$ Inside the "work scenario" you liquidate the portfolio at $t_1$ realising its PnL (allow me to simplify the notation somewhat) $begingroup$ For an alternative with value $C$, the P$&$L, with regard to modifications in the underlying asset price $S$ and volatility $sigma$, is specified by "hitparade.ch - Discographie PNL". https://www.youtube.com/watch?v=qMmsQ4kKgY4