So with this question I am unsure how to even do a binomial model with 2 risky assets never mind having n-steps. All the examples I’ve found are either not containing any risky assets or only have one. Every time I try to google it I get more confused and I really need some help.
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1$\begingroup$ Can you do a binomial model for one risky asset? Say a stock price today is 100, and one period from today, it can be either 99 or 101: that's your one period binomial model for one risky asset. Another risky asset, within the same probabilistic space, could be another stock (say the price today is 100 and one period from now it can be 102 or 98): just another binomial tree and you already have two assets in your system. Or the other risky asset could be (say) a call option on the first stock with strike price 100: in that case the option price at maturity would be either 1 or zero $\endgroup$– Jan StullerOct 31, 2020 at 16:46
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I see two possible paths for solving for the price of an option written on two underlying assets in a bi/multinomial tree.
1: Change to a stock measure and express the state space $S^{(1)}_t,S^{(2)}_t$ in terms of a common state variable $Z_t=\frac{S^{(1)}_t}{S^{(2)}_t}$. This is the Garman-Kohlhagen approach to pricing an option on two underlyings.
2: Set $U_i=e^{\sigma_i\sqrt{\Delta t}}$ as in the CRR model and find some probabilities $p_1,p_2,p_3,p_4,p_5$ such that $E(S^{(i)}_{t+\Delta t})=R$ as well as $V(S^{(i)}_{t+\Delta t})=R^2e^{\sigma_i^2\Delta_t}$ and $Cov(S^{(i)}_{t+\Delta t},S^{(j)}_{t+\Delta t})=R^2e^{\sigma_i\sigma_j\rho\Delta_t}$.
I found some recommendable course material on this on the pages of prof. Kwok, starting on p 311 here..
HTH?
answered Oct 31, 2020 at 18:48