2.1 The value (at maturity) of the futures contract is the stock price less the exercise price. If the process moved to node 2, the stock price is s2, so the future’s value is ƒ(2) = s2 – k. The other node is similar.
Then, recalling that q is (s1 exp(r δt) − s2)/(s3 − s2),
This is equal to e−r δt(s1er δt − k), which can be simplified to give V = s1 − ke−r δt. The only strike price which gives zero present value to the future is k = s1 exp(rδt).
2.2 The progression, in the first scenario, of the stock price and hedging strategy is ...