The relation between implied and realised volatility in the DAX index options market

The aim of this paper is to investigate the relation between implied volatility, historical volatility and realised volatility in the DAX index options market. Since implied volatility varies across option type (call versus put) we run a horse race of different implied volatility estimates: implied call and implied put. Two hypotheses are tested in the DAX index options market: unbiasedness and efficiency of the different volatility forecasts. Our results suggest that both implied volatility forecasts are unbiased (after a constant adjustment) and efficient forecasts of future realised volatility in that they subsume all the information contained in historical volatility.