Pricing and Valuation of Interest Rates and Other Swaps

Derivatives, LOS weight share 0.5 percent of the 365 Level I learning outcomes.

DerivativesPricing and Valuation of Interest Rates and Other Swaps

The fixed rate on a brand-new swap is set precisely so that both legs are worth exactly the same today, and the exam's favorite follow-up question is what happens to that equality the moment rates move even slightly, which is exactly when the two legs stop being equal at all.

Before you watch

Answer these three first. Getting them wrong now is normal, and it helps the lesson stick. Reveal the answers when you're done, then read on.

1. A plain-vanilla interest rate swap is best described, in terms of its cash flow structure, as being similar to:

Answer: B. Each settlement period of a swap can be viewed as a single forward contract on the floating rate for that period, so a multi-period swap is economically similar to a portfolio of forward contracts, one per settlement date, each obligating both parties to pay regardless of outcome, unlike an option's contingent payoff.

2. A swap's fixed rate is set at initiation so that:

Answer: A. The par swap rate is chosen precisely so that the present value of the fixed leg equals the present value of the expected floating leg at initiation, making the swap's value zero to both counterparties; this is a no-arbitrage pricing condition, not a guarantee of profit to either side, and the periodic cash flows themselves are not identical, only their present values are equal in total.

3. Compared to swap price, which is fixed at initiation, swap value after initiation is best described as:

Answer: B. The swap price (the fixed rate agreed at initiation) never changes over the life of the contract, but the swap's value does change as market rates move: a party locked into a below-market fixed rate gains value as rates rise, and a party locked into an above-market fixed rate loses value, exactly parallel to how a forward contract's price and value diverge after initiation.

The lesson

The video lesson for this unit is recorded and waiting to be published. Everything it teaches is written out below.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate the net settlement payment on an interest rate swap, describe why swap price and swap value are distinct the same way forward price and forward value are, describe why a swap has zero value only at initiation, and compare an interest rate swap against a currency swap.

A swap is economically similar to a portfolio of forward contracts, one per settlement date. It is priced as a single package, though, rather than as a series of separately quoted forwards. In a plain-vanilla interest rate swap, one party pays a fixed rate and receives a floating rate, both applied to the same notional principal. Only the net interest differential actually changes hands at each settlement date. The notional itself is never exchanged, since both legs sit in the same currency and there is nothing real to transfer between them.

Swap price and swap value are as distinct as forward price and forward value, and the exam tests that distinction the same way on both instruments. The swap price is the fixed rate agreed at initiation, the par swap rate, and it never changes for the life of the contract. The swap value is what the existing position is worth in the market right now. It starts at exactly zero, because the fixed rate was solved for precisely so that the present value of the fixed leg equals the present value of the floating leg the moment the swap is entered. That zero-value condition is a one-time calibration, not a permanent state of the contract. Once time passes and market rates move relative to that original fixed rate, the swap develops positive value for one side and negative value for the other.

The fixed-rate payer pays the locked-in rate and receives floating, so that party benefits when rates rise. The floating receipts grow while the fixed payment stays exactly the same. The fixed-rate receiver benefits in the opposite direction, when rates fall. A useful valuation shortcut treats the fixed-rate payer as short a fixed-rate bond and long a floating-rate bond. Paying fixed coupons resembles a bond issuer's obligation. Receiving floating resembles holding a bond that resets to par at every settlement date. That is exactly why the floating leg is easy to value: it is always worth par right at a reset date.

Currency swaps differ from interest rate swaps on exactly the dimension that makes notional exchange necessary. The two legs sit in two different currencies. Because there is a genuine economic reason to transfer both currencies, a currency swap exchanges notional principal at both initiation and maturity, unlike a plain interest rate swap. At maturity, that exchange simply reverses. Each party returns the exact original notional amount it received at initiation, regardless of where the spot exchange rate has moved to in the meantime. A currency swap can also combine fixed and floating legs in any pairing: fixed-fixed, fixed-floating, or floating-floating. A plain-vanilla interest rate swap is always one fixed leg against one floating leg.

