FRM Exam Part I · Introduction to Derivatives

Introduction to Swaps for FRM Part I

Updated 11 October 2026 · Fact-checked

A swap is an OTC contract in which two parties agree to exchange cash flows on set dates, calculated on a notional amount. In a plain vanilla interest rate swap, one side pays fixed and the other pays floating. To solve questions, find each leg's payment, then net them.

Understand Swaps Introduction

A swap is an agreement between two parties to exchange cash flows over several future dates. The cash flows are calculated from a notional principal and a rate or price. Think of a swap as a package of forward contracts, with one fixed exchange rate or rate for every date.

The most common swap is the plain vanilla interest rate swap. One party, the fixed-rate payer, pays a fixed rate on the notional. The other, the floating-rate payer, pays a floating reference rate such as SOFR. Both payments are in the same currency, so only the net difference is paid on each date. The notional itself is never exchanged. It is only used to calculate payments.

A currency swap exchanges cash flows in two different currencies. Interest is paid in each currency, and the principal is usually exchanged at the start and handed back at the end at the same exchange rate. This is the key difference from an interest rate swap: principals are exchanged in a currency swap, and they are not in a plain vanilla interest rate swap.

Swaps have two basic uses. First, you can transform a liability or an asset. A firm paying floating on a loan can enter a swap paying fixed and receiving floating, so it effectively pays fixed. Second, you can exploit comparative advantage in borrowing markets, where each party borrows where it is relatively cheaper and then swaps into the form it wants.

Swaps are mostly traded over the counter, so they carry counterparty credit risk. The risk is only on the net amount owed, and only to the party with a positive swap value. A swap starts with a value close to zero, and its value moves as rates change.

Key formulas to remember

Fixed leg payment: Fixed payment = Notional × Fixed rate × Accrual fraction; For semi-annual payments the accrual fraction is usually 0.5 (adjust for the day count given in the question).
Floating leg payment: Floating payment = Notional × Floating rate set at start of period × Accrual fraction; The rate is normally set at the start of the period and paid at the end.
Net swap payment: Net to fixed payer = Floating payment − Fixed payment; A positive result means the fixed-rate payer receives. A negative result means it pays.
Swap as bond positions: Value to fixed payer = B(floating) − B(fixed); The fixed payer is long a floating-rate bond and short a fixed-rate bond. Reverse this for the fixed receiver.
Swap as forward positions: Swap = portfolio of forward rate agreements (interest rate swap) or forward FX contracts (currency swap); Useful for valuation and for understanding why initial value is about zero.

How to solve Swaps Introduction questions

Use this method for any swap question, whether it asks for a payment, a net cash flow, or the effect of a swap on a loan.

1Identify the type of swap: interest rate (single currency, no principal exchange) or currency (two currencies, principal exchanged).
2Write down who pays fixed and who pays floating, or who pays which currency.
3Note the notional, the payment frequency and the accrual fraction (for example 0.5 for semi-annual).
4Calculate each leg: Notional × rate × accrual fraction. Use the floating rate that was set at the start of that period.
5For an interest rate swap, net the two legs. State clearly who pays and who receives.
6If the question includes an underlying loan or bond, add the swap net payment to it to find the all-in cost or yield.
7For a currency swap, convert principals at the initial exchange rate and note the final principal exchange.
8Check the sign and the unit, then confirm the answer matches the question's perspective.

Quickest way: Net payment shortcut

When to use it: Use when the question asks only for a single net payment or an all-in rate on a swap-adjusted loan.

Subtract the two rates first: floating rate minus fixed rate.
Multiply the difference by the notional and the accrual fraction.
If the difference is positive, the fixed payer receives. If negative, the fixed payer pays.
For an all-in cost, add the fixed rate to any spread on the original floating loan, because the swap's floating leg cancels the floating loan payment.

