Advanced Financial Management · Derivatives Analysis and Valuation

Interest Rate Derivatives: FRAs, Caps and Floors for CA Final AFM

Updated 5 October 2026 · Fact-checked

A forward rate agreement (FRA) fixes an interest rate today for a future loan or deposit, and only the rate difference is settled in cash. Settlement = (Reference rate − FRA rate) × Notional × days/360 ÷ (1 + Reference rate × days/360). Caps, floors and collars use options to limit rates.

Understand Interest Rate Derivatives: FRAs, Caps and Floors

Interest rate derivatives let you lock in or limit a future interest rate without changing the actual loan or deposit. You still borrow or lend in the market. The derivative pays or charges you the difference so your net rate is what you planned.

A forward rate agreement (FRA) is an over-the-counter contract on a notional amount. No principal moves. You agree a FRA rate for a future period. A '3 × 9' FRA means the period starts in 3 months and ends in 9 months, so it covers a 6-month rate. The buyer is protected against a rise in rates. The seller is protected against a fall. On the settlement date, if the market reference rate is above the FRA rate, the seller pays the buyer. If it is below, the buyer pays the seller.

Because the interest on the loan is paid at the end of the period but the FRA is settled at the start, the difference is discounted at the reference rate. That is why the settlement formula has a denominator.

Interest rate futures are exchange-traded. Price is quoted as 100 − rate. If rates rise, the futures price falls. A borrower who fears a rate rise sells futures and gains when the price falls. A lender who fears a rate fall buys futures. Futures are marked to market daily and come in standard contract sizes, so a perfect hedge is not always possible.

An interest rate cap is a series of call-type options on a rate. The buyer pays a premium and receives the excess whenever the reference rate is above the strike. Each period's option is a caplet. A floor is the reverse: the buyer receives the shortfall whenever the rate is below the strike. A collar combines the two. A borrower buys a cap and sells a floor. The floor premium received reduces the cap cost, but the borrower gives up the benefit of rates falling below the floor strike.

Key rules to remember

FRA settlement amount: Settlement = (SR − FR) × N × (d ÷ 360) ÷ [1 + SR × (d ÷ 360)]; SR = reference rate at settlement, FR = FRA rate, N = notional, d = days in the FRA period. Positive means the buyer receives; negative means the buyer pays. Use the day count given in the question (360 or 365).
Effective rate with FRA (borrower): Effective rate = FRA rate (the loan costs SR, the FRA settlement offsets SR − FR); This is exact in this framework, ignoring credit and basis effects. Check: the settlement received at the start, invested for the FRA period at SR, grows to (SR − FR) × N × d/360. That offsets the extra interest over the FRA rate.
Interest rate futures price: Price = 100 − implied annual rate (in %); Rate rise means price fall. Borrowers sell, lenders buy.
Futures gain or loss: Gain = Change in price (in %) ÷ 100 × Contract size × (Contract period in months ÷ 12) × No. of contracts; A one basis point move (0.01) on a 3-month contract is 0.0001 × size × 3/12.
Number of futures contracts: Contracts = (Exposure ÷ Contract size) × (Exposure period ÷ Contract period); Round to a whole number. The second ratio adjusts for tenor mismatch.
Cap payoff per period: Cap payoff = Max(0, Reference rate − Cap strike) × N × (d ÷ 360); Usually paid at the end of the period. Use the discounted version only if the question says it is settled in advance.
Floor payoff per period: Floor payoff = Max(0, Floor strike − Reference rate) × N × (d ÷ 360); Received by the floor buyer, paid by the floor seller.
Collar (borrower): Buy cap at higher strike + Sell floor at lower strike; Net premium = Cap premium − Floor premium; Effective rate stays between the floor strike and the cap strike (plus the net premium cost).

How to solve Interest Rate Derivatives: FRAs, Caps and Floors questions

Use this order for any FRA, futures, cap, floor or collar question.

1Identify the exposure: are you a borrower (hurt by rising rates) or a lender or depositor (hurt by falling rates)? Note amount, start date and period.
2Choose the position: borrower buys FRA, sells futures, buys cap. Lender sells FRA, buys futures, buys floor.
3Write the contract terms: FRA rate or strike, notional, days, day-count basis and premium.
4Compute the payoff under each reference-rate scenario using the right formula. Discount FRA settlements. Do not discount cap or floor payoffs unless told.
5Add the hedge result to the actual loan or deposit cash flow: loan interest less hedge gain, plus any premium.
6Convert the net cost to an effective annual rate: net amount ÷ principal × (360 ÷ days), or as the question specifies.
7State the conclusion in one line: the rate achieved, the range for a collar, and whether the hedge was better or worse than staying unhedged.

Quickest way: Rate-difference shortcut

When to use it: Use when the question asks for an FRA settlement or the effective rate under several scenarios and time is short.

Compute the raw difference: (SR − FR) × N × d/360.
Divide by (1 + SR × d/360) only for an FRA. Skip this for caps and floors.
Sign check: SR above FR means the buyer receives. SR below FR means the buyer pays.
For caps and collars, mark the three zones on a line: below floor, between strikes, above cap. The effective rate is the floor strike, market rate or cap strike in those zones, plus the net premium.
For futures, work only in price points: borrower gain = fall in price (rise in rate). Multiply by size and 3/12 (or contract months/12).

