I've got the following exercise for uni:
I have solved (a) but I'm really struggling with (b). I know that I'm looking for $V(0)$, where $V(t) = \tilde{E}[e^{-r(T-t)}1_{S(T)>K}|F(t)]$, but I'm not sure how to do this. In my book, the solution to the Black-Scholes-Merton formula is given, but this uses another payoff function $V$, so I don't think this is the key. Also, $\tilde{E}$, expectation under risk-neutral measure isn't really defined properly in my book, so I can't calculate it directly either. I'm kind of at a dead end here, could anyone help me with this? Any help is appreciated!!