Interest-Rate Swap Structure and Cash-Flow Calculations - Article

Introduction

An Interest-Rate Swap (IRS) is a derivative used to change the interest-rate characteristics of an asset, liability, or treasury position.

In the most common structure:

• one party pays a fixed interest rate;

• the other party pays a floating interest rate;

• both payments are calculated on the same agreed notional principal; and

• normally only the net interest difference is exchanged when payment dates coincide.

RBI currently defines an interest-rate swap as an OTC derivative in which two counterparties agree to exchange one stream of future interest payments for another, applied to a notional principal amount over a specified period.

The current 2026 IIBF BFM syllabus specifically includes Interest Rate and Currency Swaps under Module C – Derivative Products.

The simplest way to understand an IRS is:

Fixed Interest Stream ↔ Floating Interest Stream

Learning Objectives

After studying this topic, you should be able to:

• explain the structure of a plain-vanilla IRS;

• distinguish fixed and floating legs;

• identify pay-fixed and receive-fixed positions;

• calculate periodic fixed-leg and floating-leg cash flows;

• calculate net swap settlement;

• understand the role of the notional principal;

• explain an Overnight Indexed Swap;

• understand the par swap rate;

• distinguish swap cash flow from swap value; and

• identify common CAIIB numerical mistakes.

Basic Structure of an Interest-Rate Swap

Assume two parties enter into a swap based on an agreed notional amount.

Party A

Pays Fixed

and

Receives Floating

Party B

Receives Fixed

and

Pays Floating

The cash flows are opposite.

Therefore:

Party A's Swap Gain = Party B's Swap Loss

before considering transaction costs, credit effects, collateral, and other adjustments.

Notional Principal

The notional principal is the reference amount used to calculate interest payments.

In a conventional single-currency IRS, the notional principal is normally not exchanged between the parties.

It is only the calculation base.

Fixed Leg

The fixed-rate payer pays interest based on:

• notional principal;

• agreed fixed swap rate; and

• applicable day-count fraction.

Fixed-Leg Cash Flow = Notional Principal × Fixed Rate × Day-Count Fraction

This calculates the contractual fixed interest payable for a swap period.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

If the contract uses simple equal six-month periods with an annual fixed rate, the appropriate half-year fraction is applied according to the contract convention.

Do not automatically divide the annual rate by two without checking:

• actual payment dates; and

• day-count convention.

Floating Leg

The floating leg is calculated using the applicable reference rate for the relevant interest period.

Floating-Leg Cash Flow = Notional Principal × Floating Reference Rate × Day-Count Fraction

This calculates the floating interest amount for the relevant reset period.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

The floating rate may depend on the product and applicable benchmark framework.

RBI's rupee interest-rate derivative framework continues to govern transactions such as rupee IRS, while FBIL currently publishes the Overnight MIBOR benchmark used in the Indian market.

Net Swap Settlement

Where both legs:

• are denominated in the same currency; and

• are payable on the same date,

the parties commonly exchange only the net difference.

For a pay-fixed, receive-floating party:

Net Settlement = Floating-Leg Cash Flow − Fixed-Leg Cash Flow

This determines the net amount receivable or payable by the fixed-rate payer.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

If the result is:

• positive → fixed-rate payer receives;

• negative → fixed-rate payer pays the absolute amount.

For the receive-fixed party, the sign is reversed.

A Faster Net-Settlement Relationship

If both legs use the same:

• notional;

• accrual period; and

• day-count fraction,

the net amount can be calculated directly.

Net Settlement to Pay-Fixed Party = Notional × (Floating Rate − Fixed Rate) × Day-Count Fraction

This directly measures the periodic net settlement when the fixed and floating legs share the same calculation base.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Pay-Fixed, Receive-Floating Position

A party chooses:

Pay Fixed + Receive Floating

when it wants economic protection against rising interest rates.

Why?

If market floating rates rise:

• floating receipts under the swap increase;

• these receipts can offset higher floating-rate costs on an underlying borrowing.

Therefore, a floating-rate borrower may use a pay-fixed IRS to create an approximately fixed-rate economic exposure.

Receive-Fixed, Pay-Floating Position

The opposite position is:

Receive Fixed + Pay Floating

This may be useful when a party wants exposure to falling floating rates or wants to transform an existing fixed-rate liability into an economically floating-rate liability.

