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The futures pricing formula calculates the fair value of a futures contract by adjusting the spot price of the underlying asset for interest expenses, estimated dividends, and time to expiry. It discusses why futures pricing and spot prices aren't always the same and how this discrepancy, called the cost of carry, varies over the course of the contract. Using this technique, market players may determine if a futures contract is trading at a premium or discount to its theoretical value, as well as comprehend price convergence as expiry approaches.
Key Takeaways
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Futures prices do move in line with the spot price of the underlying asset.
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Interest rates, dividends, and time to expiry are core inputs in the futures pricing formula.
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A premium or discount to spot occurs due to the cost of carry and market conditions.
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In India, the standard method used for estimating fair value for stock futures is the cost-of-carry model.
What Is the Futures Pricing Formula?
The futures pricing formula explains how the price of a futures contract is determined in relation to its underlying asset. In simple terms, a futures price is based on the current spot price, adjusted for factors such as interest rates, dividends, and time remaining until expiry. Since futures contracts settle at a later date, the formula accounts for the cost of holding the asset over that period.
This includes the opportunity cost of money and any income, like dividends, expected before expiry. The formula helps traders estimate a fair futures price and understand why it may trade at a premium or discount to the spot price.
Futures Price = Spot Price × [1 + rf × (days to expiry / 365) − dividend]
Where,
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Futures price (F): The agreed-upon cost for the asset's delivery at a given future date.
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Spot Price (S): The underlying asset's current market price for quick delivery.
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Rf: Risk-free interest rate is the annualised interest rate (such as the rate on U.S. Treasury bills) that represents the financing cost or opportunity cost of capital for keeping the asset.
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Number of days to expiry: The number of days remaining until the contract matures.
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Income or Dividends (d): The anticipated income from owning the asset prior to its expiration.
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Cost of Carry: After accounting for revenue, the net cost of keeping the asset until it expires.
The return on a Government of India security over the course of a year is represented by a risk-free rate, which also accounts for the cost of capital until the futures expire. This yearly rate is proportionately changed in futures pricing according to the number of days left until the contract expires.
Let’s discuss it with an example. To help with the calculation, we are assuming the following values.
The spot price of XYZ Corp. = ₹2,380.5
Risk-free rate = 8.3528%
Days to expiry = 7 days
Dividend = 0
Futures Price = 2,380.5 x [1+0.083528 ( 7/365)] – 0 = ₹2,384.32
We are assuming that the company isn’t paying a dividend on it; hence, we have considered it as zero. But if any dividend is paid, it will also factor into the formula.
This futures price formula gives you what is called the ‘fair value.’ The difference between fair value and market price is caused by taxes, transaction charges, margin, and such. Using this formula, you can calculate a fair value for any expiration days.
Mid-month calculation
The number of days to expiry is 34 days
2380.5 x [1+0.083528 ( 34/365)] – 0
Far-month calculation
The number of days to expiry is 80 days
2380.5 x [1+0.083528 ( 80/365)] – 0
Few More Things To Keep In Mind While Considering Futures Price
The price of a futures contract is the spot price of an underlying asset, adjusted for interest, time, and paid-out dividends.
The variance between the spot price and futures price forms the ‘basis of spread.’ The spread is the maximum at the beginning of the series, but converges towards the settlement date. The spot price and futures prices of an underlying are ideally equal at the expiration date.
Important Definitions Related to Pricing Futures Contract
Buying vs selling futures contracts: Futures are standardised legal agreements. The buyer has a long position, and the seller has a short position in the futures.
Clearing house: Futures are traded in an active market through an exchange, also called a clearing house. In India, the NSE Clearing Limited facilitates clearing and settlement for all trades executed on the NSE.
Margin requirement: Margin is the amount deposited in the clearing house by the parties. It acts as an assurance that parties will honour the contract when the time comes. Both parties need to deposit a margin at the beginning of the trade. Due to marking to market process, if the initial margin falls below the maintenance amount, the party receives a margin call.
Marking to market: It is a process to settle future prices daily. The futures price rise or fall daily because of active trading. Clearing houses have adopted a means to pay the price difference after each trading by debiting and crediting the differential amount from the margin amount deposited by the parties.
Understanding Futures Price Quote
Speculators are traders who get involved in futures trading in the active market. They aren’t looking to receive physical delivery of the commodity, but bet on market trends to secure profit from the deal. They base their biases on futures quotes, which a technical tools to predict future price movements.
The chart is an example of a futures quote chart. This chart contains all information regarding the futures contract, along with periodic price movement. At the very top, it mentions the name of the underlying commodity and expiration date. Apart from that, at the corner, you can check the current price and the index of price movement. Open and settlement prices are mentioned at the bottom of the graph.
What Is Arbitrage In Futures?
Futures arbitrage is a trading strategy in which one participant holds positions in both the spot and futures markets to profit from the price distinction between the futures price and its theoretical fair value. This difference is often caused by interest rates, dividends, or temporary demand-supply discrepancies. The strategy is also known as cash-and-carry arbitrage or reverse cash-and-carry arbitrage, based on market conditions.
In order to ensure that futures and spot prices converge as the contract nears expiration, arbitrage activity helps align futures prices with their fair value over time. While this strategy aims to capitalise on price inefficiencies, it is not without risks, including execution delays, transaction costs, margin requirements, liquidity limits, and regulatory circumstances.
Let’s understand with an example. Assume the following conditions for a stock futures contract:
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Spot price: ₹1,280.
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Risk-free interest rate: 6.68% per year
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Days till expiry: 22.
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Dividend expected before expiration: ₹0.
The theoretical futures price is derived as follows:
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Futures price = Spot × [1 + (r × t)].
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Futures price = 1,280 x [1 + (0.0668 x 22/365)].
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Futures pricing is at ₹1,285.16.
If the futures contract trades over ₹1,285.16, there may be a chance for cash-and-carry arbitrage.
Typical Arbitrage Positions:
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Buy the shares on the spot market.
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Sell the futures contract for the higher market price.
At expiry, spot and futures prices converge, and the arbitrage outcome is the difference between the futures selling price and the spot buying price, after accounting for expenses.
If the futures price falls below the spot price, a reverse cash-and-carry arbitrage situation might develop.
Typical Arbitrage Positions:
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Sell the stock in the spot market.
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Buy the futures contract at a lower price.
Price convergence at expiry enables the participant to capitalise on the original mispricing, subject to market and operational limits.
Also Read More: How Arbitrage Trading Works?
Important Things to Keep in Mind While Analysing Future Prices
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Track the spot price closely, as futures prices usually move in line with the underlying asset.
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Consider interest rates, since higher rates can push futures prices upward.
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Check the time to expiry, as prices tend to converge with spot prices near expiration.
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Factor in dividends, which can reduce futures prices for stocks.
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Temporary departures from the theoretical fair value may result from short-term supply-demand mismatches.
Different Futures Pricing Models
Different futures pricing models help traders understand how futures prices are formed in the market. The most common one is the cost-of-carry model, which factors in interest and holding costs. Another approach is the expectations model, where prices reflect future spot expectations. Markets may also show contango or backwardation based on demand, supply, and carrying costs.
Conclusion
Using the spot price, risk-free interest rate, estimated dividends, and time to expiry, the futures pricing formula offers a systematic method to determine the fair value of a futures contract.
Knowing this formula makes it easier to understand how prices converge as the contract gets closer to settlement and why futures can be traded at a premium or discount to spot. Market players may more effectively understand futures quotations and evaluate price variations in an organised, data-driven way by concentrating on these elements.