Worked in full

In an interest rate swap on $8,000,000 notional, one party pays a fixed rate of 4.5 percent and receives a floating rate that resets to 6.2 percent for the current semi-annual period. What is the net settlement payment, and who pays whom? Net payment (to the fixed-rate payer) = (fixed rate - floating rate) x notional x period fraction = (0.045 - 0.062) x $8,000,000 x 0.5 = -0.017 x $8,000,000 x 0.5 = -$68,000. The negative sign means the fixed-rate payer receives $68,000 this period, since the floating rate they are owed, 6.2 percent, exceeds the fixed rate they owe, 4.5 percent.

The same problem, one step removed

Same swap: $8,000,000 notional, fixed rate 4.5 percent, floating rate resets to 6.2 percent, semi-annual settlement. Apply the semi-annual adjustment and compute the net settlement payment yourself.

The trap

A swap's zero value at initiation is a starting condition, not a lifetime guarantee: once market rates move even slightly away from the rate set at initiation, the two legs stop being worth the same, and treating 'zero value' as a permanent property of the contract is the exam's standard trap.

Learning outcomes covered by this module

Verbatim from the 2026 CFA Level I topic outline. Every practice question and key rule below is tagged to one of these where the stem and explanation make the match clear.

  1. describe how swap contracts are similar to but different from a series of forward contracts
  2. contrast the value and price of swaps

Key rules

Written from this module's own lesson and the 2026 CFA Level I topic outline, in teaching order, each tagged to the learning outcome it belongs to where that is clear.

LOS 01

A swap is economically similar to a portfolio of forward contracts, one per settlement date, though the pricing mechanism differs from pricing each forward independently

Because each swap settlement period exchanges a fixed amount for a floating amount determined by the rate prevailing at the start of that period, each period functions like a single forward contract on the floating rate for that specific date. A multi-period swap is therefore similar to a series (portfolio) of such forwards. The similarity is structural, not a claim that a swap is literally priced as the sum of separately quoted forward contracts; in practice a single fixed swap rate is set across all periods at once so that the whole package has zero value at initiation, rather than each implied forward rate being individually equal to the fixed swap rate.

LOS 02

Swap price and swap value are distinct concepts, exactly as with forwards: price is fixed at initiation, value fluctuates afterward

The swap price is the fixed rate agreed upon at initiation (the par swap rate); it never changes for the life of the contract. The swap value is what the existing position is currently worth in the market; it starts at zero, because the fixed rate was set specifically to equate the present values of the two legs, and then it fluctuates as market interest rates move relative to that original fixed rate. A party who locked in a fixed rate that is now below the current market rate holds a swap with positive value (as the fixed-rate payer, since they pay less than a new entrant would), and a party locked into an above-market fixed rate holds a swap with negative value.

LOS 02

Zero value at initiation is a one-time calibration condition, not a permanent state of the contract

The par swap rate is solved for precisely so that the present value of the fixed leg equals the present value of the expected floating leg at the moment the swap is entered, which is why no upfront payment changes hands and why value equals zero at that instant. This equality applies only at initiation; it is a starting condition, not a rule that holds throughout the contract's life. Once time passes and interest rates move away from the levels priced in at initiation, the two legs' present values diverge and the swap's value becomes non-zero for both counterparties, mirroring the pattern in forward contract valuation exactly.

The trick

Authored only where a key rule has an arbitrary number, list, or formula shape worth a memory device; a module with none of those has no tricks here, on purpose.

Swap price is fixed forever at initiation; swap value starts at zero and moves with rates afterward

The same price-versus-value distinction that governs forward contracts applies to swaps: the contracted fixed rate never changes, but what the contract is worth to hold changes continuously as market rates move.

Zero value at initiation is a calibration, not a lifetime guarantee

Candidates who correctly recall 'a swap has zero value at initiation' sometimes over-generalize it to 'a swap always has zero value'; the equality holds only at the moment of entry, before any rate movement.

A swap resembles a series of forwards structurally, but is priced as one package, not as separately-quoted individual forwards

The single fixed swap rate applied across every settlement period is chosen so the whole multi-period package nets to zero value, not because each period's implied forward rate independently equals that fixed rate.

The method

Authored, ordered steps for answering this module's question types; a calculation module's calculator-dependent step ends with a bracketed BA II Plus keystroke sequence.

