We assume we work in the risk-neural measure with a stock which pays no dividend and a continuous discount rate.
For PUT and CALL only: can someone please clarify if what I said is correct?
The intuitive answer is yes, because bigger volatility you are more likely to end up in a region that that is
I looked it up the wikipedia for the formula, but I am a bit lazy trying to prove it is positive
For a GENERAL PAY-OFF FUNCTION:
when is this still true? I would think it would be true for a monotone function or maybe a convex function? Does anyone know any exisiting literature on this?