Question

The spot price of oil is $50 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free (continuously compounded) interest rate is 5% per annum, continuously compounded. What is an upper bound for the one-year futures price of oil?

Answer 1

If one buys a barrel of oil by borrowing at the riskfree rate of 5% for one year

Amount repayable after one year = 50* e^(0.05*1) = $52.5636

and after one year pays the storage charges, the total amount required at the end of the year = 52.5636+3 = $55.5636

So, buying one barrel today at $50 is the same as buying the same barrel in One year futures at $55.5636

However, during the one year , depending on the buyer, the barrel of oil may give some convenience yield to the buyer having the possession of the oil barrel

Hence, the price will be less than or equal to $55.5636

So, the upper bound of the one year futures of oil is $55.5636 per barrel