# Is the price of a binary call not monotonous with vol for OTM

Is this true and how would you prove it

• Did you mean "monotonic"? Nov 10 '14 at 11:15

and $\sigma$ vary upwards in steps of 0.01 starting at 0. It peaks around 0.04.
Differentiating $d_2$ with respect to $\sigma$ makes this behaviour obvious.