for an expiring European in-the-money (ITM) call (delta = 0.9), if $T$ increases from 1 to 30, what should delta be now?
Let's say $K = 100$, $S_0 = 105$, $\sigma = 10%$.
Intuitively I think the delta would decrease since now there is more time for the option to move out of money, and we are less certain it would end ITM.
However BS pricing formula's $\mathcal{N} \left( d_1 \right)$ section seem to suggest that increased T would have a positive effect?