Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in equation (34.3) with a = 0:05 and σ = 0:15. Construct a two-timestep tree for the price of wheat in a risk-neutral world.
A farmer has a project that involves an expenditure of $10,000 and a further expenditure of $90,000 in 6 months. It will increase wheat that is harvested and sold by 40,000 bushels in 1 year. What is the value of the project? Suppose that the farmer can abandon the project in 6 months and avoid paying the $90,000 cost at that time. What is the value of the abandonment option? Assume a risk-free rate of 5% with continuous compounding.