Common mistakes in Interest Rate Derivatives: FRAs, Caps and Floors

Forgetting to discount the FRA settlement.
Students stop at (SR − FR) × N × d/360, as for a cap.
Fix: The FRA pays at the start of the period, so always divide by 1 + SR × d/360. Do not do this for caps and floors.
Using the FRA rate instead of the reference rate in the denominator.
Both rates appear in the question and the formula looks symmetrical.
Fix: Discounting uses the market (reference) rate at settlement, because that is the rate at which the amount can be invested or borrowed.
Taking the wrong side: buying futures to hedge a borrowing.
Confusing rate direction with price direction. Futures price = 100 − rate.
Fix: Borrower fears higher rates, which means lower prices, so sell futures. Say this in one line before calculating.
Applying a cap payoff when the rate is below the strike, or ignoring the premium.
Treating the cap as a forward rather than an option with a floor of zero.
Fix: Cap payoff is Max(0, SR − strike). Always add the premium (net of floor premium in a collar) to the effective cost.
Mixing up the day count or period, such as using 12 months instead of 6.
The rate is annual but the period is shorter.
Fix: Always multiply a rate by d/360 (or months/12) for the FRA or reset period. Check whether the question says 360 or 365.
Thinking a collar protects fully at both ends.
Memorising 'cap plus floor' without noting who sells the floor.
Fix: The borrower sells the floor, so the borrower gains no benefit once rates fall below the floor strike. The collar limits the cost range, not just the upside.

Worked examples

Example 1

A company will borrow ₹10,00,00,000 for 6 months starting 3 months from now at a floating rate linked to the 6-month reference rate. To hedge, it buys a 3 × 9 FRA at 8.00% p.a. When the FRA settles, the reference rate is 9.00% p.a. Use a 360-day year and 180 days for the period. Find the settlement amount and show the effective borrowing cost.

Show the solution

The company is a borrower, so it buys the FRA. SR (9%) is above FR (8%), so the company receives.
Raw difference = (0.09 − 0.08) × 10,00,00,000 × 180/360 = ₹5,00,000.
Discount factor = 1 + 0.09 × 180/360 = 1.045.
Settlement = 5,00,000 ÷ 1.045 = ₹4,78,469 (rounded).
Check: loan interest at 9% for 6 months = 10,00,00,000 × 0.09 × 0.5 = ₹45,00,000, paid at the end.
The FRA amount received at the start is invested at 9% for 6 months: 4,78,469 × 1.045 ≈ ₹5,00,000.
Net interest = 45,00,000 − 5,00,000 = ₹40,00,000, which is 40,00,000 ÷ 10,00,00,000 × 2 = 8.00% p.a.

Answer: The company receives ₹4,78,469 at settlement. Its effective borrowing cost is 8.00% p.a., which equals the FRA rate.

Example 2

A company has a ₹5,00,00,000 floating-rate loan with a 6-month reset. It buys a cap with strike 8% for a premium of ₹1,00,000 and sells a floor with strike 6% for a premium of ₹60,000, for the next period. Ignore the time value of the premiums and use 6/12 for the period. Find the effective annual cost if the reference rate at reset is (a) 9% and (b) 5%.

Show the solution

Net premium paid = 1,00,000 − 60,000 = ₹40,000.
Case (a), rate 9%: loan interest = 5,00,00,000 × 0.09 × 0.5 = ₹22,50,000.
Cap payoff = (9% − 8%) × 5,00,00,000 × 0.5 = ₹2,50,000 received. The floor is not exercised against the company because 9% is above 6%.
Net interest = 22,50,000 − 2,50,000 + 40,000 = ₹20,40,000.
Effective annual rate = 20,40,000 ÷ 5,00,00,000 × 2 = 8.16%.
Case (b), rate 5%: loan interest = 5,00,00,000 × 0.05 × 0.5 = ₹12,50,000. The cap pays nothing because 5% is below 8%.
The company must pay on the floor it sold: (6% − 5%) × 5,00,00,000 × 0.5 = ₹2,50,000.
Net cost = 12,50,000 + 2,50,000 + 40,000 = ₹15,40,000. Effective annual rate = 15,40,000 ÷ 5,00,00,000 × 2 = 6.16%.

Answer: At a 9% reference rate the effective cost is 8.16% p.a. At a 5% reference rate it is 6.16% p.a. The collar limits the rate to 8% plus the net premium cost (8.16%), and it gives up the benefit of rates below 6%, so the cost does not fall below 6.16%.

Exam tips

Write the position first (buy or sell FRA, futures, cap or floor) with a one-line reason. Examiners award marks for the correct hedge choice.
In FRA questions, always show the undiscounted difference and then the discounted settlement. This protects marks if the final figure differs.
Read the day-count basis and the FRA notation (for example 3 × 9) carefully. The period is the difference between the two numbers.
For collars, present a three-scenario table in words: rate below floor, between strikes, above cap, with the effective rate in each.
In a case-scenario MCQ, decide the direction (who gains if rates rise) before looking at the options. This removes most wrong choices quickly.

Practice questions from Derivatives Analysis and Valuation

Interest Rate Derivatives: FRAs, Caps and Floors 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 Derivatives: FRAs, Caps and Floors: frequently asked questions

How do I calculate the FRA settlement amount?

Take (reference rate − FRA rate) × notional × days/360, then divide by 1 + reference rate × days/360. A positive result is received by the FRA buyer. A negative result is paid by the buyer.

Who buys and who sells an FRA?

A borrower worried about rising rates buys an FRA. A lender or depositor worried about falling rates sells an FRA. The buyer gains when the reference rate is above the FRA rate.

What is the difference between an FRA and a cap?

An FRA is a firm commitment, so you gain if rates rise and lose if they fall. A cap is an option, so you receive a payoff only if the rate is above the strike, and you pay a premium for that protection.

Why does a borrower sell interest rate futures to hedge?

Futures price is 100 minus the rate. When rates rise, the price falls, so the short futures position makes a gain that offsets the higher loan interest.