A simple joint model for returns, volatility and volatility of volatility

We propose a model that allows for conditional heteroskedasticity in the volatility of asset returns and incorporates current return information into the volatility nowcast and forecast. Our model can capture all stylised facts of asset returns even with Gaussian innovations and is simple to implement. Moreover, we show that our model converges weakly to the GARCH-type diffusion as the length of the discrete time intervals between observations goes to zero. Empirical evidence shows that our model has a better fit, a more efficient parameter estimator as well as more accurate volatility and VaR forecasts than other common GARCH-type models.