The skew pattern of implied volatility in the DAX index options market

The aim of this paper is twofold: to investigate how the information content of implied volatility varies according to moneyness and option type and to compare the latter option based forecasts with historical volatility in order to see if they subsume all the information contained in the latter. We run a horse race of different implied volatility estimates: at the money and out of the money call and put implied volatilities and average implied that is a weighted average of at the money call and put implied volatilities with weights proportional to trading volume. Two hypotheses are tested: unbiasedness and efficiency of the different volatility forecasts. The investigation is pursued in the Dax index options market, by using synchronous prices matched in a one minute interval. The results highlight that the information content of implied volatility has a humped shape, with out of the money options being less informative than at the money ones. Overall, the best forecast is at the money put implied volatility: it is unbiased (after a constant adjustment) and efficient, in that it subsumes all the information contained in historical volatility.