Interest rate swaps: fixed vs floating

What does each side of a swap pay?

A swap is a firm commitment in which two counterparties exchange a series of cash flows in the future. Like a forward it has a start date, a maturity date and an underlying, all negotiated and written in the contract. The most common type is the interest rate swap , which exchanges a fixed rate for a floating rate.

• The floating rate is a market reference rate (MRR) that resets every period, such as the Secured Overnight Financing Rate (SOFR) or the Sterling Overnight Index Average (SONIA).
• The fixed rate is the swap rate . It stays constant for the life of the contract.
• The fixed-rate payer pays the swap rate and receives floating, so it is also the floating-rate receiver.
• The floating-rate payer pays MRR and receives the fixed rate.

Interest rate swapa series of exchanges on one notional; only the net moves

• Fixed-rate payer Memorize pays the swap rate; receives floating; same as floating-rate receiver
  • Gains when rates rise Memorize the floating payment it receives grows
• Floating-rate payer Memorize pays MRR; receives fixed; same as fixed-rate receiver
  • Gains when rates fall Memorize the floating payment it makes shrinks

Both payments are calculated on the same notional principal . In a plain interest rate swap this amount is never exchanged. It only sizes the interest. Each period’s payment is the annual rate times the notional times the fraction of the year.

$$\text{Payment} = \text{rate} \times N \times \dfrac{1}{m}$$

Here m is the number of payments a year: 2 for semiannual, 4 for quarterly. The two legs fall on the same dates, so the parties exchange only the net payment .

$$P = N \times (\text{MRR} - K) \times \dfrac{1}{m}$$

K is the swap rate. If MRR is above K the result is positive and the fixed-rate payer receives the net amount. If MRR is below K the result is negative and it pays. The floating-rate payer sees the mirror image.

Why is a swap a series of forwards?

Each period’s exchange is like a forward contract on the reference rate. The fixed side is the forward price, the same at every date, and the floating side is the unknown rate that will set at that date. A swap bundles a strip of these forwards into one contract with one fixed rate.

The swap rate is set at the start so that the present value of the fixed payments equals the present value of the expected floating payments, which come from forward rates. That is why no money changes hands at the start and the swap has zero value at inception. As rates move and time passes, its market value drifts away from zero: positive for one side and negative for the other.

Exam tip Ask “who receives the floating leg?”. That side gains when rates rise. If the question is about the fixed-rate payer, it is the same answer.

Why would anyone use one?

A borrower with a floating-rate loan can pay fixed on a swap and so fix its cost. An investor can change a portfolio’s rate exposure without trading the bonds: receiving fixed adds duration, paying fixed removes it.

Uses of an interest rate swapchange the rate exposure without trading the underlying debt or bonds

• Borrower pays fixed Use it turns a floating-rate loan into a fixed-rate one
• Investor receives fixed Use it adds duration without buying bonds
• Investor pays fixed Use it shortens duration

Swap credit terms are negotiated privately. They range from no collateral, where each side bears the other’s default risk, to margin terms like futures. Many swaps between dealers are centrally cleared, which standardizes margin and reduces counterparty risk. If a counterparty defaults, the swap is usually terminated and settled at its market value, like any other debt claim.

Go deeper Currency swaps exchange notional

A plain interest rate swap does not exchange notional, because both legs are in the same currency. A currency swap uses two currencies, so the principal is usually exchanged at the start and returned at the end. Level I concentrates on the interest rate swap.

Go deeper Day count conventions

The period fraction is not always exactly 1/m. Some markets use actual days over 360, and others use 30/360. Exam questions give you the fraction to use, normally the simple 1/m.

Go deeper Swaps and central clearing

Standardized swaps are now often cleared through a central counterparty, which takes on the credit risk and requires margin, as with futures. The earlier lessons on over-the-counter (OTC) and exchange-traded markets describe the clearing steps.