To determine the no-arbitrage futures price, we can use the cost-of-carry model. The cost-of-carry model incorporates the current spot price of the underlying asset, the cost of storing the asset (storage cost), and the cost of financing the asset (interest rate).
In the case of oil, the storage cost is $2, the interest rate is 5% (0.05 as a decimal), and the futures contract expires in 6 months, which is 0.5 of a year. The spot price of oil is $50.
The formula for the cost-of-carry model is:
Futures Price (F) = Spot Price (S) × (1 + (Storage Cost (c) + Interest Rate (r)) × Time (t))
In this case, we have:
F = 50 × (1 + (2 + 0.05 * 50) * 0.5)
We must first calculate the total cost term within the parentheses:
Cost Term = (1 + (2 + 0.05 * 50) * 0.5) = (1 + (2 + 2.5) * 0.5) = (1 + 4.5 * 0.5)
Cost Term = 1 + 2.25 = 3.25
Now we can plug the cost term into the formula to find the futures price:
F = 50 * 3.25
F = 162.50
So, the no-arbitrage price of the futures contract is $162.50