I wonder, what would happen if we use the binomial tree to price exchange option, an option to exchange one asset for another at the expiry date. Payoff is $\max(S_1-S_2,0)$
For instance, I have two assets whose payoff are the following: $\begin{bmatrix}1.1&0.9\\1.1&1.1\\0.9&1.1\end{bmatrix}$, and $S_0^1=100$ and $S_0^2=95$, risk free rate is $R_f=4\%$ and $T=6$
How to deal with the one more dimension? My intuition is to use the binomial tree as usual. However, it is difficult to tell how many possible paths lead to a payoff, given that I have listed all possible combination of payoffs of asset 1 and 2.