Conditional Heteroskedasticity in the Volatility of Asset Returns

We propose a new class of conditional heteroskedasticity in the volatility (CH-V) models which allows for time-varying volatility of volatility in the volatility of asset returns. This class nests a variety of GARCH-type models and the SHARV model of Ding (2021b). CH-V models can be seen as a special case of the stochastic volatility of volatility model. We then introduce two examples of CH-V in which we specify a GJR-GARCH and an E-GARCH processes for the volatility of volatility, respectively. We also show a novel way of introducing the leverage effect of negative returns on the volatility through the volatility of volatility process. Empirical study confirms CH-V models have better goodness-of-fit and out-of-sample volatility and Value-at-Risk forecasts than GARCH-type models