Interest Rate Swaps, OIS and FRAs for the CTP Exam
Only the interest difference ever moves. Who pays it, how much, and why the FRA amount is discounted.
An interest rate swap (IRS) is a contract in which two parties exchange one stream of interest payments for another on a notional principal, over an agreed period. RBI's own definition says exactly that. The notional itself never changes hands. Only the interest difference is settled.
A forward rate agreement (FRA) is the single-period cousin. It fixes a rate today for a future period, and on the settlement date only the difference between that fixed rate and the reference rate is paid. Module V of the Certified Treasury Professional syllabus names both, along with PV01 of swaps and option Greeks. This page works each one with numbers you can repeat on the basic calculator the exam allows.
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The Vocabulary First
- Notional principal
- The amount interest is calculated on. It is never exchanged in a single-currency swap or an FRA.
- Fixed leg and floating leg
- Each stream of payments is a leg. In the common fixed-for-floating swap, one leg uses an agreed fixed rate and the other resets to a floating index.
- Swap rate
- The fixed rate on the fixed leg. At the start it is set so both legs have equal present value, so a new swap is worth zero to both sides.
- Fixed payer (payer swap)
- Pays fixed, receives floating. Gains when rates rise. A borrower with a floating-rate loan uses this to lock a fixed cost.
- Fixed receiver (receiver swap)
- Receives fixed, pays floating. Gains when rates fall. An investor who expects rates to fall can do this instead of buying bonds.
- Basis swap
- Floating against floating, on two different indices, with a spread added to one leg.
Worked Example: One Swap Payment, Netted
Illustrative. Notional ₹100 crore, half-yearly payments, fixed rate 6.50%, floating rate fixed for this period at 6.80%. The half-year is taken as 0.5 to keep the arithmetic clean.
- 1
1. Fixed leg
₹100 crore × 6.50% × 0.5 = ₹3.25 crore, owed by the fixed payer.
- 2
2. Floating leg
₹100 crore × 6.80% × 0.5 = ₹3.40 crore, owed by the fixed receiver.
- 3
3. Net it
Only the difference moves: ₹3.40 crore minus ₹3.25 crore = ₹15 lakh. Shortcut: ₹100 crore × 0.30% × 0.5 = ₹15 lakh.
- 4
4. Who pays
The floating rate is above the fixed rate, so the fixed receiver pays ₹15 lakh to the fixed payer. Had the floating rate been 6.20%, the fixed payer would have paid ₹15 lakh instead.
Overnight Indexed Swaps
An overnight indexed swap (OIS) is an IRS whose floating leg is built from an overnight rate compounded daily over each coupon period. The swap can run for years. Only the underlying reference rate is overnight.
Abroad, the overnight rates used are benchmarks such as SOFR for the US dollar, a secured Treasury repo rate, and SONIA for sterling, an unsecured wholesale rate. Because the overnight rate for a period is only known at its end, the payment is calculated in arrears. The gap between IBOR-based swap rates and OIS rates for the same term was long read as a measure of stress among banks.
IRS, OIS and FRA Side by Side
Periods covered
IRS
Many, over the swap's life
OIS
Many, over the swap's life
FRA
One future period
Floating reference
IRS
A term index, traditionally an IBOR
OIS
An overnight rate compounded daily
FRA
A term reference rate for the forward period
What is exchanged
IRS
Net interest each period
OIS
Net interest each period
FRA
One discounted difference at the start of the period
Notional exchanged?
IRS
No
OIS
No
FRA
No
| Point | IRS | OIS | FRA |
|---|---|---|---|
| Periods covered | Many, over the swap's life | Many, over the swap's life | One future period |
| Floating reference | A term index, traditionally an IBOR | An overnight rate compounded daily | A term reference rate for the forward period |
| What is exchanged | Net interest each period | Net interest each period | One discounted difference at the start of the period |
| Notional exchanged? | No | No | No |
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How an FRA Settles
An FRA quoted "3x6" covers a period starting 3 months from now and ending 6 months from now. The buyer locks in a borrowing rate and is paid if the reference rate fixes above the FRA rate. The seller is paid if it fixes below.
Settlement happens at the start of the forward period, but the interest it replaces would have been paid at the end. So the difference is discounted back at the reference rate: settlement = N × d × (r - R) / (1 + d × r), where N is the notional, d the day count fraction, r the reference rate and R the FRA rate. Seen from the seller's side, the sign flips to (R - r).
Worked Example: FRA Settlement
Illustrative. A bank buys a 3x6 FRA on ₹50 crore at 7.00%. The forward period is 92 days, counted on an Actual/365 basis here. On the fixing date the reference rate is 7.40%.
