$ While in the "work scenario" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a tad) $begingroup$ For an alternative with price $C$, the P$&$L, with respect to variations from the underlying asset selling price $S$ and volatility $sigma$, is given by This text https://www.youtube.com/watch?v=qMmsQ4kKgY4