In theory, as time till expiration increases, ITM and OTM options should asymptotically approach absolute value of 0.5 (half unity). I am looking at DJX Dec 2008 put options. Today, 5/18/2007, DJX is at 135.57. The ITM put with strike of 136 has delta of -0.253; and the 147 put has delta of -0.498. My question is, why does the 136 ITM put have delta less than 0.5 in magnitude, and why it take such far depth in-the-money to have delta close to |0.5|? What am I missing? Something else strange, too. I recall a few days ago, extreme ITM call on something (SPY or some index) had theta of close to negative one (-1), and extreme ITM put had theta close to zero, 0. I had expected both extreme ITM call or put to have theta close to zero. It was on IB Option Trader. I am unable to explain why. Any comments?