FRM Exam Part I · Swaps

Currency Swap Valuation for FRM Part I

Updated 11 October 2026 · Fact-checked

A currency swap exchanges interest payments, and usually principal, in two currencies. To value it, treat each side as a bond in its own currency, then convert the foreign bond at spot. Or value each cash flow as a forward exchange contract. Both methods give the same value.

Understand Currency Swaps

A currency swap is an agreement to exchange cash flows in two different currencies. In the most common form, a fixed-for-fixed swap, one party pays fixed interest in currency A and receives fixed interest in currency B. The other party does the opposite.

The key difference from an interest rate swap is the principal. In an interest rate swap, principal is the same currency on both sides, so it is only notional and never exchanged. In a currency swap, the two principals differ in currency. They are usually exchanged at the start and again at the end, both at the same agreed rate, which is normally the spot rate at initiation. The final exchange is what creates exchange rate risk.

At initiation, the swap is set up so it has zero value. The principals are equal in value at spot, and the fixed rates are the market swap rates for each currency. Later, interest rates and the exchange rate move, and the swap gains value for one side and loses it for the other.

Other types exist. Fixed-for-floating swaps (cross-currency basis style) pay fixed in one currency and floating in another. Floating-for-floating swaps pay floating in both. A floating leg is valued as worth par just after each reset, which keeps valuation simple.

There are two valuation methods. In the bond method, the swap is a long position in one bond and a short position in another. In the forward method, each exchange of cash flows is a forward contract on the exchange rate, valued using forward rates from covered interest parity. Both use discounting at each currency's own zero rates.

Key formulas to remember

Value to the party receiving foreign currency (bond method): V = S0 × B_F − B_D; S0 is the spot rate in domestic currency per 1 unit of foreign currency. B_F is the foreign bond value in foreign currency. B_D is the domestic bond value in domestic currency. The party receives foreign and pays domestic.
Value to the party receiving domestic currency: V = B_D − S0 × B_F; The negative of the other party's value.
Bond value for each leg: B = Σ [c × e^(−r_t × t)] + L × e^(−r_T × T); c is the fixed payment, L is the principal, and r_t is the zero rate for that currency. With discrete compounding, use the matching discount factors.
Forward exchange rate (continuous compounding): F_t = S0 × e^((r_D − r_F) × t); Domestic currency per 1 foreign. r_D is the domestic rate and r_F is the foreign rate, both for maturity t. If r_D > r_F, then F_t > S0: the foreign currency trades at a forward premium and the domestic currency at a forward discount.
Forward method value: V = Σ (foreign cash flow × F_t − domestic cash flow) × e^(−r_D × t); Use net cash flow at each date, signed for the party you value. Discount at the domestic rate.
Value of a forward contract to receive foreign currency: PV = (foreign cash flow × F_t − domestic cash flow) × discount factor; Applies to each date, including the final principal exchange.

How to solve Currency Swaps questions

Use this method for any currency swap valuation question. Decide first which party you are valuing.

1Identify the party. Write down what it pays and what it receives in each currency.
2List every cash flow: periodic interest in each currency and the final principal exchange. Check the initial exchange is already done.
3Choose the method. Use the bond method if zero rates for both currencies are given. Use the forward method if forward rates or rate differentials are given.
4Bond method: value the foreign bond in foreign currency using foreign discount rates. Value the domestic bond using domestic rates.
5Convert the foreign bond to domestic currency at spot, and take the difference. Sign it for the party you value.
6Forward method: compute a forward rate for each date, convert each foreign flow, subtract the domestic flow, and discount at domestic rates.
7Check the sign and the units. Make sure the quote is domestic per foreign, and say which party the answer is for.

Quickest way: Bond method shortcut with two bonds

When to use it: Use when both zero rates are flat or given, and the swap has few payments left. It is faster than building forward rates for every date.

Write the two bond values: B_F in foreign currency, B_D in domestic currency.
Compute each as coupons plus principal, discounted with e^(−rt). Use a calculator memory for discount factors.
Multiply B_F by spot to get domestic value.
Subtract in the right order: value to the foreign receiver is S0 × B_F − B_D.
Eliminate options by sign. If foreign interest rates are lower and the foreign currency has appreciated, check your sign makes sense.

