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Derivative Products

Pricing Forwards & Futures

Future Value of a Cash Flow (FV)

Pricing a Futures Contract

To price a futures contract, we start by calculating the Future Value of the spot price of the commodity and adjust from there. The Deliverable grade of crude oil futures “WTI” has Sulfur: 0.42% or less by weight, and Gravity: Not less than 37 degrees nor more than 42 degrees (measured by API)

STEP ONE – pricing a futures contract

UNDERLYING WTI Crude Oil (deliverable grade )
MATURITY one month Crude Oil Futures Contract
SPOT PRICE OF CL $50 per barrel

STEP TWO transportation & storage costs

Other costs or income associated with the underlying asset adjust the Future Value number above.

  • If our underlying asset were a bond, then we would include the income of the coupon.
    • Storage of crude oil for one month
    • Transportation of crude oil for one month
  • Same with Stock Index futures where dividends are paid. But since we are pricing oil, we only have costs to add:

Transportation by Sea requires a bit of background, so this example will keep us on dry land. Due to larger tankers, investment in canals and other issues, historical numbers skew the cost of transporting oil. To get our futures Price and presume our oil will travel by pipeline from Calgary to Cushing, Oklahoma and stored for the remaining days. The total cost of storage and transportation for 30- days will be $3.78 per barrel. To make our calculation easier, convert it to an annual percentage figure: $3.78/$50.00 = 7.56%.

Hedging Crude Oil Risk

Hedging using futures is done using the SIMPLE HEDGE RATIO or the OPTIMAL HEDGE RATIO. The simple hedge ratio is more focused on the timing of the hedge. The Optimal Hedge Ratio also wants to adjust for the difference in volatility & correlation between the futures & the exact grade/location of crude oil the hedger buys (sells). Example: Let’s assume a refiner is looking to hedge his crude oil purchases beginning in April 2017. Recall the refiner buys crude oil to convert it into gasoline and heating oil. Our refiner needs to purchase a total of 150 million barrels of crude oil over four months from May to August 2017. REFINER’S SIMPLE HEDGE = 150,000,000/1000 = 37,500 contracts each month from May, June July & August. REFINER’S SIMPLE HEDGE: BUY 37,500 May, June, July & August Crude Oil Futures.

Optimal Hedge Ratio

Let’s continue with the same example used to calculate the simple hedge ratio and introduce the concept of optimal hedge ratio. Our refiner still needs to purchase 150 million barrels over four months beginning in May 2017. But in reality, the crude he will purchase is Gulf Coast crude oil. His refinery is along the gulf coast and it’s easier for him to take delivery at that port. To hedge using the futures contracts we need to adjust for two major variables.

  1. The difference in volatility between the two crude oils and
  2. The correlation between the two types of crude oils

We need to adjust for both of these variables because even though we expect all oils to move in the same direction, if the two oils are less than +.985 correlated, the futures are not likely to be the most efficient hedge. Volatility measures something very different. Volatility measures the magnitude of price returns. If we buy too many contracts we will be over-hedged. If the price of WTI goes down more than we expected we will lose money using futures as our hedge. Adjusting for both of these variables the futures will mimic the performance of Calgary Crude.

Relative Volatility
WTI 29%
Relative Volatility = 89.7%
Positive Correlation = +.99

If you’d like to learn more about Commodities forward curves, physical versus futures arbitrage and others topics, they will be covered in Our Learning Center

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