$ In the "do the job situation" you liquidate the portfolio at $t_1$ realising its PnL (allow me to simplify the notation a bit) $begingroup$ For a choice with value $C$, the P$&$L, with regard to alterations of your underlying asset value $S$ and volatility $sigma$, is specified by In https://www.youtube.com/watch?v=qMmsQ4kKgY4