How do I price a commodity forward using the cost of carry model?

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AcadiFi · Accepted Answer

The cost-of-carry model for commodity forwards extends the financial forward formula by adding storage costs (u) and subtracting convenience yield (y). The continuous-compounding version is F = S * e^((r + u - y) * T)...

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Worked example: Suppose Kestrel Metals has spot copper at $8,400/ton, a one-year risk-free rate of 4%, annualized storage cost of 1.8%, and convenience yield of 2.5%. The one-year forward is F = 8,400 * e^((0.04 + 0.018 - 0.025) * 1) = 8,400 * e^0.033 = $8,682/ton.

Interpret each term intuitively: r is the opportunity cost of capital tied up in the spot commodity, u reflects warehousing and insurance for holding the physical good, and y captures the non-monetary benefit of holding inventory (such as avoiding stockouts during supply disruptions). When y exceeds r + u, the forward curve slopes downward (backwardation). When y is small relative to carry costs, the curve slopes upward (contango).

For no-arbitrage enforcement, remember the inequality F <= S * e^((r + u) * T) holds as an upper bound because investors without access to the physical commodity cannot short-sell to enforce equality. This asymmetric bound is a key distinction from financial forwards where y = 0 and arbitrage is symmetric.

How do I price a commodity forward using the cost of carry model?

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