  1. For a swap-structure question, describe the swap as similar to a series of forward contracts, one per settlement date, each an unconditional obligation for both parties.
  2. For a swap-price question, identify the fixed rate as set once at initiation and unchanging for the life of the contract.
  3. For a swap-value question, determine whether the question refers to the moment of initiation (value = zero, by construction) or a later point (value fluctuates with how market rates have moved relative to the original fixed rate).

One card

Condensed from the key rules and tricks above, nothing new. What you'd want on one index card the night before.

Practice questions

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. 10 question(s) available for this unit.

Question 1Exam level

Two parties enter a plain vanilla interest rate swap. Party A pays a fixed rate of 5% annually and Party B pays the floating rate. The notional principal is $10 million. At the first settlement date, the floating rate (SOFR) has reset to 6%. Which of the following best describes the net settlement payment?

How sure are you?

Correct: B. The correct answer is Party B pays Party A $100,000.
A. You might confuse which party is the 'payer'. They think 'fixed-rate payer' means the party receiving fixed payments. Fixed-rate payer = the party obligated to PAY fixed. When floating rises above fixed, the floating-rate payer owes more and makes the net payment.
C. You might divide the difference by 2, confusing semi-annual with annual settlement. The problem specifies annual settlement, so the full annual rate difference applies. No division by 2.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 2Exam level

In an interest rate swap, the notional principal is most likely described as:

How sure are you?

Correct: B. The correct answer is The amount used to calculate periodic interest payments but not exchanged.
A. Currency swaps DO exchange notional principal. You might generalize this to all swaps. IRS notional is not exchanged because both legs are in the same currency. There is no currency risk requiring principal transfer.
C. Sounds financially sophisticated and relates to swap valuation. This describes the swap's market value, not the notional principal itself. The notional is a fixed reference amount, not a present value.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 3Exam level

A company has issued floating-rate debt tied to SOFR + 150 bps and is concerned that interest rates will rise significantly. The company enters a pay-fixed, receive-floating interest rate swap. Which of the following describes the company's effective borrowing cost after the swap, most likely?

How sure are you?

Correct: C. The correct answer is The company has converted its floating-rate debt to synthetic fixed-rate debt at a cost equal to the fixed swap rate plus 150 bps.
A. Partially true. The company does have fixed-rate exposure. But 'benefits if SOFR rises' implies a speculative gain, which misframes the hedging purpose. If SOFR rises, the swap gain offsets the higher debt cost. The company is hedged, not speculating for a profit.
B. The underlying debt contract itself does not change. Literally true, but misleads about the combined position. The combined position (debt + swap) creates a synthetic fixed rate. The swap overlay changes the effective exposure even though the debt contract is unmodified.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 4Exam level

Which of the following most likely explains why a plain vanilla interest rate swap has zero value at initiation?

How sure are you?

Correct: B. The correct answer is Because the fixed rate is set so that the present value of fixed payments equals the present value of expected floating payments.
A. Notional not being exchanged sounds like a reason there is no value to the instrument. The absence of notional exchange is unrelated to valuation. Value depends on the relationship between PVs of each leg, not on whether principal moves.
C. Financial regulation does require margin and collateral. Sounds plausible as a rule-based answer. The zero-value-at-initiation is a no-arbitrage economic condition, not a regulatory requirement. The exam tests understanding of the economic logic.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 5Harder

Party X enters a 2-year interest rate swap as the fixed-rate payer at 4%. Six months later, market interest rates have risen so that the fixed rate on a comparable new 1.5-year swap is now 5%. The value of Party X's swap position is most likely:

How sure are you?

Correct: C. The correct answer is Positive, because Party X locked in a below-market fixed rate relative to current market.
A. Paying 'below-market' sounds like a disadvantage. A language trap. For the PAYER of the below-market rate, this is an ADVANTAGE. They pay less than the current market requires. 'Below-market fixed payment' = favorable obligation.
B. The zero-value-at-initiation rule is overgeneralized to all points in the swap's life. Zero value only applies at initiation. Once rates move, one side of the swap gains value and the other loses it. The zero-value rule is an initiation condition only.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 6Exam level

In a currency swap between a US company and a German company, compared to a plain vanilla interest rate swap, the treatment of notional principal is most likely described as:

How sure are you?

