# I’m trying to construct a binomial model that uses 2 risky model - number of steps varied

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.

• 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 Oct 31, 2020 at 16:46

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 $$Cov(S^{(i)}_{t+\Delta t},S^{(j)}_{t+\Delta t})=R^2e^{\sigma_i\sigma_j\rho\Delta_t}$$.