Augmented Real-Time GARCH : A Joint Model for Returns, Volatility and Volatility of Volatility

We propose a model that extends the RT-GARCH model by allowing conditional heteroskedasticity in the volatility process. We show we are able to filter and forecast both volatility and volatility of volatility simultaneously in this simple setting. The volatility forecast function follows a second-order difference equation as opposed to first-order under GARCH(1,1) and RT-GARCH(1,1). Empirical studies confirm the presence of conditional heteroskedasticity in the volatility process and the standardised residuals of return are close to Gaussian under this model. We show we are able to obtain better in-sample nowcast and out-of-sample forecast of volatility