If floating rates fall:

• floating payments under the swap decline;

• fixed receipts remain contractually fixed.

Converting Floating-Rate Borrowing into Fixed

Assume a borrower has:

Floating-Rate Loan

The borrower enters:

Pay-Fixed / Receive-Floating IRS

The combined structure becomes approximately:

Loan: Pay Floating

Swap: Receive Floating

These floating amounts offset, subject to basis and other differences.

What remains economically is approximately:

Pay Fixed

Therefore:

Floating Liability + Pay-Fixed IRS → Synthetic Fixed Liability

Converting Fixed-Rate Borrowing into Floating

Now assume the borrower already pays fixed interest.

It enters:

Receive-Fixed / Pay-Floating IRS

Conceptually:

Loan: Pay Fixed

Swap: Receive Fixed

The fixed streams offset approximately.

The borrower is then economically left with:

Pay Floating

Therefore:

Fixed Liability + Receive-Fixed IRS → Synthetic Floating Liability

Important Role of the Borrowing Spread

Suppose an underlying loan costs:

Benchmark + Credit Spread

and the swap exchanges:

Benchmark ↔ Fixed Swap Rate

The swap may hedge the benchmark component, but the borrower's credit spread may remain.

Therefore:

Pay-fixed IRS does not automatically fix every component of borrowing cost.

This is a common CAIIB trap.

The effective cost can still include:

• loan spread;

• fees;

• basis difference; and

• derivative transaction costs.

Day-Count Fraction

Interest is calculated according to the day-count convention specified in the swap.

Conceptually:

Day-Count Fraction = Relevant Accrued Days ÷ Applicable Year Basis

This converts the swap accrual period into the contractual fraction of a year.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Possible conventions depend on the instrument and contract.

Do not automatically use:

• 365;

• 360; or

• exactly 0.50

unless the question or applicable contract convention supports it.

Reset Date vs Payment Date

The reset date determines the floating rate applicable to an interest period according to the contract.

The payment date is when the resulting interest amount becomes payable.

These need not be the same date.

A typical sequence is:

Rate Reset → Interest Accrual Period → Payment

Therefore, when solving a numerical question, identify which floating rate belongs to which payment period.

Overnight Indexed Swap

An Overnight Indexed Swap (OIS) is an important form of IRS.

Typically:

• one leg pays a fixed rate; and

• the other is linked to a compounded overnight reference rate over the relevant period.

In India, overnight-rate-based swaps are an important part of the rupee interest-rate derivative market. RBI material identifies MIBOR-based OIS as a widely used onshore interest-rate derivative, while FBIL currently publishes the Overnight MIBOR benchmark.

The important CAIIB distinction is:

Ordinary fixed-floating IRS → floating leg based on contractual reference-rate mechanics

OIS → floating leg based on an overnight rate accumulated/compounded over the period

OIS Floating Cash Flow

Where the question directly provides the effective compounded overnight rate for the period:

OIS Floating-Leg Cash Flow = Notional × Effective Compounded Overnight Rate × Applicable Period Fraction

This calculates the floating cash flow when the effective overnight-index return for the period is already given.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

If individual overnight observations are supplied, follow the exact compounding and day-count convention stated in the question.

Do not simply calculate an arithmetic average unless the contract specifies that method.

Swap Fixed Rate at Inception

A properly priced new plain-vanilla IRS is normally structured so that:

Present Value of Fixed Leg = Present Value of Floating Leg

at inception.

Therefore, the initial economic value of the swap is approximately zero, excluding transaction costs and related adjustments.

The fixed rate satisfying this equality is often called the:

Par Swap Rate

Par Swap Rate

Where discount factors for fixed-payment dates are supplied:

Par Swap Rate = (1 − Final Discount Factor) ÷ Σ(Accrual Fraction × Discount Factor)

This gives the fixed rate that makes the present values of the fixed and floating legs equal for a standard par swap under the stated assumptions.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

The exact form depends on:

• payment frequency;

• accrual factors;

• discount curve; and

• swap structure.

For CAIIB, use the data and conventions specified in the question.

Present Value of Fixed Leg

For remaining fixed payments:

PV of Fixed Leg = Σ [Fixed Cash Flow × Relevant Discount Factor]

This calculates the present value of remaining fixed-leg cash flows.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

If notional principal is not contractually exchanged, do not incorrectly add a principal repayment merely because a bond valuation would contain one.