- 1
1. Day count fraction
d = 92 / 365 = 0.252055.
- 2
2. Undiscounted difference
₹50 crore × 0.252055 × (7.40% - 7.00%) = ₹5,04,110.
- 3
3. Discount factor
1 + (0.252055 × 0.074) = 1.018652.
- 4
4. Settlement
₹5,04,110 / 1.018652 = ₹4,94,879, paid by the seller to the buyer, because the rate fixed above 7.00%.
- 5
5. Common slip
Forgetting step 3 gives ₹5,04,110. In an MCQ, that wrong answer is usually one of the options.
PV01 of a Swap
PV01 is the change in a position's value for a 1 basis point (0.01%) move in rates. For a swap, the fixed leg's value is the sum of rate × day count fraction × discount factor across all payment dates. So a 1 bp change in the fixed rate moves the swap's value by roughly notional × 0.0001 × the sum of (day count fraction × discount factor).
Illustrative: a 3-year swap on ₹100 crore with annual payments, discounted at a flat 6.50%. The three discount factors (1/1.065, 1/1.065², 1/1.065³) add to 2.6485. PV01 ≈ ₹100 crore × 0.0001 × 2.6485 = about ₹2.65 lakh per basis point. A fixed payer gains roughly that much for each 1 bp rise in swap rates; a fixed receiver loses it. This is the swap version of the duration idea on the bond pricing page.
Option Greeks in One Table
Module V asks for a basic understanding only. Each Greek measures how an option's price responds to one input, with the others held constant.
Delta
Measures
Change in option price for a ₹1 move in the underlying
Illustration
Delta 0.6: a ₹10 rise in the underlying adds about ₹6
Gamma
Measures
Rate of change of delta as the underlying moves
Illustration
Gamma 0.05: a ₹10 move changes delta by 0.5
Theta
Measures
Loss of value from the passage of time
Illustration
Theta -2: the option loses about ₹2 a day
Vega
Measures
Change in price for a 1% change in implied volatility
Illustration
Vega 10: volatility up 2% adds ₹20
Rho
Measures
Change in price for a 1% change in interest rates
Illustration
Rho 1.5: rates up 1% adds ₹1.50 to a call
| Greek | Measures | Illustration |
|---|---|---|
| Delta | Change in option price for a ₹1 move in the underlying | Delta 0.6: a ₹10 rise in the underlying adds about ₹6 |
| Gamma | Rate of change of delta as the underlying moves | Gamma 0.05: a ₹10 move changes delta by 0.5 |
| Theta | Loss of value from the passage of time | Theta -2: the option loses about ₹2 a day |
| Vega | Change in price for a 1% change in implied volatility | Vega 10: volatility up 2% adds ₹20 |
| Rho | Change in price for a 1% change in interest rates | Rho 1.5: rates up 1% adds ₹1.50 to a call |
How the CTP Exam Tests This
- check_circleDirection: who pays in a swap or FRA when the floating or reference rate is above or below the fixed rate. Get this wrong and every number is wrong.
- check_circleNetting: only the interest difference is paid, never the notional. Options that exchange ₹100 crore are traps.
- check_circleFRA discounting: the settlement amount is divided by (1 + d × r), using the reference rate, not the FRA rate.
- check_circleHedging choice: a floating-rate borrower afraid of rising rates buys an FRA or pays fixed in a swap. An investor afraid of falling rates sells an FRA or receives fixed.
- check_circleGreeks: match each Greek to the input it tracks. Theta is time, vega is volatility, rho is interest rates.
- check_circleThe exam allows only a basic 8-function, 12-digit calculator. Work in crore and lakh and keep the day count fraction to six decimals.
FAQs
What is the difference between an IRS and an FRA?expand_more
An FRA covers one future period and settles once, at the start of that period, on a discounted basis. An IRS covers a series of periods and settles the net interest at each payment date. Both work on a notional that is never exchanged.
Who gains in a payer swap when rates rise?expand_more
The fixed payer. It keeps paying the agreed fixed rate while the floating rate it receives goes up, so the net payment turns in its favour.
Why is the FRA settlement amount discounted?expand_more
Because it is paid at the start of the forward period, while the interest it stands in for would have been paid at the end. Dividing by (1 + d × r) brings it back to the settlement date.
What is an overnight indexed swap?expand_more
An interest rate swap whose floating leg is an overnight rate compounded daily over each period, such as SOFR or SONIA abroad. The swap's term can be years; only the reference rate is overnight.
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