Put-Call Parity and options\u2019 forecasting power

Numerous papers have investigated the forecasting power of Black-Scholes volatility versus a time series volatility forecast (see e.g. Poon (2005)). However, as far as we know, little is the evidence about the different information content of implied volatilities obtained from options with different type (call or put). Even if theoretically call and put options with the very same strike price and expiration date should yield the same implied volatility due to no arbitrage considerations, empirically there are many reasons that may cause call and put implied volatilities to differ (see e.g. Hentshle (2003), Buraschi and Jackwerth (2001)). The aim of this paper is twofold: to investigate how the information content of implied volatility varies according to 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. Two hypotheses are tested: unbiasedness and efficiency of the different volatility forecasts w.r.t. historical volatility. The investigation is pursued in the Dax index options market. Differently from previous studies, that use settlement prices, we are using the more informative synchronous prices, matched in a one minute interval. This is very important to stress, since our implied volatilities are real \u201cprices\u201d, as determined by synchronous no-arbitrage relations