Modeling and Forecasting DAX Index Volatility

The recent introduction of the realized variance measure defined as the sum of the squared intra-daily returns stamped on some high frequency basis has spurred the research in the field of volatility modeling and forecasting into new directions. First, the realized variance is a much better estimate of the latent volatility than the sum of the weighted daily squared returns. As such it is better suited for comparing the out-of-sample performances of competing volatility models. Additionally, it can enter as a parameter in these models proving better information than the daily returns commonly used in the standard volatility models. These two innovations have been utilized in several recent papers. We extend this line of research by estimating and comparing a wide class of volatility models for the DAX index futures that use the realized variance or the daily returns. To give a new view of the question whether time series volatility models or implied volatility have better predictive power we estimate a model which incorporates both the historical realized variance and the historical implied volatility. Our results suggest that using realized variance leads to superior performance compared to the previous approaches. Also, the inclusion of the implied volatility produces a slight improvement.