$ Within the "work scenario" you liquidate the portfolio at $t_1$ realising its PnL (let me simplify the notation a little bit) $begingroup$ For an option with cost $C$, the P$&$L, with respect to changes in the fundamental asset price tag $S$ and volatility $sigma$, is supplied by David has https://www.youtube.com/watch?v=qMmsQ4kKgY4