$ From the "operate circumstance" you liquidate the portfolio at $t_1$ realising its PnL (allow me to simplify the notation a bit) $begingroup$ For an option with price tag $C$, the P$&$L, with regard to modifications in the fundamental asset price tag $S$ and volatility $sigma$, is specified by PNL https://www.youtube.com/watch?v=qMmsQ4kKgY4