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 option-based forecasts with historical volatility. The different information content of implied volatility is examined for the most liquid at-the-money and out-of-the-money options: put (call) options for strikes below (above) the current underlying asset price. 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. It was found 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.