Advanced Financial Management · Derivatives Analysis and Valuation

Swaps: Interest Rate and Currency (CA Final AFM)

Updated 5 October 2026 · Fact-checked

A swap is an agreement to exchange cash flows on a notional amount. In an interest rate swap you exchange fixed for floating interest. In a currency swap you also exchange principal in two currencies. To solve, find each party's cost, compute the comparative advantage gain, split it after any bank fee, then check each net cost.

Understand Swaps: Interest Rate and Currency

A swap is a contract between two parties to exchange streams of payments over a fixed period. Each side swaps because the other stream suits its needs better. Swaps are usually over the counter and often run through a bank.

In a plain vanilla interest rate swap, one party pays a fixed rate and the other pays a floating rate (such as MIBOR) on the same notional principal. The notional is never exchanged. Only the interest difference is settled, usually net, on each payment date.

Why would both sides gain? Because of comparative advantage. A firm with a better credit rating borrows cheaper in both markets. But the gap between the two firms is rarely the same in fixed and floating markets. Each firm borrows where its relative advantage is larger, then they swap. The total saving equals the difference between the two gaps.

In a currency swap, the parties exchange principal in two currencies at the start, pay interest in the currency they received, and re-exchange principal at maturity, normally at the same initial rate. This fixes the cost of foreign currency funding and removes exchange risk on the principal. The fixed-for-floating idea can also be added, but the exam usually tests fixed-for-fixed in two currencies.

A swap can also be valued after it starts. Its value to a party is the present value of the cash flows it receives minus the present value of the cash flows it pays. A swap quote is the fixed rate a dealer will pay or receive against floating. The dealer's bid is lower than its offer, and the gap is its margin.

Key rules to remember

Net settlement in an interest rate swap: Net payment = Notional × (Fixed rate − Floating rate) × (days ÷ 360 or the period fraction given); The fixed payer pays this if it is positive and receives it if it is negative. Use the day count given in the question.
Total gain from comparative advantage: Total gain = |Fixed rate differential − Floating rate differential|; Differential = rate for the weaker-rated firm minus rate for the stronger-rated firm in that market. Total gain is before any bank fee.
Gain to each party with a bank: Gain per party = (Total gain − Bank fee) ÷ 2; This holds only when the question says the balance is shared equally. Otherwise use the stated ratio.
Who borrows where: Each firm borrows in the market where its comparative advantage is greater (or its disadvantage is smaller); Then the firm swaps into the stream it actually wants.
Currency swap principals: Principal in currency B = Principal in currency A × Spot rate (B per A); Principals are exchanged at the start and re-exchanged at maturity at the same rate, unless the question says otherwise.
Swap valuation: Value to a party = PV of cash flows it receives − PV of cash flows it pays; Discount each flow at the current rate for its date. Right after a floating reset, the floating leg is worth the notional.
Fixed swap rate from discount factors: Par swap rate = (1 − Z_n) ÷ Σ Z_t; Z_t is the discount factor for period t, and the sum runs over all payment periods to maturity. Fixed payments are per period, so annualise if needed.

How to solve Swaps: Interest Rate and Currency questions

Use this order for any swap question, with or without a bank. Write the cash flows as a small table so you can check them at the end.

1Read what each party wants: fixed or floating, and in which currency. Note the notional and the tenor.
2List each party's borrowing rates in the fixed and floating markets. Compute both differentials.
3Total gain = difference between the two differentials. Decide who has the comparative advantage: the party with the smaller disadvantage in a market borrows there.
4Deduct the bank fee, if any, and split the balance as stated (equally unless told otherwise).
5Fix the swap flows. Let each party borrow in its chosen market, then set what it pays and receives from the bank or counterparty so its net cost equals the target cost.
6Check: each party's net cost should equal its direct cost less its share of the gain. The bank's receipts minus payments should equal its fee.
7For a currency swap, convert the principal at the stated spot, compute interest in each currency, and convert any rupee equivalents at the rates given.
8State the result in rates and in rupees (gain × notional), and add a one-line interpretation.

Quickest way: Differential shortcut for comparative advantage swaps

When to use it: Use this for gain-sharing questions with two firms, with or without a bank, when you only need the gains and the final net rates.

Compute fixed differential and floating differential. Subtract the smaller from the larger to get the total gain.
Deduct the bank fee, divide the rest by 2, and subtract this from each firm's direct cost for the stream it wants.
The firm with the larger differential in a market borrows there. The other firm borrows in the other market.
Choose the bank's pay and receive rates so the bank's spread equals the fee. Keep the floating leg at plain MIBOR for simplicity.
Multiply each gain by the notional for rupee savings, then check both firms' net costs once.

Common mistakes in Swaps: Interest Rate and Currency

Choosing the wrong market for each firm because the stronger firm is picked for both.
Students think the better-rated firm should borrow wherever it is cheaper.
Fix: Look at differentials, not levels. A firm borrows where its advantage is greater (or disadvantage smaller), then swaps.
Splitting the total gain without deducting the bank fee first.
The fee is stated late in the question and is easy to miss.
Fix: Always compute Total gain − Bank fee before dividing. Re-read the question for a fee.
Getting gain as the sum of differentials instead of the difference.
Students add the two gaps by habit.
Fix: Gain = |fixed gap − floating gap|. If the two gaps are equal, there is no gain from the swap.
Net cost does not match the target after setting swap rates.
The bank's pay and receive legs are chosen without checking each firm's full flow.
Fix: For each firm, add what it pays to the lender and the bank, subtract what it receives, and compare with the target. Fix the legs until both match.
Exchanging notional in an interest rate swap or forgetting the re-exchange in a currency swap.
The two swaps get mixed up.
Fix: Interest rate swap: notional is never exchanged. Currency swap: principal is exchanged at start and end, usually at the same rate.
Valuing a swap by discounting only the fixed leg or using one rate for all dates.
Students treat the floating leg as zero or ignore the term structure.
Fix: Value both legs. Use the discount rate for each date as given, and recall that the floating leg equals notional right after a reset.

