Forecasting Volatility:Evidence from the German Stock Market

Abstract

In this paper we compare two basic approaches to forecast volatility in the German stock market. The first approach uses various univariate time series techniques while the second approach makes use of volatility implied in option prices. The time series models include the historical mean model, the exponentially weighted moving average (EWMA) model, four ARCH-type models and a stochastic volatility (SV) model. Based on the utilization of volatility forecasts in option pricing and Value-at-Risk (VaR), various forecast horizons and forecast error measurements are used to assess the ability of volatility forecasts. We show that the model rankings are sensitive to the error measurements as well as the forecast horizons. The result indicates that it is difficult to state which method is the clear winner. However, when option pricing is the primary interest, the SV model and implied volatility should be used. On the other hand, when VaR is the objective, the ARCH-type models are useful. Furthermore, a trading strategy suggests that the time series models are not better than the implied volatility in predicting volatility.