Question

You are given the following information:

The current price of copper is $83 per 100 lbs. The term structure of interest rates is flat at 5% per year continuously compounded. Assume there are no costs associated with storing copper and that the trader can borrow and lend at the riskless rate.The convenience yield for all maturities is 7% per year continuously compounded.

Consider a forward contract in which the short position has to make two deliveries: 10,000 lbs of copper in one month and 10,000 lbs of copper in two months. The common delivery price is P. That is the short receives P dollars for delivery after one month and another P dollars for delivery after two months.

Establish the fair value of this unusual forward contract. That is find the value for P. make sure to define all terms and to carefully explain how you arrived at your answer.

Answer 1

Now the fair price of P should be such that one should be indifferent between buying 20000 lbs today, and delivering them after one month and two months & shorting forward contracts of one and two months

So,

Present value of cost of buying 20000 lbs = $83*20000/100 = $16600

Present value of price Paid after one months and two months

=P*exp((-0.05+0.07)*1/12)+ P*exp((-0.05+0.07)*2/12)

(convenience yield is subtracted from riskfree interest rate to find the discounting factor)

=2.005007*P

Thus 2.005007*P = 16600

So, fair value of P = 16600/2.005007 = $8279.27