Understanding Futures Pricing and Formula Mechanics

The Pricing Formula Introduction

If you are undertaking a conventional course on futures trading, the pricing formula would typically be discussed at the outset. We have chosen to address it later in our curriculum as for most individuals who trade futures based on technical analysis, there exists no pressing need to understand the pricing formula initially. This does not mean advanced knowledge proves unhelpful. However, if one wishes to trade using quantitative strategies such as Calendar Spreads or Index Arbitrage, then comprehending how futures prices are determined becomes essential. We shall delve into these strategies more comprehensively later in our dedicated module on Trading Strategies; this early discussion serves to establish a foundation for those studies.

The value of a futures instrument derives from the price of its underlying asset. The movement of the futures instrument follows that of the underlying, with declines in the latter resulting in corresponding decreases in the former. However, it proves important to note that their prices are not identical; presently, Nifty Spot trades at 22,385.60 whilst the current month contract is priced at 22,398.40. This difference between spot and futures prices is referred to as ‘the basis or spread’, and in this instance, it amounts to 12.8 points (22,398.40 – 22,385.60).

Understanding Spot-Future Parity

The ‘Spot–Future Parity’ constitutes the source of the price difference. Variables like interest rates, dividends, and time till expiry contribute to this phenomenon. It essentially represents a mathematical formulation to align the underlying cost with its respective futures cost. This arrangement is otherwise referred to as the futures pricing formula.

The futures pricing formula simply states:

Futures Price = Spot price × (1+ rf) – d

Where:

rf = Risk-free rate

d = Dividend

Take into account that the risk-free rate referred to here applies annually; if the duration until expiration differs, adjust the formula in accordance with the time period. Thus, a comprehensive formulation would be:

Futures Price = Spot price × [1+ rf × (x/365)] – d

Where:

x = number of days to expiry

The RBI’s 91-day Treasury bill can serve as an indication of the short-term risk-free rate. It remains obtainable from the RBI homepage, as demonstrated in the snapshot.

The image shows that the current rate stands at 7.1253%, and with this in mind, it’s time to analyse a pricing example: suppose ICICI Bank spot trades at 1,186.25 with just eleven days remaining until its expiry. What should the current month futures contract be priced at?

Calculation:

Futures Price = 1,186.25 × [1+7.1253% × (11/365)] – 0

ICICI Bank is not anticipated to dispense any dividend for the upcoming fortnight, thus I assumed it as zero. From this equation, the futures cost amounts to 1,188.85—known as the ‘Fair value’ of futures. In comparison, the current trading price of the futures contract is labelled as the ‘Market Price’, which can be observed from the image at 1,189.50.

The divergence between fair value and market price is mainly attributed to costs incurred in the market, including taxes, transaction fees, and margins. In most cases, this fair value reflects where futures contracts should trade at a given risk-free rate and number of days left until expiration. Now let us take this thought further and comprehend how we can determine mid- and far-month contract prices.

Mid-Month Calculation

The contract will terminate on 26th March 2025, with only 42 days until then.

Futures Price = 1,186.25 × [1+7.1253% × (42/365)] – 0

= 1,196

Far-Month Calculation

Number of days to expiry = 94 (as the contract expires on 30th April 2025)

Futures Price = 1,186.25 × [1+7.1253% × (94/365)] – 0

= 1,208

From the NSE website, let us examine the actual market prices.

It becomes evident that the fair value and market price are not identical, which can most likely be attributed to various costs. In addition, one should also consider financial year-end dividends that may be factored into the market price. Ultimately, with more time until expiry, it is expected that the divergence between these two values continues to grow.

Premium and Discount Terminology

In fact, this leads us to another important commonly used market terminology—the discount and the premium.

If the futures trade at a higher rate than the spot, mathematically speaking, this proves normal. It is described as ‘premium’ in the equity derivatives market, and ‘contango’ in the commodity derivatives market. Despite the different terms for it, both refer to a situation of futures trading higher than spot.

This plot displays the Nifty spot and correlated futures for January 2025. Throughout the series, you can observe that futures trade in excess of the spot.

Key Observations

I would like to direct your attention to these points. These points are important and should be noted:

At the outset of the series (signified by the initial point), there exists a wide gap between spot and futures. This occurs because the days left until expiry are considerable, which then yields a higher x/365 factor in the formulas used to calculate future prices.

Throughout the series, futures remained at a higher rate than the spot.

At the end of the series (highlighted by the final point), futures and spot will always converge, no matter what their relationship beforehand. This phenomenon constitutes an invariable reality.

If you don’t close your futures position before the expiry date, the exchange will execute it for you, and the settlement value will be determined by the spot price on that day, as the gap between futures and spot closes.

Backwardation Phenomenon

Sometimes futures do not trade more expensively than the spot. This typically occurs due to short-term demand and supply imbalances which can cause futures to sell for less than their spot figure. This phenomenon is known as ‘trading at a discount’ in equity parlance, or ‘backwardation’ in commodities terminology.

Understanding these futures pricing dynamics proves essential for advanced trading strategies and helps traders comprehend why price discrepancies exist between spot and futures markets. This knowledge becomes particularly valuable when identifying arbitrage opportunities or managing positions across different contract months within the derivatives market ecosystem.