Futures pricing ($F_{tT}={\mathbb{E}}_Q[S_T\mid {\mathcal{F}}_t]$)

With continuous cash settlement and a money-market risk-neutral measure, discounted futures gains have zero drift; under the necessary true-martingale integrability, the futures quote is a martingale ending at the terminal spot price. The forward contract discount-weighted expectation is a different valuation expression.

A futures contract delivery quote below current spot for the maturity considered, or a falling futures curve across maturities. This spot comparison should be distinguished from comparisons with the future physical-measure expected spot.

A futures contract delivery quote above the current spot price for the maturity considered; a rising quoted curve across maturities is also described as contango. This compares delivery prices rather than the current zero value of a newly settled contract.