Interest Rate Derivatives: FRAs, Futures, Options and Swaps

The traditional methods of the last topic reduce interest rate risk but cannot remove it where assets and liabilities do not match. For the rest, the financial markets offer derivatives built on interest rates, which work in the same way as the currency instruments but fix a rate of interest instead of a rate of exchange.

A forward rate agreement fixes the rate on a future loan or deposit; an interest rate future does the same through a standardised exchange-traded contract; an interest rate option, in the form of a cap or a floor, protects against an adverse move while leaving the benefit of a favourable one, for a premium; and an interest rate swap changes a floating-rate liability into a fixed-rate one, or the reverse.

None of them requires the company to change its actual borrowing. This topic explains each (how a bank derives a forward interest rate, how a forward rate agreement settles, the pricing and use of interest rate futures, caps and floors, and swaps), with worked calculations, and how to choose between them, as the last topic of the course.

It brings together the ideas of the course on risk, return and the choice between a fixed and an uncertain outcome.

The syllabus asks candidates to explain the methods of hedging interest rate risk. Read interest rate risk and traditional hedging first.

Forward rate agreements

A forward rate agreement (FRA) is a forward contract for an interest rate. It is arranged with a bank over the counter and fixes the rate for a future interest period on a notional loan or deposit: no money is lent or borrowed under the FRA, and only a settlement payment is made.

A 3v9 (or 3/9) FRA fixes the rate for a six-month period starting in three months; a 2v5 FRA for a three-month period starting in two months.

How a bank derives a forward rate

Banks can fix a forward interest rate because they can borrow and lend in the money market. If a bank can borrow for nine months at 24% and deposit for three months at 22%, the interest on ₦1 borrowed for nine months is 24% × 9 ÷ 12 = 18%, giving 1.18; the deposit grows to 1 + 22% × 3 ÷ 12 = 1.055 after three months. The rate needed on lending from month 3 to month 9 is (1.18 ÷ 1.055 − 1) = 11.85% for six months, or 23.70% a year.

That is the forward rate, from which the bank quotes a bid and an offer.

Buying and selling, and settlement

• A company that will borrow in the future buys an FRA to fix its cost (the bank quotes the higher rate). A company that will deposit sells one (at the lower rate).
• At the start of the notional period the benchmark rate is compared with the FRA rate. If the benchmark is higher than the FRA rate, the seller pays the buyer; if lower, the buyer pays the seller. The payment is the difference in rates × the notional amount × the length of the period (in practice discounted, since it is paid at the start rather than the end of the period).

Example (borrower). A company will need to borrow ₦3bn for three months starting in two months. A bank quotes the 2v5 FRA at 24.60% – 24.40%; the company buys at the higher 24.60%. It can borrow at the benchmark plus 1.5%. At the fixing date the benchmark is 27.00%. The seller pays (27.00 − 24.60)% × 3bn × 3 ÷ 12 = ₦18,000,000 (about ₦16.9m if discounted at the benchmark).

The loan costs 28.5% × 3bn × 3 ÷ 12 = ₦213,750,000, so the net cost is ₦195,750,000, an effective rate of 195.75 ÷ 3,000 ÷ 0.25 = 26.10%, which is the FRA rate plus the margin, 24.60 + 1.5. If the benchmark had fallen to 22.00%, the company would pay the bank (24.60 − 22.00)% × 3bn × 0.25 = ₦19.5m, but its loan at 23.5% would cost only ₦176.25m; the total is again ₦195.75m, 26.10%. The FRA fixed the rate either way, and the company gave up the benefit of the fall.

1. If the benchmark at the fixing is 23%, the buyer pays the company (25.80 − 23.00)% × 2bn × 6 ÷ 12 = ₦28m
2. the deposit earns 23% × 2bn × 0.5 = ₦230m, together ₦258m, which is 25.80% for the six months.

Interest rate futures

Interest rate futures are standardised, exchange-traded contracts that work like FRAs but with fixed sizes, periods and dates (short-term contracts cover a three-month period starting on a standard date, usually in March, June, September or December). The price is 100 minus the interest rate: a price of 74.50 means 25.5%. So when interest rates rise the futures price falls.

• A borrower fears a rise in rates, which would lower the price; so it sells futures now, and buys back later at the lower price for a profit that offsets the extra interest.
• A depositor fears a fall, which would raise the price; so it buys futures now and sells later at the higher price.
• A tick is 0.01% (one hundredth of a percentage point, 0.0001), and its value on a three-month contract is contract size × 3 ÷ 12 × 0.0001.
• The number of contracts must be a whole number, and there is basis risk: the futures price may not move exactly with the rate the company pays.

1. Contracts = 2bn ÷ 100m = 20; the company sells 20.
2. A tick is worth 100m × 3 ÷ 12 × 0.0001 = ₦2,500.
3. Rates rise by 2.5 points and the price falls to 72.00.

