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.
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.
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.
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.
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.