FI 8360

Special Topics in Corporate Finance

Assignment 2

Due Monday, April 25

The table below presents spot- and forward prices for three commodities (corn, cocoa and coffee) as well as annualized risk-free interest rates at the close of trading on Monday, April 14 2003.[1]

  1. For each commodity, create two line chart with months on the X-axis and two price series on the Y-axis:
  2. The forward prices that actually appear in the chart above, and
  3. The forward prices that would occur if there were no costly storage or convenience yield on the commodity.
  1. Calculate the (annual) convenience yield or cost of storage for each of the five forward contracts on each of the three commodities, and clearly label each as either convenience yield or cost of storage.
  1. In a 12-step binomial tree, calculate the value of a one-year American call option on 1 ton of Cocoa with a strike price equal to $3,000. Assume that the risk-free rate of return is 1.5% per year, and that the volatility of returns on cocoa is 40%. Use the convenience yield/cost of storage implied by the 8-month forward in problem 2. Make sure to highlight the states of nature when early-exercise occurs.
  1. Redo problem 3, this time using the convenience yield/cost of storage on cocoa implied by the 3-month forward (from problem 2). What happened?
  1. Redo problem 3 one more time, this time setting the convenience yield on cocoa equal to zero. What happened this time?
  1. In a 12-step binomial tree, calculate the value of a one-year American put option on one pound of coffee with a strike price equal to 50 cents. Assume that the risk-free rate of return is 1.5% per year, and that the volatility of returns on coffee is 30%. Use the convenience yield/cost of storage implied by the 8-month forward in problem 2. Make sure to highlight the states of nature when early-exercise occurs.
  1. Redo problem 6, this time setting the convenience yield on coffee equal to zero. What happened here?

1

[1] Technically, these are actually futures prices; nevertheless, we will interpret them as forward prices for this exercise. Corn futures trade at the Chicago Board of Trade in lots of 5,000 bushels. Cocoa futures trade at the Coffee, Sugar and Cocoa Exchange in New York, and each contract is for 10 metric tons. Coffee also trades at the CSCE, with a lot size of 37,500 lbs. The rules of trading, including delivery points, premia or discounts associated with varying quality, testing, etc. are quite interesting. For Cocoa, see http://www.nybot.com/rulebooks/csce/viewable/L.%20Cocoa%20Trade%20Rules.htm; for coffee, see http://www.nybot.com/rulebooks/csce/viewable/K.%20Coffee%20C%20Rules.htm; and for an abbreviated description of the corn contract, see http://www.cbot.com/cbot/www/prod_detail/0,1499,14+58+138+10,00.html .