Present Value of Floating Leg

The floating leg must be valued according to:

• current forward/reference rates;

• remaining reset structure; and

• applicable discount factors.

For examination questions, the required future floating cash flows or their present value may be directly supplied.

Use the information provided rather than assuming that every future floating payment equals today's current floating rate.

Swap Value to Pay-Fixed Party

A pay-fixed party receives the floating leg.

Therefore:

Value to Pay-Fixed Party = PV of Floating Leg − PV of Fixed Leg

This determines the current value of the swap from the perspective of the party paying fixed and receiving floating.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

Swap Value to Receive-Fixed Party

The receive-fixed party has the opposite position.

Value to Receive-Fixed Party = PV of Fixed Leg − PV of Floating Leg

This determines the current value from the fixed-rate receiver's perspective.

Refer to the Formula Section for a detailed explanation, variables, and solved examples.

The two values are opposite before considering counterparty and other valuation adjustments.

Effect of Interest-Rate Changes on Swap Value

For a conventional fixed-for-floating IRS:

Market Rates Rise

The existing fixed rate becomes relatively less expensive.

Therefore, generally:

Pay-Fixed Position Gains Value

and

Receive-Fixed Position Loses Value

Market Rates Fall

The existing fixed receipt becomes more attractive.

Therefore, generally:

Receive-Fixed Position Gains Value

and

Pay-Fixed Position Loses Value

This is the swap equivalent of basic fixed-income interest-rate sensitivity.

Swap Cash Flow vs Swap Value

These must not be confused.

Swap Cash Flow

The actual periodic payment or receipt due on a settlement date.

Swap Value

The present value of all remaining expected future swap cash flows.

Therefore:

Today's Net Settlement ≠ Entire Swap Market Value

A swap can make a payment today and still have a positive or negative remaining market value.

Notional Amount vs Market Value

Another important distinction:

Notional Amount

Reference amount on which interest is calculated.

Market Value

Current economic value of the swap.

A swap with ₹1,000 crore notional does not normally have a ₹1,000 crore market value.

Its value depends on the difference between:

• contractual swap terms; and

• current market rates.

Interest-Rate Swap Cash-Flow Table

Counterparty Risk

An IRS can reduce interest-rate risk but creates counterparty exposure.

Suppose the swap moves strongly in a bank's favour.

The contract now has positive replacement value.

If the counterparty defaults, the bank may lose that value.

Current RBI directions therefore apply risk-management, valuation, documentation and counterparty requirements to OTC derivative market-making, while non-centrally cleared OTC derivatives can also be subject to margin requirements.

Basis Risk

An IRS hedge may not perfectly match the underlying borrowing.

For example:

Loan Rate = Benchmark A + spread

but

Swap Floating Leg = Benchmark B

If Benchmark A and Benchmark B move differently, the hedge leaves:

Basis Risk

Other mismatches can involve:

• reset dates;

• payment frequency;

• maturity;

• day-count conventions; and

• notional amortisation.

Therefore:

Pay fixed + receive floating does not guarantee a perfectly fixed total borrowing cost.

Numerical Workflow for CAIIB

Use this sequence.

Step 1: Identify the Position

Is the party:

• pay fixed / receive floating; or

• receive fixed / pay floating?

Step 2: Identify the Notional

Do not confuse it with actual principal exchanged.

Step 3: Identify Rates

Find:

• fixed rate;

• applicable floating rate; and

• underlying benchmark/spread.

Step 4: Check Accrual Period

Identify:

• number of days;

• day-count basis; and

• payment frequency.

Step 5: Calculate Each Leg

Calculate:

• fixed-leg cash flow;

• floating-leg cash flow.

Step 6: Net the Legs

If payment dates and currency permit netting, find the difference.

Step 7: Determine Who Pays

For pay-fixed:

Floating − Fixed

gives the net amount from the fixed payer's perspective.

Step 8: If Valuation Is Asked

Discount remaining cash flows and compare the present values of both legs.

Step 9: Check Reasonableness

For the pay-fixed party:

Floating Rate ↑ → Position should generally improve

If your answer shows the opposite without another factor explaining it, recheck the signs.

