Forecasting Volatility with Time-Varying Leverage and Volatility of Volatility Effects

The prediction of volatility is of primary importance for business applications in risk management, asset allocation and pricing of derivative instruments. This paper proposes a novel measurement model which takes into consideration the possibly time-varying interaction of realized volatility and asset returns, according to a bivariate model aiming at capturing the main stylised facts: (i) the long memory of the volatility process, (ii) the heavy-tailedness of the returns distribution, and (iii) the negative dependence of volatility and daily market returns. We assess the relevance of "volatility in volatility"and time-varying "leverage" effects in the out-of-sample forecasting performance of the model, and evaluate the density forecasts of the future level of market volatility. The empirical results illustrate that our specification can outperform the benchmark HAR-RV, both in terms of point and density forecasts.