The spot price of copper is $0.60 per pound. Suppose that the futures prices (dollars per pound)

are as follows:

3 months 0.59 6 months 0.57 9 months 0.54 12 months 0.50 The volatility of the price of copper is 40% per annum and the risk-free rate is 6% per annum.

Use a binomial tree to value an American call option on copper with an exercise price of $0.60 and a time to maturity of one year. Divide the life of the option into four 3-month periods for the purposes of constructing the tree. (Hint: As explained in Section 13.7, the futures price of a variable is its expected future price in a risk-neutral world.)