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FRM Part I · FRM Exam Part I

Swaps for FRM Part I: Chapter Study Guide

A swap is an agreement to exchange cash flows on set dates, based on a notional amount. To solve swap questions, split the swap into a fixed-rate bond and a floating-rate bond, or into a strip of forward contracts. Discount each cash flow, then take the difference. Par swap rate = (1 − final discount factor) ÷ Σ discount factors, for periodic payments with accrual fractions.

What this chapter covers

This chapter covers how swaps work, how to value them, and how to judge their risk. You start with the mechanics: two parties exchange a fixed payment for a floating payment on a notional amount that is usually not exchanged. You then value a plain vanilla interest rate swap, move to currency swaps, study how swap rates and discounting curves are built, and finish with credit risk and other swap types.

The core idea is simple. A swap is a package of simpler instruments. A pay-fixed, receive-floating swap equals a long position in a floating-rate bond and a short position in a fixed-rate bond. It also equals a series of forward rate agreements. If you can price a bond and a forward, you can price a swap.

This chapter links to several other parts of the paper. It builds on time value of money, forward rates and bond pricing from the valuation material. It connects to forwards and futures through the idea of replication. It also leads into counterparty risk, central clearing and margin, which appear in the risk management topics. Treat it as a chapter that ties earlier ideas together.

Swaps are a core tool in banks and asset managers, so GARP tests them as a practical skill, not as theory. Questions are mostly numerical: value a swap, find a fixed rate, compute a currency swap value, or reason about exposure. They reward a clear method and punish sloppy discounting. Because the same logic (replication and discounting) runs through bonds, forwards and credit exposure, time spent here pays off in other chapters too. With 100 questions in 4 hours, you need to solve a standard swap valuation in a couple of minutes, and that comes only from practice.

Swaps: topics in the order to study them

  1. 1Swap Mechanics and Market StructureLearn who pays what, when, and how the market is organised before you attempt any numbers.
  2. 2Plain Vanilla Interest Rate Swap ValuationThis is the core calculation of the chapter, and every later topic builds on its two methods: bond approach and FRA approach.
  3. 3Swap Rates, LIBOR/OIS and DiscountingOnce you can value a swap, learn how the par rate is derived and which curve is used to discount.
  4. 4Currency SwapsThis reuses the bond-difference method, with two currencies and an exchange rate added.
  5. 5Swap Credit Risk and Other Swap TypesFinish with exposure, netting, collateral and variants, which make sense only after you know what a swap is worth.

How to prepare Swaps

Aim to be able to value any swap from scratch, then speed up. Work in this order and keep a one-page formula sheet.

  1. Read the mechanics once and write the cash flows of a pay-fixed swap in your own words: what you pay, what you receive, and what is not exchanged.
  2. Learn both valuation methods. Bond method: Value to the fixed payer = B_float − B_fix. FRA method: discount the net payment (forward rate − fixed rate) × notional × accrual for each period.
  3. Practise the par rate formula: swap rate = (1 − Z_n) ÷ Σ (accrual × Z_i), where Z_i are discount factors. Check that a swap at this rate has zero value at start.
  4. Do several valuations with a financial calculator or spreadsheet. Use the time value keys (N, I/Y, PV, FV) for bond legs, and store discount factors so you do not retype them.
  5. For currency swaps, value each leg in its own currency, convert at the spot rate, then take the difference. Always note which leg you pay and which you receive.
  6. Write short notes on credit risk: only the party with a positive value is exposed, netting reduces exposure, and collateral and central clearing cut it further.
  7. Finish with timed mixed sets of swap questions. Review every error by asking whether it was a method, discounting or sign error.

Common mistakes in Swaps

  • Mixing up the sign: giving the value to the floating payer instead of the fixed payer.

    Fix: Write down your side first. Fixed payer value = floating bond − fixed bond. The floating payer value is the negative of this.

  • Valuing the floating leg as a bond with a fixed coupon between reset dates.

    Fix: Treat the floating leg as worth (notional + next known coupon) discounted to today, since it resets to par on the next reset date.

  • Forgetting accrual fractions or using the wrong period length.

    Fix: Multiply each rate by the period fraction, such as 0.5 for semi-annual, before applying the notional.

  • Using a single discount rate instead of the discount factor for each date.

    Fix: Use the discount factors given. Only use one yield if the question states a flat curve.

  • Treating the currency swap notional as irrelevant.

    Fix: In a standard currency swap, the principals are exchanged at start and end. Include them in both legs.

  • Confusing credit exposure with the notional amount.

    Fix: Remember exposure is the positive market value of the swap, after netting and collateral where stated. Notional is only a scale for the payments.

Last-day revision: Swaps

  • A swap exchanges cash flows on a notional; in an interest rate swap the notional is normally not exchanged.
  • Pay-fixed swap = long floating-rate bond + short fixed-rate bond.
  • Value to fixed payer = PV of floating leg − PV of fixed leg.
  • Just after a reset date, a floating-rate bond is worth its par value.
  • The swap rate makes the swap worth zero at start.
  • Par swap rate = (1 − final discount factor) ÷ Σ (accrual × discount factors).
  • FRA approach: value each period as (forward rate − fixed rate) × notional × accrual × discount factor.
  • Currency swaps usually exchange notional at start and end; swap value is the difference of two bond values in one currency.
  • Modern practice discounts collateralised swaps on the OIS curve, not on LIBOR.
  • Only a party with positive swap value faces credit loss; exposure is the positive replacement value.
  • Netting and collateral reduce credit exposure; central clearing moves it to a clearing house.
  • Interest rate swap exposure tends to be lower than a loan of the same size, because only net flows and value changes are at risk.

Swaps practice questions

Swaps in other exams

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

Swaps: frequently asked questions

How do I value an interest rate swap in the FRM exam?

Use either the bond method or the FRA method. In the bond method, value the fixed and floating legs as bonds and take the difference. Both give the same answer when they use the same discount factors.

Why do swaps use OIS discounting?

Collateralised swaps earn a rate close to the overnight rate on posted margin, so their cash flows are discounted at a near risk-free rate. Practice therefore moved from discounting at LIBOR to discounting on the OIS curve. Read your curriculum for the exact treatment tested.

Do I need a financial calculator for swaps?

It helps. You can use the time value keys to price the bond legs quickly and check discount factors. Practise with the model you will use on exam day, as GARP permits only approved calculators.

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

An interest rate swap exchanges fixed and floating interest in one currency, usually without exchanging principal. A currency swap exchanges interest, and normally principal, in two currencies. That makes exchange rates central to its valuation.