The company buys back at 72.00, a gain of 2.50 points = 250 ticks, so 250 × 2,500 × 20 = ₦12,500,000, which exactly offsets the extra interest of 2bn × 2.5% × 3 ÷ 12 = ₦12.5m. (If rates had fallen, the futures would lose and the cheaper loan would offset it.)

Interest rate options: caps and floors

An interest rate option gives the right but not the obligation to borrow or lend at a stated rate. A cap protects a borrower: if the floating rate rises above the strike, the seller pays the difference; if it stays below, nothing is paid and the borrower enjoys the lower rate. A floor protects a depositor in the same way against a fall.

The buyer pays a premium at the start.

Example: a company with a ₦3bn six-month floating loan buys a cap at 26% for a premium of 0.4% of the notional amount, ₦12m. If the rate at the reset is 29%, the cap pays (29 − 26)% × 3bn × 6 ÷ 12 = ₦45m, so the net gain is ₦33m and the effective rate is capped at 26% plus the premium; if the rate is 24%, the cap is worth nothing, the company has lost the premium and gained from the lower rate.

A combination of a cap and a floor (a collar) lowers the net premium by giving up some of the benefit.

Interest rate swaps

An interest rate swap is an agreement to exchange interest payments on a notional principal in the same currency, usually a fixed rate against a floating rate. There is no exchange of principal. A company with a floating-rate loan that wants certainty enters a pay-fixed, receive-floating swap: it keeps paying the floating rate to its lender, receives floating from the swap counterparty (cancelling it) and pays the fixed rate.

Example: ₦5bn loan at the benchmark plus 2%; swap fixed rate 25%. If the benchmark is 23%, the loan costs 25% (₦1,250m); the company pays 25% and receives 23% on the swap, a net payment of 2% × 5bn = ₦100m, so the total is ₦1,350m, which is 27%. If the benchmark is 28%, the loan costs 30% (₦1,500m) and the swap pays the company 3% (₦150m), the total is again ₦1,350m, 27%.

The effective rate is fixed at the swap rate plus the margin, 25% + 2%. Swaps run for longer periods than FRAs or futures (several years) and are arranged with banks; the main risk is the counterparty’s default.

Choosing the instrument

The ideas in more depth

Why an FRA settles on a notional amount

The company still borrows from its own bank at the benchmark plus a margin. The FRA is a separate bet on the benchmark, and its payment compensates for the difference between the actual and the agreed rate. Because the loan costs more when rates rise and the FRA pays more at the same time, the two cancel; the opposite when rates fall.

The company ends with the FRA rate plus its margin whatever happens. That is why an FRA, like a forward exchange contract, gives certainty and no benefit from a favourable move.

Why option protection costs a premium

A cap gives the borrower the best of both outcomes: protection against a rise and the benefit of a fall. Since the seller bears the risk of paying out and gets none of the upside, it charges a premium at the start. The premium is rarely recovered if rates stay low, so the choice is between a certain price and an uncertain gain, as with the currency options.

Sources and references

• Interest rate derivatives are arranged through banks and recognised exchanges, under the Securities and Exchange Commission and Central Bank of Nigeria rules; the rates, contract sizes and prices in the examples are illustrative. International Financial Reporting Standard (IFRS) 9 deals with hedge accounting, and IFRS 7 with the disclosure of risk.

These points are stated as at 5 November 2026.

Worked examples

1. Difference.
   27.00 − 24.60 = 2.40%.
2. Settlement.
   2.40% × 3bn × 3 ÷ 12 = ₦18,000,000, received by the buyer.

1. Price.
   100 − 25.5 = 74.50.

1. Tick.
   100m × 3 ÷ 12 × 0.0001 = ₦2,500.

How to answer in the exam

• Decide whether the company is a borrower or a depositor and so which side to take.
• Compute the settlement or gain and add it to the underlying cost to show the effective rate.
• Show the result for a rise and a fall in the benchmark.
• Compare the instruments by cost, flexibility and basis risk.

Common mistakes in the exam

• Buying an FRA or futures on the wrong side.
• Forgetting that futures prices fall when rates rise.
• Using the annual rate for a part-year period in the settlement.
• Ignoring the margin on the loan in the effective rate.
• Forgetting the premium on a cap or floor.
• Treating an FRA as an actual loan.

Quick revision

• FRA: notional; buy to fix borrowing, sell to fix a deposit; seller pays if the benchmark is higher.
• Futures price.
  100 − rate; borrower sells, lender buys; tick = size × 3 ÷ 12 × 0.0001.
• Cap protects a borrower, floor a depositor; premium paid.
• Swap: pay fixed and receive floating to turn a floating loan into a fixed one.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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