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Pricing: cost of carry, basis, contango and backwardation

9 minute read · By Krishna Avadhani, Vestora Academy · Updated 18 October 2026

The fair futures price equals the spot price plus the cost of carrying the asset until expiry (interest, storage, insurance) minus any income it pays (dividends, convenience yield). For an index: F = S e^((r - q)T).

The basis is spot minus futures. It shrinks to zero at expiry (convergence). When futures prices are above spot and later months are higher, the curve is in contango, typical for stored commodities. When futures are below spot, it is backwardation, often a sign of current shortage.

In April 2020, WTI crude oil futures for May delivery settled at about minus $37 a barrel because storage at Cushing was nearly full and holders could not take delivery. It shows that physical-delivery contracts can do extreme things near expiry.

Formula

F = S x e^((r + storage - income) x T)
Index futures: F = S x e^((r - q)T)
Basis = Spot - Futures

Key takeaways

  • F = S x e^((r - q)T) for financial futures.
  • Contango: futures above spot; backwardation: below.
  • Basis converges to zero at expiry.

Check your understanding

1. Index 6,000, r = 4%, dividend yield 2%, T = 0.5 years. Fair futures ≈

  • 5,940
  • 6,000
  • 6,060
  • 6,240
Show the answer

6,060. 6,000 x e^(0.02 x 0.5) ≈ 6,060.

2. Why did WTI oil futures go negative in April 2020?

  • A data error
  • Storage was nearly full, so holders paid to avoid delivery
  • OPEC banned oil
  • Inflation
Show the answer

Storage was nearly full, so holders paid to avoid delivery. Physical delivery with no storage left forced sellers to pay buyers.

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General education only, not financial advice. Examples are illustrations. Rules, tax settings and products change; check official sources.