The Exponential HEAVY Model: An Improved Approach to Volatility Modeling and Forecasting

This paper proposes an Exponential HEAVY (EHEAVY) model, which specifies the dynamics of returns and realized measures of volatility in an exponential form. The model ensures positivity of volatility and allows for asymmetric effects without restrictions on parameters, hence is more flexible. A joint quasi-maximum likelihood estimation and closed-form multi-step ahead forecasting is derived. The EHEAVY model is applied to 31 assets from the Oxford-Man Institute's realized library, and the empirical results demonstrate that return volatility dynamics are driven by the realized measure, while the asymmetric effect is captured by the return shock. The out-of-sample forecast results show that the EHEAVY model has superior forecasting performance compared the HEAVY, AHEAVY, and realized EGARCH models. The portfolio exercise further confirms the superior economic value of the EHEAVY model, as measured by the certain equivalent return and expected utility.