Common mistakes in Currency Swaps

Treating principal as notional only, as in an interest rate swap.
Students carry over the vanilla swap rule that principal is never exchanged.
Fix: In a currency swap, principal is exchanged at the end, and usually at the start. Include the final principal in both bonds.
Discounting both currencies at the same rate.
Students use one discount curve out of habit.
Fix: Discount each currency's cash flows at that currency's own zero rates.
Using the wrong quote direction for the exchange rate.
Quotes can be domestic per foreign or foreign per domestic.
Fix: Write the units next to S0. If the rate is given as foreign per domestic, take the reciprocal before multiplying a foreign amount.
Getting the sign wrong for the party.
Students value the swap without deciding who receives which currency.
Fix: Receiver of foreign currency has V = S0 × B_F − B_D. The other party has the negative.
Using the initial spot rate for the forward calculations.
The swap principals are fixed at the original rate, so students apply that rate to everything.
Fix: Use the original rate only to fix the principal amounts. Base all forward rates and bond conversions on the current spot rate.
Using the wrong forward rate direction.
Mixing up r_D and r_F in the forward formula.
Fix: Domestic per foreign: F = S0 × e^((r_D − r_F)t). If r_D > r_F, the foreign currency trades at a forward premium (F > S0) and the domestic currency trades at a forward discount.

Worked examples

Example 1

A US firm receives 5% annual in JPY and pays 8% annual in USD on principals of JPY 1,200 million and USD 10 million. Payments are annual and the swap has 2 years left, with the next payment in 1 year. Continuously compounded zero rates are flat at 9% in USD and 4% in JPY. Spot is 110 JPY per USD. Find the swap value to the US firm in USD millions. Use e^(−0.04) = 0.96079, e^(−0.08) = 0.92312, e^(−0.09) = 0.91393, e^(−0.18) = 0.83527.

Show the solution

The US firm receives JPY and pays USD, so V = S0 × B_F − B_D, where S0 is USD per JPY = 1/110.
JPY discount factors (4%): 0.96079 for year 1 and 0.92312 for year 2. USD discount factors (9%): 0.91393 for year 1 and 0.83527 for year 2.
JPY bond: coupons are 5% × 1,200 = 60 million per year. B_F = 60 × 0.96079 + 1,260 × 0.92312.
60 × 0.96079 = 57.6474. 1,260 × 0.92312 = 1,163.1312. B_F = 1,220.7786 million JPY.
USD bond: coupons are 8% × 10 = 0.8 million. B_D = 0.8 × 0.91393 + 10.8 × 0.83527.
0.8 × 0.91393 = 0.73114. 10.8 × 0.83527 = 9.02092. B_D = 9.75206 million USD.
B_F in USD = 1,220.7786 ÷ 110 = 11.09799 million.
V = 11.09799 − 9.75206 = 1.34593 million.

Answer: The swap is worth about USD 1.346 million to the US firm.

Example 2

A party receives 4% in USD and pays 6% in GBP on notional USD 15 million and GBP 10 million. Payments are annual, with 1 year left until the final payments. The USD zero rate is 3% and the GBP zero rate is 5%, both continuously compounded. Spot is USD 1.50 per GBP. Use the forward method to find the value in USD to the party receiving USD. Use e^(−0.03) = 0.97045 and e^(0.02) = 1.02020.

Show the solution

The party receives USD and pays GBP. Final flows at t = 1: receives USD 0.04 × 15 + 15 = 15.6 million; pays GBP 0.06 × 10 + 10 = 10.6 million.
Forward rate: F = S0 × e^((r_D − r_F) × t) = 1.50 × e^(−0.02). e^(−0.02) = 1 ÷ 1.02020 = 0.98020.
F = 1.50 × 0.98020 = 1.47030 USD per GBP.
GBP payment in USD at the forward rate: 10.6 × 1.47030 = 15.5852 million.
Net at t = 1: 15.6 − 15.5852 = 0.0148 million.
Discount at the USD rate: 0.0148 × 0.97045 = 0.01436 million.

Answer: The value to the USD receiver is about USD 0.0144 million, or about USD 14,360.

Exam tips

Read which currency the party receives. Many questions turn on the sign alone.
Check the quote convention before you multiply. Write the units of S0 next to it.
Include the final principal in both bonds. Forgetting it gives answers that are far off.
If the question gives forward rates, use the forward method. If it gives zero rates only, the bond method is faster.
Eliminate options by sign first. Often two of the four choices have the wrong sign.

Practice questions from Swaps

Currency Swaps in other exams

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

Currency Swaps: frequently asked questions

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

An interest rate swap exchanges fixed and floating interest in the same currency, and principal is only notional. A currency swap exchanges cash flows in two currencies and usually exchanges principal at the start and end. This gives it exchange rate risk as well as interest rate risk.

Why is principal exchanged in a currency swap?

The two principals are in different currencies, so they are not offsetting. Exchanging them at the start provides funding in the needed currency. Exchanging them back at the end, at the same rate, fixes the exchange rate for the whole deal.

How do you value a currency swap using forward rates?

Treat each exchange as a forward contract. Compute the forward exchange rate for each date, convert the foreign cash flow at that rate, and subtract the domestic cash flow. Discount the result at the domestic rate and sum. The result matches the bond method.

What is the value of a currency swap at inception?

At inception, a swap at market rates has zero value. The principals are equal at the spot rate and the fixed rates are the current swap rates. Value then changes as rates and the exchange rate move.