Price discovery and convergence of cash and futures prices on the expiry

Price discovery is the process through which market participants collectively determine the most probable future price of an underlying asset, such as an equity index, by trading its futures contracts. In the Indian context, the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) provide a transparent order‑book where supply and demand for futures interact with the spot market, leading to a market‑driven futures price.

The futures price reflects not only the current spot price but also the cost of carrying the position until expiry – this includes the risk‑free rate, expected dividend yield, and any financing or storage costs (the latter is negligible for equities). Because the price is set by participants, the concept is called "price discovery" rather than a price being imposed by an authority.

For the NISM exam, you will often be asked to identify which factor influences price discovery the most, or to calculate the fair value of a futures contract using the cost‑of‑carry model. Remember that price discovery is a dynamic process; the futures price updates continuously as new information arrives, which is why the spot‑futures relationship changes over time.

• Key driver: interaction of spot market expectations with financing costs.
• Exam tip: focus on the cost‑of‑carry components rather than the underlying's historical price alone.

The formula shows that the futures price is the spot price adjusted for the net cost of holding the position until expiry. In Indian equity futures, the dividend yield (d) is subtracted because shareholders receive dividends, reducing the cost of carry.

When the risk‑free rate (r) rises, the fair futures price increases, reflecting higher financing costs. Conversely, a higher expected dividend yield pushes the futures price lower. The term \(e^{(r+u-d)T}\) captures continuous compounding, which is the method used by SEBI for marking‑to‑market calculations.

Exam relevance: NISM frequently asks you to compute the fair value of a futures contract and then compare it with the quoted market price to identify arbitrage opportunities. Remember to convert percentages to decimals and express time in years.

The basis measures the deviation between the actual market futures price and the spot price. A positive basis (spot > futures) often indicates backwardation, while a negative basis (spot < futures) signals contango. In Indian equity futures, contango is more common because financing costs usually exceed dividend yields.

As the contract approaches expiry, the time component \(T\) in the cost‑of‑carry formula shrinks, causing the exponent to approach zero. Consequently, the theoretical futures price converges toward the spot price, and the basis moves toward zero. This convergence is the cornerstone of arbitrage: if the market futures price deviates significantly from the fair value, traders can lock in risk‑free profits.

For the exam, you may be asked to state the expected sign of the basis at a given time or to calculate the basis and infer whether an arbitrage opportunity exists. Always remember that at expiry, the basis must be zero (ignoring transaction costs).

At the moment of expiry, the futures contract is settled by physical delivery or cash settlement based on the final settlement price, which is the spot price of the underlying index on the expiry day. Because the settlement price equals the spot price, the futures price and spot price become identical – the basis collapses to zero.

Arbitrageurs enforce this convergence. If the futures price is above the spot price shortly before expiry, a trader can sell the futures, buy the underlying in the cash market, and lock in a profit after accounting for financing costs. The opposite trade is executed when futures trade below spot. These actions push the two prices together.

SEBI mandates daily marking‑to‑market of futures positions, which means unrealised gains and losses are realised each day. This daily settlement accelerates convergence because any persistent price gap is immediately reflected in margin requirements, discouraging large deviations.

1. Using simple interest instead of continuous compounding – the syllabus specifies the exponential form \(e^{(r+u-d)T}\). Using \(1 + (r+u-d)T\) yields a small error that can cost marks.

2. Forgetting to convert percentages to decimals – 6% must be entered as 0.06. A common slip is to plug 6 directly into the formula.

3. Assuming basis is always positive – Indian equity futures often trade in contango, giving a negative basis.

4. Ignoring the effect of dividend yield – dividends reduce the cost of carry and can flip the sign of the exponent.

5. Overlooking SEBI’s daily marking‑to‑market rule – it forces convergence faster than a theoretical model without daily settlement would suggest.

SEBI mandates that all futures contracts be marked‑to‑market at the end of each trading day. The daily settlement price is derived from the underlying index's closing value, ensuring that the futures price never drifts far from the spot price without triggering margin calls.

This regulatory framework reinforces price discovery because any large deviation instantly affects the margin requirement, prompting participants to trade and restore alignment. It also guarantees that at expiry the futures price equals the spot price, satisfying the convergence principle.

Exam relevance: Questions may reference SEBI’s marking‑to‑market rule when asking why convergence is guaranteed, or they may present a scenario where a trader’s margin call forces a position to be closed before expiry, affecting the realized basis.