Question

An oil importer is thinking to hedge against future pric He decided to enter into a Long futures oil Contract, given the Current spot price is $60/barrel, and each barrel requires $2 storage Cost per barrel every two months. if The - Contract matures in 9 months, the free rate is given at 4% per annum Compounded quarterly. After 4 months the oil price is realized at $75/barrel, and the storage cost agreement has charged to become 3% of the oil price paid annually, and the interest rate has also charged to 5% annually Contineously Compounded What is the Value of the Contract?

Answer 1

Assumption: Storage Cost is Payable at the BEGINNING of every 2 months AND at the end of 8th month FULL storage Cost will be Payable.

Value of Forward Contract at the time of entering = [Spot Price+PV of Cost of Carry]*Future Value Factor

where,

Spot Price = $60

PV of Cost of Carry = 2*(Sum of PV Factors of every Payment) = 2*[1+e^(-0.04/6) + e^(-0.04/3) + e^(-0.04/2) + e^(-0.04/0.6667)] = 2*[1+0.9967+0.9868+0.9802+0.9737](from table) = 9.8748

Future Value Factor = e^(0.04*9/12) = 1.0305(from table)

Therefore, Value of Contract = [60+9.8748]*1.0305 = $72.006

Value of Forward Contract after 4 months = Spot Price*e^(Risk Free Rate-Storage Cost)

where,

Spot Price = $75

e^(Risk Free Rate-Storage Cost) = e^[(0.05-0.03)*5/12] = e^0.00833 = 1.00833(from table)

Therefore, Value of Contract = 75*1.00833 = $75.62475