Strategic Financial Management · Interest Rate Derivatives

Interest Rate Futures: Pricing, Margins and Hedging

Updated 11 October 2026 · Fact-checked

An interest rate future is an exchange-traded contract to buy or sell a notional bond or T-bill at a fixed price on a future date. Price it by cost of carry: spot plus financing cost minus coupon income. To hedge, sell futures if you lose when rates rise, buy if you lose when rates fall.

Understand Interest Rate Futures

An interest rate future is a standardised contract traded on an exchange. Its underlying is a notional debt instrument, such as a government bond or a T-bill. You agree today on a price. Delivery or cash settlement happens on a fixed future date. Because the underlying is a debt instrument, the futures price moves opposite to interest rates. When rates rise, bond and T-bill prices fall, and so does the futures price.

This gives you a simple rule for direction. A short futures position (you sell) gains when rates rise. A long futures position (you buy) gains when rates fall. A borrower who fears higher rates sells futures. An investor who fears lower reinvestment rates buys futures.

Pricing follows the cost of carry idea. If you buy the bond now and sell it forward, you pay the spot price and fund it at the market rate. You also receive any coupon during the period. So the fair futures price is the spot price grown at the financing rate, less the future value of the coupons received. If the market price differs, an arbitrage profit exists. Buy the bond and sell the future if the future is too dear. Do the reverse if it is too cheap. Short-rate contracts on T-bills or deposits are often quoted as 100 minus the annualised rate, so a price of 93.00 implies a rate of 7%.

Exchanges collect margins. Initial margin is paid when you open the position. The position is marked to market every day, and the gain or loss (variation margin) is settled daily. If your balance falls below the maintenance level, you must top it up. This daily settlement removes most credit risk. It is also the main practical difference from a FRA, which is a private over-the-counter contract settled once, at the start of the interest period. A FRA can be tailor-made in amount and date. A future has fixed contract sizes and dates, so the hedge is rarely perfect. The gap between the spot-based exposure and the futures price is called basis risk.

Key rules to remember

Cost of carry price (coupon bond): F = S × (1 + r × t) − FV of coupons; S is the full (dirty) spot price, r the financing rate p.a., t the time in years. Coupons are carried forward at the reinvestment rate to the futures expiry date. Adjust for accrued interest and conversion factor only if the question gives them.
Price and rate for rate futures: Futures price = 100 − futures rate (%); Used for T-bill or deposit-rate contracts. A fall in price means a rise in the implied rate.
Value of one basis point: Value of 1 bp = Notional × 0.0001 × (contract period in days ÷ day-count basis); For a 3-month contract on ₹1 crore, 1 bp = ₹1,00,00,000 × 0.0001 × 3/12 = ₹250. Use the day-count basis the question gives.
Number of contracts (rate hedge): N = (Exposure ÷ Contract size) × (Exposure period ÷ Contract period); Scale for both amount and time. A ₹10 crore exposure for 6 months needs twice as many 3-month contracts as one for 3 months.
Number of contracts (price-sensitivity hedge): N = (PVBP of portfolio) ÷ (PVBP of one futures contract); PVBP is the rupee change in value for a 1 bp change in yield. The duration form is N = (D of portfolio × value of portfolio) ÷ (D of futures × value of one futures contract).
Gain or loss on a futures position: Short: (Entry price − Exit price) × contract size; Long: (Exit price − Entry price) × contract size; For price-quoted rate contracts, convert the price move into bp and then into rupees using the value of 1 bp.
Effective hedged rate: Effective rate = Rate paid in the market − Futures gain (as a rate) or + Futures loss; If the hedge is perfect, the effective rate equals the rate locked in by the futures price.

How to solve Interest Rate Futures questions

Use this order for any interest rate futures question, whether it asks for pricing, a hedge or a final cost.