Common mistakes in Swaps Introduction

Thinking the notional is exchanged in a plain vanilla interest rate swap.
Currency swaps do exchange principal, and students mix the two.
Fix: Remember that both legs are in the same currency, so exchanging principal would be pointless. Only interest is netted.
Forgetting the accrual fraction on semi-annual or quarterly swaps.
Rates are quoted per annum and students apply them to a full year.
Fix: Multiply by 0.5 for semi-annual, 0.25 for quarterly, unless the question gives a day count.
Using the floating rate at the end of the period instead of the rate set at the start.
Students assume the payment date rate applies.
Fix: Use the rate fixed at the start of the period, paid at the end, unless the question says otherwise.
Mixing up who benefits when rates rise.
Payer and receiver terms are confusing.
Fix: A fixed-rate payer gains when floating rates rise because it receives more floating than before. A fixed receiver loses.
Treating the full notional as the credit exposure.
Students link notional to money at risk.
Fix: Exposure is the positive replacement value of the swap, which is far smaller than the notional. In currency swaps it is larger than in interest rate swaps because of the principal exchange.
Ignoring the original loan when asked for the net cost of a swap-hedged position.
Students look only at the swap legs.
Fix: Combine the loan payment and the swap net payment, then see which parts cancel.

Worked examples

Example 1

A company enters a 2-year plain vanilla swap with semi-annual payments on a notional of $50 million. It pays a fixed rate of 4% per annum and receives the floating rate. The floating rate set at the start of the first period is 4.6% per annum. Find the net payment for the first period and who makes it.

Show the solution

Fixed leg = 50,000,000 × 4% × 0.5 = $1,000,000.
Floating leg = 50,000,000 × 4.6% × 0.5 = $1,150,000.
Net to the company = 1,150,000 − 1,000,000 = $150,000.
The company is the fixed payer and the floating receiver, so a positive net means it receives.

Answer: The company receives a net $150,000 at the end of the first period.

Example 2

A firm has a $20 million loan paying SOFR + 1.2% per annum, with annual payments. It enters a swap paying 3.5% fixed and receiving SOFR on $20 million. What is the firm's all-in annual interest rate and annual interest cost?

Show the solution

Loan payment = SOFR + 1.2%.
Swap: the firm pays 3.5% and receives SOFR.
Total = (SOFR + 1.2%) + 3.5% − SOFR.
The SOFR terms cancel, leaving 1.2% + 3.5% = 4.7%.
Annual cost = 20,000,000 × 4.7% = $940,000.

Answer: The all-in rate is 4.7% per annum, which is $940,000 a year.

Exam tips

Read the perspective carefully. Questions often ask for the fixed receiver, not the payer, and the sign flips.
Check whether the question is about an interest rate swap or a currency swap before calculating. Principal exchange is the usual trap.
For hedged-loan questions, write out the loan and swap legs in one line and cancel the floating terms.
Know the bond-portfolio and forward-portfolio views of a swap. Conceptual questions use them.
Do not spend time on long calculations. Most introductory swap questions need one multiplication and one subtraction.

Practice questions from Introduction to Derivatives

Swaps Introduction: frequently asked questions

How does an interest rate swap work?

Two parties agree to exchange interest payments on a notional amount. One pays a fixed rate and the other pays a floating rate. Only the net difference changes hands on each payment date, and the notional is never exchanged.

What is the difference between a currency swap and an interest rate swap?

An interest rate swap exchanges interest in one currency and does not exchange principal. A currency swap exchanges interest in two currencies and normally exchanges principal at the start and the end. This makes currency swap exposure more sensitive to exchange rates.

Why is a swap's initial value close to zero?

The fixed rate is set so that the present value of the fixed payments equals the present value of the expected floating payments. Neither side pays to enter. Its value then moves as interest rates change.

Do swaps carry credit risk?

Yes, especially when traded over the counter. The risk is that the party owing the net amount defaults when the swap has positive value to the other side. Netting, collateral and central clearing reduce this risk.