I have two assets, $S_1$ and $S_2$, which follow geometric Brownian motion processes. This implies that both $S_1$ and $S_2$ have a lognormal distribution.
I'm trying to get the exchange option price formula through the risk neutral valuation, or, in other words $$C(t,S_1,S_2)=e^{-r(T-t)}E(\max\{S_1-S_2,0\})$$.
How do I calculate the expected value $E(\max\{S_1-S_2,0\})$??
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