A futures price is currently $3000 and its volatility is 25%. The risk-free interest rate is 5% per annum.

a) Use a two-step binomial tree to derive the value today of a one-year European put option with a strike price of $2900 written on the futures contract.

b) Use put-call parity to value the one-year European call option with a strike price of $2900 written on the futures contract.

c) How would you hedge today a short position in the put option? Derive the futures position you would take.