For all problems where a risk free rate or a dividend yield is given, assume that the interest rate and the dividend yield are annual and continuously compounded rates.

A futures contract price is currently $1000 and its volatility is 20%. The risk-free interest rate is 4% per year. Use a two-step binomial tree to calculate the value of a one-year European call option on the futures contract with a strike price of $1005. What futures position should you take today to hedge the option if you sold it and the option was written on 100 futures contracts? Explain your answers with the appropriate calculations. Printouts from Derivagem will not receive full credit without the appropriate calculations.