I'm given the aforementioned parameters for a two-step binomial model where the underlying pays no dividend, $S_0=50$ and $T=2$. With this information I was able to calculate the risk-neutral probabilities ($p$) and I am able to set up the following binomial tree for stock prices:
I am asked to calculate the Futures price $F_0$ (not the contract price) using this binomial model.
I am also asked to calculate the expected value of the underlying at $T_2$ given the risk-neutral probabilities and compare this to the answer of the previous question.
I know I can get the forward price by pricing a zero-coupon bond (with payment = 1) at maturity for every state, then determining the current price of that bond ($B=0.8868$) using risk-neutral valuation and then derive the yield ($y=0.061899$) based on which the forward price must be $50*(1+0.061899)^2=56.38$
However, I assume that the forward price mustn't equal the futures price due to these varying interest rates given before.
Therefore, how would one go about calculating the Futures price and the expected value given risk neutral valuation?