Forecasting DAX Volatility: A Comparison of Time Series Models and Implied Volatilities

Abstract

This study provides a comprehensive comparison of different forecasting approaches for the German stock market. Additionally, this thesis presents an application of the MCS approach to evaluate DAX volatility forecasts based on high-frequency data. Furthermore, the effects of the 2008 financial crisis on the prediction of DAX volatility are analysed.

The empirical analysis is based on data that contain all recorded transactions of DAX options and DAX futures traded on the EUREX from January 2002 to December 2009. The volatility prediction models employed in this study to forecast DAX volatility are selected based on the results of the general features of the forecasting models, and the analysis of the considered DAX time series. Within the class of time series models, the GARCH, the Exponential GARCH (EGARCH), the ARFIMA, and the Heterogeneous Autoregressive (HAR) model are chosen to fit the DAX return and realised volatility series. Additionally, the Britten-Jones and Neuberger (2000) approach is applied to produce DAX implied volatility forecasts because it is based on a broader information set than the BS model. Finally, the BS model is employed as a benchmark model in this study.

As the empirical analysis in this study demonstrates that DAX volatility changes considerably over the long sample period, it investigates whether structural breaks induce long memory effects. The effects are separately analysed by performing different structural break tests for the prediction models. A discussion of the impact on the applied forecasting methodology, and how it is accounted for, is also presented. Based on the MCS approach, the DAX volatility forecasts are separately evaluated for the full sample and the subperiod that excludes the two most volatile months of the financial crisis. Because the objective of this work is to provide information to investment and risk managers regarding which forecasting method delivers superior DAX volatility forecasts, the volatilities are predicted for one day, two weeks, and one month. Finally, the evaluation results are compared with previous findings in the literature for each forecast horizon.

Umfassender Vergleich verschiedener Ansätze zur Prognose von Volatilitäten auf Basis des Model Confidence Set Ansatzes für den Deutschen Aktienmarkt