# Price futures option via replication

I ran into some difficulties when trying to price a futures option via replication in a simple one-period binomial model. I am quite aware that this is easy with risk-neutral probabilities and backward calculation but I cannot see how to price it via replication.

The question with which I am confronted - $\textit{no}$ homework, just to be sure - is to price via replication in a one-period binomial model a European call option which matures in 3 months on a futures contract with strike price $K = 20$ and current futures price of 30. The volatility of the futures price is 30% p.a. and the risk-free rate 5%.

What I did was to approximate the up- and down-factors $u$ and $d$ for the future price development which gives me 34.855 in the upper node and 25.8212 in the down node. What I somehow have to do now is to set up a replication portfolio of some underlying asset (e.g. stocks, futures, risk-free investments) which will have the same value in $t = 1$ as the derivative. But how do I do that with futures? I don't have any other information about a stock or the maturity of the given future contract.