$ In the "do the job scenario" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a little) $begingroup$ For a possibility with rate $C$, the P$&$L, with respect to alterations with the fundamental asset price $S$ and volatility $sigma$, is specified by Juice journal's https://pnl02334.blogozz.com/33213347/indicators-on-pnl-you-should-know