Correct: C. The correct answer is Exchanged at both initiation and maturity in the currency swap but not in the interest rate swap.
A. Students memorize 'notional is not exchanged' from IRS and apply it universally to all swap types. This is true ONLY for IRS. Currency swaps must exchange principal because the two currencies have different values and create exchange rate exposure that requires actual transfer.
B. Reversing the true answer. A classic CFA distractor technique. IRS notional is not exchanged. Currency swap notional IS exchanged. The opposite of this answer.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 7Exam level

A US company wants to borrow in euros to fund its European subsidiary but can borrow more cheaply in US dollars. A German company faces the mirror-image situation. They enter a currency swap. Which of the following most likely accurately describes what happens at swap initiation?

How sure are you?

Correct: B. The correct answer is The US company receives euros and pays an equivalent amount of dollars to the German company.
A. You might apply IRS logic (no principal exchange) to currency swaps. Currency swaps exchange principal precisely because the two amounts are in different currencies with real exchange rate risk.
C. Describes a cross-currency basis swap variant, not a standard currency swap. Standard currency swaps exchange both principal AND interest in different currencies. The structure in C is a more complex instrument not tested at Level 1.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 8Exam level

In a plain vanilla interest rate swap with semi-annual payments, the fixed rate is 4.5% per year and the floating rate resets to 5.2% at the start of the period. The notional principal is $20 million. The net payment at this settlement date is CLOSEST to:

How sure are you?

Correct: B. The correct answer is $70,000 paid by the floating-rate payer to the fixed-rate payer.
A. Correct dollar amount, wrong direction. You might get the number right but reverse the payment direction. Floating-rate payer owes MORE (5.2% > 4.5%), so they PAY the net difference to the fixed-rate payer, not the reverse.
C. You might forget to halve the annual rates for semi-annual frequency. Use annual rates without dividing by 2. Semi-annual payment uses half the annual rate. Using full annual rates doubles the result incorrectly to $140,000.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 9Above the exam

A company enters a 2-year interest rate swap, paying a fixed rate and receiving floating (SOFR), to hedge floating-rate debt. One year into the swap, interest rates have risen significantly since initiation. Combining how swap value evolves with changing rates and the perspective of the fixed-rate payer, the value of this swap TO THE COMPANY (the fixed-rate payer) at this point is most likely:

How sure are you?

Correct: B. A swap has zero value to both parties ONLY at initiation (when the fixed rate is set so the present values of the fixed and floating legs are equal). As market rates change over the swap's life, its value shifts: since the fixed-rate PAYER benefits when rates RISE (their fixed obligation becomes relatively cheaper compared to the now-higher floating payments they receive), a rate increase since initiation makes the swap valuable TO the fixed-rate payer (the company here), and correspondingly creates a matching loss in value for the fixed-rate receiver on the other side.
A. Rising rates do not hurt every party to a swap equally; the effect depends on which side of the swap a party is on. The FIXED-RATE PAYER specifically benefits from rising rates, since receiving a higher floating rate while paying a fixed rate locked in earlier becomes more favorable, not less.
C. A swap only has zero value at the moment of initiation, when its terms are set to make the two legs' present values equal; once time passes and market rates move away from the original fixed rate, the swap's value to each party generally becomes nonzero.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

Question 10Above the exam

A dealer is the fixed-rate receiver on an interest rate swap with a notional principal of $10 million. Combining the mechanics of periodic net settlement with the fact that only the difference between the fixed and floating legs is exchanged, if the fixed rate is 4% and the floating rate resets at 5.5% for a given period (with a full-year day count for simplicity), the dealer should most likely:

How sure are you?

Correct: B. Interest rate swaps settle on a NET basis each period: only the difference between what each side owes is actually exchanged. As the fixed-rate RECEIVER, the dealer is owed 4% x $10 million = $400,000 but owes the floating amount, 5.5% x $10 million = $550,000; on a net basis, the dealer must PAY the $150,000 difference ($550,000 - $400,000), since the floating leg exceeds the fixed leg this period.
A. Swap payments are settled NET, not gross; the dealer does not simply receive the full fixed amount owed to them without also netting out the larger floating amount they owe, which flips the direction of the actual cash flow entirely once netted.
C. Standard interest rate swaps settle PERIODICALLY (e.g., quarterly or semi-annually) over the life of the swap, not only at maturity; periodic net settlement is a defining mechanical feature of how swaps actually function.

Unit: pricing-and-valuation-of-interest-rates-and-other-swaps

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