I have daily Close data of ODAX-options, obtained from ivolatility.com. One third of the daily data shows premiums that are just above the inner value. Even when inserting an implied vola of almost zero into Black Scholes resulting premiums are higher than those shown in those data. That's quite surprising to me - although I have't analyzed historical options data before. Are those data to be conidered as nonsense/crap? If somebody has access to historical data fron another source I would be glad to do a crosscheck on a few data points.