$ While in the "function circumstance" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a bit) $begingroup$ For an alternative with selling price $C$, the P$&$L, with regard to adjustments of your underlying asset price tag $S$ and volatility $sigma$, is specified by Juice https://www.youtube.com/watch?v=qMmsQ4kKgY4