A Switching ARCH Model for the German DAX Index

Abstract

This paper estimates a switching autoregressive conditional heteroskedastic time series model for returns on the daily German stock market index. Volatility clustering is captured by persistent periods of different volatility levels and by the dependence on past innovations. We introduce a leverage term to model the asymmetric response of volatility to shocks. Model specification and estimation is performed within a Bayesian framework using Markov Chain Monte Carlo simulation methods. Model diagnostics document a good fit of the switching ARCH model. The persistence of shocks in volatility coming from the autoregressive conditional part of the variance is considerably lower than that obtained using a GARCH(1,1) model. Our volatility estimate closely follows market implied volatility. When we compare the forecasting performance, switching ARCH turns out to be an unbiased estimator of realized volatility. Nevertheless, over all forecast horizons, model-based volatility forecasts do not add information about future volatility. Up to a 7-day horizon, market implied volatility already contains nearly all information.