Convergence (basis narrowing into expiry)

Convergence is the tendency of a futures price and the price of its underlying to come together as the contract approaches delivery, also called a narrowing of the basis. For cash-settled index futures it is exact by construction, since the final settlement is the index value; for physically delivered contracts it holds up to delivery costs and terms.

Senzoukria · Glossary · Updated September 2026

Definition

The CFTC glossary defines convergence as the tendency for prices of physicals and futures to approach one another, usually during the delivery month, and notes it is also called a narrowing of the basis. The logic is arbitrage: at delivery the futures contract becomes the underlying, so any remaining gap would be free money.

How the basis shrinks

For an equity index future, most of the basis is carry, and carry is proportional to the time left. If rates and dividend expectations do not change, the basis falls roughly in a straight line toward zero.

Worked example: 60 days before expiry the basis is +12.00 index points. With unchanged inputs, at 30 days it is about 12.00 × 30 / 60 = 6.00, and on the last day it approaches 0.

Consequences for a futures chart

  • An offset used to map cash-index levels onto ES or NQ is not a constant; it shrinks through the quarter.
  • At the roll the offset jumps back up, because the new contract has about three more months of carry.
  • Near expiry the expiring contract tracks the index almost exactly, while the next contract keeps its full carry.

Physically delivered contracts

For commodities, convergence is to the delivery terms: location, grade and timing set by the contract. A futures price can remain apart from a quoted spot price that refers to another place or quality. What converges is the futures price and the value of what can actually be delivered against it.

In Senzoukria

The application does not compute the basis. Levels derived from options are reported on their underlying with the spot at the snapshot time, and re-measuring the basis before each transposition is left to the trader, which is exactly what convergence requires: yesterday's offset is wrong today by roughly one day of carry.

Common mistakes

  • Keeping the same cash-to-futures offset for a whole week.
  • Expecting a physically delivered future to match a spot quote for a different grade or place.

In the same section

Sources

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Frequently asked questions

Does the basis reach exactly zero at expiry?
For cash-settled index futures the final settlement is set from the index, so the expiring contract ends on the index value by construction. For delivered contracts the futures price converges to the value of the deliverable, which may differ from a generic spot quote.
Why does my ES-to-SPX offset change every week?
Because carry is proportional to time to expiry and also moves with rates and dividends. Each week removes about a thirteenth of a quarter's carry, and a roll resets the offset to a new contract's full carry.

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