returns and volatilities separately, implicitly assuming that their innovations are independent. We empirically investigate the dependency relationship among innovations of returns and realized measures of volatility using CSI-300 index 5-minute high-frequency data from 8 April 2005 to 23 May 2011. Based on the empirical results, we propose a joint model for returns and realized measures of volatility which characterizes the dependencies among innovations and provide the maximum likelihood estimation method. Empirical results confirm that the joint model effectively separates out the actual independent innovations and improves the parameter estimation performance.


realized volatility, continuous-time volatility, jump volatility, dependencies among innovations, joint model.

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