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Forward and Futures Pricing

Forward price, no carry
F=S erTF = S\,e^{rT}

Spot carried to delivery at the financing rate. Storage and income change the exponent and never the argument.

for an asset with no income or storage cost. With them:

F=S e(r+c−y)TF = S\,e^{(r + c - y)T}

The derivation, which is one paragraph

Two ways to hold the asset at time TT:

  1. Enter a forward at FF and pay at maturity.
  2. Borrow SS now at rate rr, buy the asset, and repay SerTSe^{rT} at maturity.

Both end with the asset and no risk taken. By the law of one price they must cost the same, so F=SerTF = Se^{rT}.

That is the entire argument. Nothing about expected future prices enters, which is the point worth carrying.

Key takeaway

A forward price is not a forecast. It is today's price adjusted for the cost of carrying the asset, and an upward-sloping curve says storage and financing are expensive, not that prices are expected to rise.

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