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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.