CFA Level I · CFA Level I Exam

Pricing and Valuation of Interest Rate and Other Swaps

A swap is a contract to exchange cash flows. At initiation its value is zero, so the fixed rate is set to make the present values of fixed and floating legs equal. Afterwards you value it by discounting each leg's remaining cash flows with current rates. The difference between the two legs is the swap's value to each party.

What this chapter covers

This chapter shows how swaps are priced and valued. Pricing means finding the fixed rate that gives the swap zero value at the start. Valuation means finding what the swap is worth later, after rates have moved. You use the same tool throughout: discount factors from the current yield curve.

You begin with plain vanilla interest rate swaps, where one side pays fixed and the other pays a floating rate such as SOFR. You then extend the ideas to currency swaps, which exchange cash flows in two currencies and usually exchange notional, and to equity swaps, where one leg is linked to the return on a stock or index. The chapter closes with swaptions and credit considerations.

The chapter sits in Derivatives and Risk Management, and it builds on forwards, futures and the no-arbitrage principle. It also uses time value of money from Quantitative Methods and yield curves and bond pricing from Fixed Income. If you are comfortable with discount factors, the rest is mostly careful bookkeeping.

Derivatives and Risk Management carries a topic weight of 6-9% in the 2027 curriculum, and swaps are a core part of it. Questions are often short calculations, such as finding a swap fixed rate from discount factors or marking a swap to market. These are scoring opportunities if you know the method, because there is no penalty for wrong answers and each question has only three options. The same discounting skills also help you in forwards, bond and portfolio questions, so the effort pays back across the paper.

Pricing and Valuation of Interest Rate and Other Swaps: topics in the order to study them

1Interest Rate Swap Basics and Cash FlowsYou need the vocabulary, notional, net payments and the fixed and floating legs before any pricing makes sense.
2Swap Pricing and Swap Fixed Rate CalculationThis introduces the zero-value-at-start condition and the discount factor formula that every later topic reuses.
3Valuation of Interest Rate Swaps After InitiationIt applies the same discounting to a swap that is already running, and shows how value moves when rates change.
4Currency Swaps Pricing and ValuationIt adds a second currency and notional exchange to the framework you already know.
5Equity Swaps Pricing and ValuationOne leg becomes an equity return, so you reuse the floating-leg logic with a different underlying.
6Swaptions and Swap Credit and Pricing ConceptsIt builds on swap values and rates as options and credit exposure, so it comes last.

How to prepare Pricing and Valuation of Interest Rate and Other Swaps

Treat this chapter as one method applied six ways. Master the discount factor method first, then practise variations.

Read the basics and draw the cash flow diagram for a pay-fixed, receive-floating swap. Label who pays what and who receives what.
Learn the discount factor formula for the swap fixed rate: fixed rate = (1 − final discount factor) ÷ sum of discount factors. Practise with a three-period curve until you can do it quickly on your calculator.
Value a swap after initiation by finding the present value of remaining fixed payments and the floating leg, then take the difference. Check the sign from the viewpoint of the fixed payer and the fixed receiver.
Work currency swaps by valuing each leg in its own currency, then converting at the current spot rate. For equity swaps, value the equity leg at the current equity value (the notional adjusted for the return since the last reset), value the fixed or floating leg by discounting, and take the difference.
Add swaptions and credit last. Know which party holds the option, what a payer and receiver swaption give, and why credit risk sits with the party that is owed money.
Finish with timed mixed practice at about 90 seconds per question. For each wrong answer, note whether it was a method, sign or arithmetic error.

Common mistakes in Pricing and Valuation of Interest Rate and Other Swaps

Using the wrong sign when valuing a swap for the fixed payer versus the fixed receiver.
Fix: Write the party first. Fixed payer value = floating PV − fixed PV. Then flip the sign for the other party.
Forgetting to include the notional exchange in currency swap valuation.
Fix: For currency swaps, include the remaining interest payments and the final notional exchange in each leg's present value. Include the initial exchange only if it has not yet occurred.
Discounting with the wrong rates or skipping the day-count fraction.
Fix: Adjust each period's rate by its fraction of the year, and use discount factors from the correct curve date.
Treating the floating leg as worth par at any date.
Fix: On a reset date the floating leg is worth par. Between resets, value it as (notional + next floating payment) × the discount factor for the next payment date.
Confusing payer and receiver swaptions.
Fix: Remember the label always describes the fixed leg: payer pays fixed, receiver receives fixed.
Mixing up interest rate gains and swap gains in the direction of rate moves.
Fix: When market rates rise, the fixed payer is paying a fixed rate that is below the new market swap rate, so the swap gains value for the payer and loses value for the fixed receiver.

Last-day revision: Pricing and Valuation of Interest Rate and Other Swaps

A swap has zero value at initiation, which sets the fixed rate.
Plain vanilla swap: one party pays fixed and receives floating; the other does the opposite.
Swap fixed rate = (1 − final discount factor) ÷ Σ discount factors, with period fractions included in the sum when relevant.
Value to the fixed payer = PV of floating leg − PV of remaining fixed payments.
Value to the fixed receiver is the opposite sign of the fixed payer's value.
If rates rise after initiation, the fixed payer gains because the fixed rate it pays is below the new market swap rate; the fixed receiver loses.
Just after a reset, a floating-rate leg is worth its notional, ignoring credit effects.
Currency swap: value each leg in its own currency, then convert at current spot.
Currency swaps usually exchange notional at start and end; interest rate swaps do not.
Equity swap: value the equity leg at the current equity value (notional adjusted for the return since the last reset), value the fixed or floating leg by discounting, and take the difference.
A payer swaption gives the right to pay fixed; a receiver swaption gives the right to receive fixed.
Credit exposure sits with the party for whom the swap has positive value.

Pricing and Valuation of Interest Rate and Other Swaps practice questions

Pricing and Valuation of Interest Rate and Other Swaps in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Pricing and Valuation of Interest Rate and Other Swaps: frequently asked questions

How do I calculate the swap fixed rate on the exam?

Use discount factors for each payment date. The fixed rate equals (1 − the last discount factor) ÷ the sum of all discount factors, adjusted for any day-count fraction. Do the sum on your calculator and check that the answer lies near the average of the spot rates.

Why is a swap worth zero at the start?

Neither party pays anything upfront, and the market makes the fixed rate so that the present values of both legs are equal. If the value were not zero, one side would receive a free gain, which no-arbitrage rules out.

Do I need to memorise many formulas for swaps?

No. You need the discount factor method and the logic of each leg. Most questions use the same steps, with small changes for currency, equity or option features.

How much time should I give this chapter?

Give it enough to do the calculations without hesitation, because it is a short set of repeating methods. Spend most of your time on practice questions, and link it to forwards and fixed income review.