$ In the "do the job scenario" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a bit) $begingroup$ For an option with rate $C$, the P$&$L, with regard to adjustments of the fundamental asset cost $S$ and volatility $sigma$, is given by The above https://www.youtube.com/watch?v=qMmsQ4kKgY4