Sorry if it's a duplicate but i didn't find an answer to my simple question in the other posts.
Let say we short a call option on a stock. $K = 100$, $C = 1$, $S = 100$ and $\Delta = 0.5$. No dividends or transaction fees. We buy 0.5 stock then our portfolio $\Pi = -1 + 50 = 49$. If the stock goes to 101, the call worths theoretically 1.5 so we have $\Pi = -1.5 + 50.5$. Also, $\Delta = 0.6$ now. But due to the convexity, C = 1.6 and $\Pi = -1.6 + 50.5 = 48.9$ our $PnL = -0.1$
If the stock goes by to 100 and the call to 1, is the only way to "erase" the PnL of -0.1 not to hedge by buying 0.6 stock at 101 ? Or even if we don't hedge, the PnL will be realized also at 100 ? If the latter, why ?