1Identify the exposure. Decide whether you are a borrower or lender, the amount, the start date and the period. Ask: do I lose when rates rise or when they fall?
2Choose the position. If you lose when rates rise (borrowing, or holding bonds), sell futures. If you lose when rates fall (future investment or reinvestment), buy futures.
3Find the futures price or implied rate. For rate contracts, rate = 100 − price. For bond futures, compute the fair price by cost of carry, with coupons carried forward.
4Compute the number of contracts. Scale for both the amount and the period, or use PVBP or duration if the question gives them. Round to a whole number of contracts.
5Work out the futures gain or loss from the change in price. Convert the basis-point move into rupees using the value of 1 bp and multiply by the number of contracts.
6Work out the cash market result. Compute the actual interest cost or income at the new rate.
7Combine both results to get the net outcome and the effective rate. Compare it with the unhedged result.
8State a clear conclusion. Mention any basis risk, margin requirement or rounding that leaves the hedge imperfect.

Quickest way: Direction, count, bp, net

When to use it: Use this for a hedging numerical where the futures price move is given and you need the net cost. It also works as a check on a longer answer.

Write the direction: borrower or bond holder sells, future investor buys.
Count contracts: (amount ÷ contract size) × (months ÷ contract months).
Take the price move in bp (for example 93.00 to 91.50 is 150 bp).
Multiply: contracts × bp × value of 1 bp = futures gain or loss.
Compare with the extra interest in the cash market. In a perfect hedge they are equal and the net rate equals the original futures-implied rate.

Common mistakes in Interest Rate Futures

Buying futures when the company is a borrower fearing a rate rise.
Students link 'rate rise' with 'buy' instead of thinking about the price. Futures prices fall when rates rise.
Fix: Think in prices. A borrower needs a gain when the price falls, so the borrower sells futures. Write 'rates up, price down, short gains' before you start.
Ignoring the time scaling when counting contracts.
Students divide the exposure by the contract size and stop there.
Fix: Multiply by (exposure period ÷ contract period). A 6-month exposure with 3-month contracts needs double the contracts.
Mixing up price change and rate change.
The quote is 100 minus the rate, so a drop from 93.00 to 91.50 looks like 1.5 rupees rather than 150 bp.
Fix: Convert every price move into basis points first (1.00 in price = 100 bp), then use the value of 1 bp.
Using the clean price and leaving out coupon income in cost of carry pricing.
Students copy the stock futures formula and forget that a bond pays coupons during the contract life.
Fix: Start from the full (dirty) price, add financing cost, and subtract the coupons carried forward at the reinvestment rate up to expiry.
Claiming the hedge is perfect.
Textbook numbers often give a perfect result, so students assume it always happens.
Fix: State that contract sizes are fixed, the expiry may not match your dates, and the cash rate may not move one-for-one with the futures rate. This is basis risk. Mention it in the conclusion.
Treating futures like a FRA and ignoring margins.
Both lock in a rate, so students treat them as the same.
Fix: Note that futures need initial margin and daily variation margin, so cash flows occur every day. A FRA is settled once, at the start of the interest period, and has no daily margin.

Worked examples

Example 1

Anand Textiles Ltd will borrow ₹10,00,00,000 for 3 months, starting 3 months from now. It fears rates will rise. 3-month interest rate futures with a notional value of ₹1,00,00,000 are quoted at 93.00. When the loan is taken, the market borrowing rate is 8.5% p.a. and the futures price is 91.50. Show how the company hedges and find the effective borrowing cost. Ignore margins and basis risk.

