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When Cost of Carry Determines Futures Prices—and When It Does Not

Article Quant Q&A · Author: Aksel
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Summary

The document distinguishes futures contracts whose prices are constrained by arbitrage from those whose prices are harder to model. For a storable commodity with an observable spot price and no convenience yield, the cost-of-carry relationship can determine the futures price through arbitrage. The key idea is that the model's usefulness depends on its underlying market conditions being satisfied.

When those conditions do not hold, the response offers no alternative formula. It characterizes the futures price as reflecting the market's expectation of the commodity's delivery-date value, potentially adjusted by a risk premium. In that setting, expectations alone do not imply a unique price, and the response says the price can vary widely. The explanation is brief: it does not quantify risk premia, describe how to estimate expectations, or compare pricing approaches across different assets and market structures.

Key ideas

  • Cost of carry can pin down futures prices through arbitrage when its assumptions hold.
  • The stated assumptions include a storable commodity, an observable spot price, and no convenience yield.
  • Outside those conditions, the response gives no universal alternative pricing formula.
  • Market expectations of delivery-date value may be reflected in futures prices with a risk premium.

Tags

FuturesCommoditiesArbitrageCarry
Full text
# Which methods are there to determine the price of futures contracts?


# Which methods are there to determine the price of futures contracts?












Which method apart from the cost of carry model exists, and which works best in real life? How does the market expectations impact on the futures price?

## Answer by Alex C (score 2)

https://quant.stackexchange.com/a/43630

When the required conditions are fulfilled ( a storeable commodity, an observable spot price, no "convenience yield") the cost of carry model determines the futures price by arbitrage.

Otherwise, to my knowledge, there is no alternative model. The futures price will just be the market's expectation (possibly plus or minus a risk premium) of what the commodity will be worth at the delivery date. In other words it can be just about anything in that case.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.