Convergence
Also written Convergence of futures and spot · Price convergence
The certainty that a futures price and the spot price of its underlying meet at expiry — because on the last trading day the contract settles at the cash market price, leaving no room for a difference.
In plain language
Through its life a futures contract trades at a price of its own, above or below the spot. On expiry day that freedom ends.
The reason is not a rule someone imposed; it is arithmetic. A futures price is the market's estimate of the spot price at maturity. On maturity day, "the spot price at maturity" is simply today's spot price — there is nothing left to estimate. So the two prices must be the same number, and the workbook draws the conclusion directly: this is why all futures contracts on expiry settle at the underlying cash market price.
The gap that closes is the basis. Convergence is the statement that basis goes to zero at expiry, always, for every underlying.
How it works
Convergence is what makes hedging and arbitrage work at all.
- For the hedger: a short futures position against a cash holding pays off precisely because the two prices meet. If they could drift apart permanently, a hedge would be a second bet rather than an offset.
- For the arbitrageur: cash-and-carry arbitrage holds a long spot against a short futures to expiry and takes the mispricing as profit. The profit is certain because the prices converge. The workbook's own illustration makes both expiry cases produce an identical net gain of Rs 1,587 — the same number whether the stock rose or fell.
The path to zero varies. In a contango market the futures sit above spot, so the basis is negative on the NISM convention and rises to zero. In backwardation the futures sit below spot, the basis is positive, and it falls to zero. Either way the destination is fixed and the date is known.
That is the difference between a futures position and every other trade on the exchange: one of its two unknowns has a guaranteed answer.
The formula
Basis (NISM convention) = Spot price − Futures price
During the contract's life: Basis ≠ 0
On the expiry date: Futures price = Spot price, so Basis = 0
Carried to expiry, cash-and-carry arbitrage returns:
Profit = (Traded futures price − Fair futures price) × Lot size
A worked example
On 3 October 2025 the Nifty October futures close at 25,006.60 while the underlying index stands at 24,894.25. The contract expires on 28 October 2025. Lot size 65.
Basis today = 24,894.25 − 25,006.60 = −112.35 (negative: contango)
In money = 112.35 × 65 = Rs 7,302.75 per contract
Lock it in. Buy the index basket and short one futures contract today. Hold both to 28 October. Whatever the index does:
| Index on 28 Oct | Gain on spot | Gain on short futures | Total |
|---|---|---|---|
| 26,000 | +1,105.75 | −993.40 | +112.35 |
| 24,894.25 | 0 | +112.35 | +112.35 |
| 23,500 | −1,394.25 | +1,506.60 | +112.35 |
Rs 7,302.75 a contract, identical in every column, because on expiry day the futures price is the index. There is no scenario in which the basis survives.
The workbook makes the same point with the second expiry it works: the May 2024 index futures at 22,308.70 on 14 May 2024 is nothing more than the market's collective prediction of where the index closes on the last trading day of that contract — and on that day, prediction and outcome are the same number.
What the arbitrageur is not paid for: direction. What he is paid for is financing the basket from today to expiry, which is why the Rs 7,302.75 must be set against cost-of-carry before anyone calls it profit.
Why NISM asks about it
Chapter 15.8 (Price discovery and convergence of cash and futures prices on the expiry) states the principle and gives the May 2024 illustration; Chapter 17.1 relies on it for both cash-and-carry and reverse cash-and-carry arbitrage. Expect a conceptual question on what happens to the basis at expiry — it becomes zero — and an arbitrage computation held to maturity.
Common exam traps
- Convergence is about the basis, not about profit. The prices meet; whether you made money depends on where you opened the position.
- Basis is spot minus futures on NISM's convention. A futures price above spot therefore gives a negative basis, and the sign is examinable.
- Convergence happens on the expiry date, not gradually and predictably before it. The basis can widen mid-life.
- The workbook is inconsistent on the expiry day itself. Chapter 15 says Nifty and Bank Nifty futures expire on the last Tuesday, while its own May 2024 convergence example uses the last Thursday (30 May 2024); Chapter 16 gives Nifty options the last Tuesday and Sensex options a Thursday. Exchanges may now use either Tuesday or Thursday, uniformly, with prior SEBI approval. Answer with the day the question supplies.
- Cash settlement is a consequence of convergence, not a separate rule. Settling at the cash close is convergence.
- Arbitrage profit is certain only if the position is carried to expiry. Squared off early, the basis is whatever the market says it is.
Where this is taught
- Series V-D · Chapter 15: Introduction to Forwards and Futuresintroduced here
- Series XVI · Chapter 3: Commodity Futuresintroduced here
- Series IV · Chapter 3: Exchange Traded Interest Rate Futuresintroduced here
- Series I · Chapter 3: Exchange Traded Currency Futuresintroduced here
- Series V-D · Chapter 20: Exchange Traded Interest Rate Futures
Related terms
- BasisThe difference between the spot price and the futures price of an asset — positive when spot exceeds futures, negative when futures exceeds spot, and zero at expiry.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- Price discoveryThe process by which the free interaction of buyers and sellers produces a price that reflects every participant's expectation of what the underlying will be worth at a future date.
- UnderlyingThe asset a derivative contract derives its value from — the index, stock, bond or currency whose spot price drives the contract. The derivative has no value of its own without it.
- BackwardationA market in which the futures price sits below the spot price — the cost of carry says futures should be dearer, and something is overriding it.
- ContangoA market in which the futures price sits above the spot price, normally because the futures buyer is paying for the cost of carrying the commodity through to delivery.
- RolloverCarrying a derivatives position past expiry by closing the expiring contract and opening the same position in the next series simultaneously — the only way to hold a view longer than one contract cycle.
- Fair valueThe theoretical futures price — spot plus the cost of carrying the commodity to expiry — at which a buyer is indifferent between buying today and buying forward.
- ArbitragerA participant who locks a profit by entering opposite transactions in two markets at once — carrying no exposure and taking no view, and in the process pulling the two prices back together.