Cost-of-carry forward
F(0,T) = S_0 exp((r - q)T)Financing raises the delivery price while income or convenience yield lowers it.
Foundations
Forwards and Futures Pricing (Cost of Carry)
Forwards and futures lock in a future price; cost-of-carry and convenience yield link them to today’s spot.
Mental model
Carry and financing connect today’s spot value with a price agreed for future delivery.
In a frictionless market without income, the forward price satisfies F(0,T) ≈ S₀ / DF(0,T): spot grown at the funding curve.
Cost-of-carry models adjust for storage, funding, income, and convenience yield, leading to F(0,T) = S₀ · exp((r + u − y)T) under continuous compounding.
Explore the mechanism
How do financing, income, and storage economics connect spot value to a future delivery price?
A forward price is today’s spot adjusted by carry: funding and storage push it up, convenience yield (or income) pulls it down. Turn on a “market quote” to see implied carry and a cash-and-carry sanity check.
Numbers
Net carry c = r + u − y ≈ 3.50% per year
Model forward F(0,T) at T=1.00 ≈ 103.56
Interpretation
The forward curve shape is governed by the sign of r + u − y. If funding and storage dominate, the curve tends to sit above spot. If convenience yield dominates, the curve can sit below spot (backwardation).
When you turn on the market quote, the “implied carry” is simply the carry that would make that quote consistent with the cost-of-carry relation. Large discrepancies usually mean either (i) data issues, (ii) missing carry terms, or (iii) a genuine cash-and-carry style opportunity once frictions are modelled.
UNDERSTAND
What to notice
In commodities, forwards and futures are the primary liquid objects; spot is often an illiquid delivery index derived from them.
Misaligned spot–forward–rate relationships signal data issues or true arbitrage opportunities such as cash-and-carry trades.
The quantitative structure
Notation
S_0- spot price today
F(0,T)- forward price for maturity T
r- continuously compounded financing rate
q- continuous income or convenience yield
This model assumes
- The asset can be financed, held, and where required shorted under the stated carry terms.
- Rates and yields in the formula are deterministic over the contract horizon.
A small example
A one-year financial forward
Spot is 100, the financing rate is 5%, and the continuous income yield is 2%.
- Net carry is 5% - 2% = 3%.
- Apply continuous carry: 100 * exp(0.03) = 103.05.
ResultThe no-arbitrage one-year forward price is approximately 103.05.
Where it appears
- hedging commodity and financial exposures
- checking futures curves for carry consistency
- valuing forward commitments
Where the intuition breaks
What this view leaves out
- Simple cost-of-carry formulas can fail when assets are difficult to short, storage is constrained, convenience yield varies, or credit and funding terms matter.
Common mistakes
“The forward price is the market forecast of the future spot price.”
Not quite.A forward price is primarily a no-arbitrage delivery price; it need not equal the expected future spot price.
Where this concept sits
Follow the strongest prerequisites, applications, extensions, and contrasts.
Connections for Forwards and Futures Pricing (Cost of Carry)
Forwards and Futures Pricing (Cost of Carry)YOU ARE HERE
Built onArbitrage and No-ArbitrageCost-of-carry pricing is derived by comparing replicating cash-and-carry strategies under no-arbitrage.
Built onDiscounting and Present ValueForward values compare spot and future cash flows on a common present-value basis.
Used byGas Storage OptionalityStorage value is driven by the ability to move inventory across time in response to forward and spot price spreads.
Used bySpark and Dark SpreadsForward spark and dark spreads are constructed from forward power, fuel and carbon prices.
Related toLocation and Basis Risk in Power MarketsBasis risk arises when the traded forward or futures contract does not perfectly match the location of the underlying exposure.
Built on · Arbitrage and No-Arbitrage
Cost-of-carry pricing is derived by comparing replicating cash-and-carry strategies under no-arbitrage.
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