Current Regulatory Context

The RBI's current Market-makers in OTC Derivatives Directions, 2021 defines an IRS and governs eligible OTC derivative market-makers. It operates together with the relevant governing directions, including the Rupee Interest Rate Derivatives (Reserve Bank) Directions, 2019, as amended from time to time.

RBI's current framework also separately addresses margining for non-centrally cleared OTC derivatives through the 2024 Margining Directions.

For CAIIB numerical questions, focus mainly on:

• swap structure;

• fixed and floating cash flows;

• net settlement;

• benchmark matching; and

• direction of exposure.

CAIIB Exam Focus

IRS exchanges interest-payment streams on a notional principal.

Notional principal is normally not exchanged in a conventional single-currency IRS.

Pay-fixed party receives floating.

Receive-fixed party pays floating.

Fixed cash flow depends on notional, fixed rate and accrual fraction.

Floating cash flow depends on notional, applicable floating rate and accrual fraction.

When both legs settle on the same date in the same currency, only the net difference is commonly exchanged.

Floating-rate borrower fearing rising rates can use pay-fixed/receive-floating IRS.

Fixed-rate borrower seeking floating exposure can use receive-fixed/pay-floating IRS.

Loan spread may remain outside the swap hedge.

Reset date and payment date are different concepts.

Day-count convention matters.

OIS exchanges a fixed leg against an overnight-index-linked floating leg.

At inception, a par swap is normally priced so that PV of fixed leg approximately equals PV of floating leg.

Pay-fixed swap value generally improves when market interest rates rise.

Receive-fixed swap value generally improves when market interest rates fall.

Periodic swap settlement and total swap market value are different concepts.

IRS reduces interest-rate risk but may create counterparty, basis, liquidity, legal and operational risks.

Common Exam Traps

Trap 1: Notional Principal Must Be Exchanged

Incorrect for a conventional single-currency IRS.

It is normally only the calculation base.

Trap 2: Pay-Fixed Party Also Pays Floating

Incorrect.

The pay-fixed party normally receives floating.

Trap 3: Floating-Rate Borrower Should Receive Fixed to Protect against Rising Rates

Incorrect.

The usual hedge is:

Pay Fixed + Receive Floating

Trap 4: Fixed Cash Flow Is Fixed Rate × Notional Only

Incomplete.

The relevant accrual/day-count fraction must also be considered.

Trap 5: Use the Current Floating Rate for Every Future Payment

Incorrect.

Floating rates reset according to the contract.

Trap 6: Ignore Day-Count Convention

Incorrect.

The accrual basis affects the cash-flow amount.

Trap 7: Notional Amount Equals Swap Market Value

Incorrect.

The notional is a reference amount; swap value depends on current market rates and remaining cash flows.

Trap 8: Net Settlement Equals Entire Swap Value

Incorrect.

Net settlement concerns a particular payment period. Swap value concerns remaining future cash flows.

Trap 9: OIS Floating Leg Is Always a Simple Arithmetic Average of Overnight Rates

Incorrect.

OIS normally uses the contractual overnight-index accumulation/compounding methodology.

Trap 10: Swap Completely Fixes a Loan Carrying Benchmark Plus Credit Spread

Not necessarily.

Credit spread and basis differences may remain.

Trap 11: Pay-Fixed Position Loses When Market Rates Rise

Generally incorrect for a conventional IRS.

An existing below-market fixed payment becomes more valuable to the fixed payer as market rates rise.

Trap 12: Receive-Fixed Position Benefits from Rising Rates

Generally incorrect.

Its fixed receipt becomes relatively less attractive.

Trap 13: IRS Provides the Actual Loan Principal

Incorrect.

An IRS manages interest-rate exposure; funding is a separate transaction.

Trap 14: Interest-Rate Risk Disappears Completely after a Swap

Incorrect.

Basis, reset, tenor, counterparty and other residual risks may remain.

Memory Technique

Remember:

P-F-R-F

Pay Fixed → Receive Floating

and the opposite:

Receive Fixed → Pay Floating

For a borrower:

Floating loan + Pay Fixed Swap = Synthetic Fixed

Fixed loan + Receive Fixed Swap = Synthetic Floating

For cash flow:

Notional × Rate × Time

For settlement:

Calculate both legs → Net the difference

And remember the central CAIIB principle:

An interest-rate swap changes the interest-rate character of an exposure by exchanging cash-flow streams—not by normally exchanging the underlying principal.