Question

Consider a forward contract for 1,000 barrels of crude oil with one year to delivery. The current spot price of oil is $60 per barrel, oil costs $4 per barrel to store for a year (paid in advance), and the risk-free rate is 5% annually. Assume that there are no benefits to holding oil at the current time.

What is the fair price for the forward contract? Give your answer in dollars per barrel, round to the nearest penny.

Answer 1

We use cost of carry model inorder to find the future price

According to cost of carry model the

Future price = Spot price + Cost of Carrying

Here cost of carrying involves investment in crude oil and investment in storage cost

Hence cost of carry = $60 * 5% * 1000( Cost to invest in oil)

And also storage cost = 4*1000 + 4 * 1000 * 5% ( Storage cost and interest cost on the same)

= 60,000 * 0.05 + 4000 * 0.05 + 4000

= 3200 + 4000

= 7200

Hence the carrying cost will be 7200 for 1000 barrels

Now the spot price is 60* 1000 = 60,000 per 1000 barrels

Hence the Total future price = 60,000 + 7200

= 67200

So the fair pice per barrel will be 67200/1000 = 67.2 per barrel