Show the solution

Exposure: the company is a borrower and loses when rates rise, so it sells futures.
Implied rate at the start: 100 − 93.00 = 7.00% p.a.
Number of contracts = (₹10,00,00,000 ÷ ₹1,00,00,000) × (3 ÷ 3) = 10 contracts.
Price move: 93.00 − 91.50 = 1.50 = 150 bp, which is a gain for the short position.
Value of 1 bp per contract = ₹1,00,00,000 × 0.0001 × 3/12 = ₹250.
Futures gain = 10 × 150 × ₹250 = ₹3,75,000.
Interest on the loan at 8.5% = ₹10,00,00,000 × 8.5% × 3/12 = ₹21,25,000.
Net interest cost = ₹21,25,000 − ₹3,75,000 = ₹17,50,000.
Effective rate = ₹17,50,000 ÷ ₹10,00,00,000 × 12/3 = 7.00% p.a.

Answer: Sell 10 contracts. The futures gain of ₹3,75,000 offsets the extra interest, so the net cost is ₹17,50,000, an effective rate of 7.00% p.a., the rate locked in by the futures price. Unhedged, the cost would have been 8.5%.

Example 2

A government bond has a full (dirty) spot price of ₹104 per ₹100 face value. A futures contract on this bond expires in 6 months. The financing and reinvestment rate is 8% p.a. (simple interest). The bond pays a coupon of ₹4 after 2 months. Find the fair futures price. If the futures contract trades at ₹106, state the arbitrage action and profit per ₹100. Ignore accrued interest at delivery and conversion factors.

Show the solution

Cost of buying and carrying the bond for 6 months = 104 × (1 + 0.08 × 6/12) = 104 × 1.04 = ₹108.16.
The coupon of ₹4 is received after 2 months and reinvested for the remaining 4 months.
Future value of coupon = 4 × (1 + 0.08 × 4/12) = 4 × 1.026667 = ₹4.1067.
Fair futures price = 108.16 − 4.1067 = ₹104.0533, about ₹104.05.
Market futures price ₹106 is higher than ₹104.05, so the future is overpriced.
Arbitrage: borrow at 8%, buy the bond at ₹104 and sell the futures at ₹106.
At expiry, deliver the bond and receive ₹106. Repay the loan, net of the carried coupon, at an effective cost of ₹104.05.
Profit = 106 − 104.0533 = ₹1.9467, about ₹1.95 per ₹100 face value.

Answer: The fair futures price is about ₹104.05. At ₹106 the future is overpriced, so buy the bond and sell the future (cash-and-carry), earning about ₹1.95 per ₹100 face value with no price risk.

Exam tips

Write the direction of the position and the reason in one line first. Examiners give marks for the logic even if the arithmetic slips.
Show the conversion from price move to basis points and then to rupees. Many students lose marks by jumping straight to the final figure.
For comparison questions on FRA and futures, give three points: exchange-traded vs OTC, daily margining vs single settlement, standard vs tailor-made terms. Add basis risk for futures.
In MCQs, check the sign: for a short position, a falling price means profit. Eliminate options that give the wrong direction first.
End a hedging answer with the effective rate or net cost and a one-line comment on residual basis risk.

Practice questions from Interest Rate Derivatives

Interest Rate Futures in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Interest Rate Futures: frequently asked questions

How do I hedge with interest rate futures?

First decide whether you lose when rates rise or fall. Borrowers and bond holders sell futures. Investors who will reinvest later buy futures. Then compute the number of contracts by amount and period, and add the futures gain or loss to the cash market result.

What is the difference between a FRA and interest rate futures?

A FRA is a private over-the-counter agreement on a rate for a future period, with the amount and dates tailored to you, and it is settled once. Interest rate futures are exchange-traded with fixed sizes and dates, and they are marked to market daily with margins. Futures carry basis risk because they rarely match your exposure exactly.

Why does the futures price fall when interest rates rise?

The underlying is a bond or T-bill. When market rates rise, the present value of its fixed payments falls, so the price falls. For rate contracts quoted as 100 minus the rate, a higher rate means a lower price directly.

How is a bond futures price calculated in the exam?

Use cost of carry. Take the full spot price, grow it at the financing rate for the period, and subtract the future value of the coupons received before expiry. If the question gives accrued interest or a conversion factor, adjust for them as stated.