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?

The upper bound for one year future price = $55.56

Explanation:

Let risk free rate be represented as x = 5% = 0.05

The cost of storing a barrel of oil, c = 3

The current value of storage cost, p = c / (eˣ) = 3 / (e0.05) = 2.853688

The upper bound for one year future price = (spot price + p) * e0.05 = (50+2.853688) * e0.05

52.853688*1.05127

= $55.56

Therefore, the upper bound for one year future price = $55.56

Answer: $55.56

Explanation:

Given the following;

Spot price per barrel = $50

Storage cost = $3 per barrel

Interest rate (i) = 5% (continously compounded)

Period (t) = 1

Upper bound future price.

Upper bound future price = spot price per barrel + storage cost

Storage cost per barrel = $3, compounded at 5 % per annum for one year.

5:100 = 0.05

Mathematically, present value of storage cost per barrel =

3e^ - (i * t) = 3e^ - (0.05*1)

3e^ - (0.05) = 2.854

Upper bound for one year future price

($50+$2.854) e^0.05*1

52.854e^0.05 = $55.56