Worked examples

Example 1

Firm A (high rating) and Firm B (lower rating) can borrow as follows. Fixed: A 8%, B 10%. Floating: A MIBOR + 1%, B MIBOR + 2%. A wants floating funds and B wants fixed funds, each for ₹50 crore. A bank arranges the swap for a total fee of 0.2% p.a. and the rest of the gain is shared equally by A and B. Find the swap structure, each firm's net cost and the annual gains in rupees.

Show the solution

Fixed differential = 10% − 8% = 2%. Floating differential = (MIBOR + 2%) − (MIBOR + 1%) = 1%.
Total gain = 2% − 1% = 1%. A has the larger advantage in fixed, so A borrows fixed at 8%. B borrows floating at MIBOR + 2%.
Gain after the bank fee = 1% − 0.2% = 0.8%. Each firm gets 0.4%.
A's target floating cost = (MIBOR + 1%) − 0.4% = MIBOR + 0.6%. B's target fixed cost = 10% − 0.4% = 9.6%.
Set the swap: A pays the bank MIBOR and receives 7.4% fixed. B pays the bank 7.6% fixed and receives MIBOR.
Check A: pays lender 8% + pays bank MIBOR − receives 7.4% = MIBOR + 0.6%. Check B: pays lender MIBOR + 2% + pays bank 7.6% − receives MIBOR = 9.6%.
Check the bank: receives 7.6% fixed and MIBOR, pays 7.4% fixed and MIBOR. Net = 0.2%, equal to its fee.
Rupee amounts on ₹50 crore: each firm gains 0.4% × ₹50,00,00,000 = ₹20,00,000 a year. The bank earns 0.2% × ₹50,00,00,000 = ₹10,00,000 a year.

Answer: A borrows fixed at 8% and ends with a net cost of MIBOR + 0.6%. B borrows floating and ends with a net cost of 9.6%. Each gains 0.4% (₹20,00,000 a year) and the bank earns 0.2% (₹10,00,000 a year).

Example 2

An Indian company borrows ₹8,00,00,000 at 9% in rupees and enters a 3-year currency swap. Spot is ₹80 per USD. It receives USD at the start, pays 6% interest in USD annually, and receives 9% interest in rupees from the counterparty. Principals are re-exchanged at maturity at ₹80. (a) Find the USD principal. (b) Find annual interest flows on each leg. (c) If the rate at the end of year 1 is ₹84 per USD, find the rupee cost of the USD interest and its percentage of the rupee principal.

Show the solution

USD principal = ₹8,00,00,000 ÷ 80 = USD 10,00,000.
USD interest paid = 6% × USD 10,00,000 = USD 60,000 a year.
Rupee interest received = 9% × ₹8,00,00,000 = ₹72,00,000 a year. This matches the interest on the company's own rupee loan, so that cost is covered.
At ₹84, USD 60,000 costs 60,000 × 84 = ₹50,40,000.
As a percentage of the rupee principal: ₹50,40,000 ÷ ₹8,00,00,000 = 6.3%.
The principal is re-exchanged at ₹80 at maturity, so the company pays USD 10,00,000 and receives ₹8,00,00,000 to repay its loan. The principal is therefore fixed in the swap and does not change with the spot rate.

Answer: USD principal is USD 10,00,000. Each year the company pays USD 60,000 and receives ₹72,00,000. At ₹84, the year-1 USD interest costs ₹50,40,000, which is 6.3% of the rupee principal.

Exam tips

Write the differentials first. In most gain-sharing questions, every other number follows from them.
Read for bank fees, unequal sharing and who bears the fee. These small phrases change the answer.
Always do the check: each firm's net cost and the bank's net spread. The exam rewards numbers that reconcile.
In currency swaps, show principal exchange at start and end, and show interest in each currency separately.
For valuation questions, set out the cash flows by date, discount each one, and state which party is in the money.

Practice questions from Derivatives Analysis and Valuation

Swaps: Interest Rate and Currency in other exams

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

Swaps: Interest Rate and Currency: frequently asked questions

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

In an interest rate swap, both legs are in one currency and the notional is not exchanged. Only the interest difference is paid. In a currency swap, the legs are in two currencies and principal is exchanged at the start and returned at maturity, usually at the same rate.

How do I calculate the gain from a swap using comparative advantage?

Find the fixed-rate differential and the floating-rate differential between the two firms. The total gain is the difference between them. Subtract any bank fee and split the rest as the question states, normally equally.

How does a bank intermediary change the swap?

The bank sits between the two parties and each firm swaps with the bank, not with the other firm. The bank keeps a spread, which is its fee, and this reduces the gain shared by the firms.

Is the notional principal exchanged in an interest rate swap?

No. The notional is only a base for calculating interest. Only the net interest difference is settled on each date.

How is a swap valued after it starts?

Value it as the present value of what you receive minus the present value of what you pay, using discount rates for each date. Right after a floating reset, the floating leg is worth the notional, so the fixed leg is compared with that.