For delta to be exactly 50, it means that N(d1) = 50 -->d1 = 0, which solves that s has be below k by a discount factor involving r, t, var/2. Therefore, delta isn't 50 for spot or even slightly different for atm forward
Noobish Q: Why isn't the delta on ATM options always 50%?
- Thread starter mitchell_1
- Start date
M-maybe. Or your statement could be overly strong. Delta is actually a predictive rate of change of the option relative to the underlying. Actual mileage may vary (and does) because price is set by actual B/A and TnS.
I've frequently seen OTM options move far less than their deltas would suggest.
Robert Morse
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That occurs when a stock goes up, IVol drops, so OTM calls often do not match their delta. Then you have to take into account decay.
Try to understand the intuitive interpretations of N(d1) and N(d2)