If a stock has zero vol and some positive drift $\alpha$ (in a BS-setting) and we delta hedge a long call option dynamically over a year with some positive implied volatility.... how would that work out for us?
Would the answer depend on how often we hedge, i.e. every day, month, week?
In usual circumstances, when we delta hedge, we make money everytime we get significant $\Delta S$s, due to the call options $\Gamma$ (gamma).
However in the case of positive $\alpha$, zero $\sigma$, $\Delta S$ is going to be huge, but .... do we then make huge amounts of money off of $\Gamma$?