Strategic Financial Management · Swaps

Swap Valuation and Pricing: Comparative Advantage and Discounting

Updated 11 October 2026 · Fact-checked

Swap valuation finds what an existing swap is worth today; swap pricing sets the fixed rate at which a new swap has zero value. For comparative advantage, compute the quality spread differential, deduct the bank's fee, share the balance, and set each party's net cost. For valuation, discount fixed and floating legs and take the difference.

Understand Swap Valuation and Pricing

A swap is an agreement to exchange cash flows on a notional amount. In an interest rate swap, one side pays a fixed rate and the other pays a floating rate. The notional is never exchanged. Only the interest difference matters.

There are two separate questions in this topic. The first is why a swap creates a gain. The answer is comparative advantage. A better-rated borrower usually has a cheaper rate in both fixed and floating markets, but the gap between the two borrowers is not the same in both markets. The borrower with the relatively bigger advantage in one market borrows there. The two then swap. The total saving is the quality spread differential (QSD).

The second question is what a swap is worth and what rate it should carry. A swap is a pair of cash flow streams. Value each stream at today's discount factors. A new swap is priced so that the fixed leg and the floating leg have equal present value. That fixed rate is the swap rate. Once market rates move, an old swap has a positive value for one party and a negative value for the other.

The floating leg has a useful shortcut. Just after a reset date, a floating-rate bond is worth its par value. So the floating leg of a swap is valued as a bond that resets to par at the next payment date. Equivalently, you can forecast floating payments using forward rates and discount them. Both methods give the same answer.

In exam questions you will see either a gain-sharing problem (with or without a bank as intermediary) or a valuation and swap rate problem using given zero rates or discount factors. Identify which one first.

Key rules to remember

Quality spread differential (QSD): QSD = |Fixed-rate spread difference − Floating-rate spread difference|; Spread difference = Borrower B's rate − Borrower A's rate in that market. This is the total gain available to share.
Net gain to parties: Gain to parties = QSD − Bank's fee (if any); If gain is shared equally between two parties, each gets half of this amount. Follow the sharing ratio given in the question.
Net cost after swap: Net cost = Cost without swap − Share of gain; Apply it to the rate the party actually wanted (fixed or floating), not the rate it borrowed at.
Discount factor: DF(t) = 1 ÷ (1 + z_t)^t; z_t is the annual zero (spot) rate for t years.
Swap rate (par swap, annual payments): Swap rate = (1 − DF_n) ÷ Σ DF_t, for t = 1 to n; Makes the swap's value zero at start. For half-yearly payments, use period rates and multiply by the number of periods per year to annualise.
Forward rate from discount factors: F(t1, t2) = (DF_t1 ÷ DF_t2 − 1) ÷ (t2 − t1); Gives the simple forward rate for the period from t1 to t2. This is the floating rate you assume for future payments.
Value of swap by bond approach: Value to fixed payer = B_float − B_fixed; Value to fixed receiver = B_fixed − B_float; B_fixed = PV of fixed coupons plus notional. B_float = (Notional + next floating payment) × DF to next payment date.
Value of swap by FRA approach: Value to fixed payer = Σ (Forward rate − Fixed rate) × Notional × period × DF; Each period is treated as a forward rate agreement settled at its payment date. Both approaches agree.

How to solve Swap Valuation and Pricing questions

Decide first whether the question is about gain sharing or about valuation. Then follow the matching steps.

1Read what each party wants. Note whether it needs fixed or floating funds. This may differ from the market where it has the advantage.
2Tabulate the fixed and floating rates for both parties. Compute the spread difference in each market.
3Find the QSD, the gap between the two spread differences. The party with the bigger advantage in a market borrows in that market.
4Deduct the bank's fee, if any. Divide the balance in the ratio given (equal if the question is silent, and state this assumption).
5Compute each party's target net cost. Then build the cash flows: what each pays the lender, pays the bank and receives from the bank. Check that the net cost equals the target.
6For valuation, convert given zero rates to discount factors. Find the fixed leg PV and the floating leg value (par at reset, or forward rates discounted).
7Take the difference. State the sign from the viewpoint of the party asked about. Add the swap rate if asked.
8Write one line of conclusion: the gain to each party, or the value and who owes whom.

Quickest way: Four-line check for gain-sharing questions

When to use it: Use this when the question gives two borrowers, two markets and a bank fee, and asks for the swap terms.

Write the spread in each market for both firms. Subtract to get QSD.
Subtract the bank fee. Split the rest as instructed.
Set the bank's floating leg flat (MIBOR in, MIBOR out) so that only the fixed rates differ. The bank's fee is then the gap between the fixed rate it receives and the fixed rate it pays.
Confirm: gain to firm 1 + gain to firm 2 + bank fee = QSD. If this fails, your cash flows are wrong.

Common mistakes in Swap Valuation and Pricing

Letting each firm borrow in the market where its own rate is lower.
Students think absolute advantage decides who borrows where. A stronger borrower is cheaper in both markets.
Fix: Compare the spread differences. Each firm borrows where its relative advantage is greatest, and the swap converts to the form it wants.
Forgetting the bank's fee when the bank is an intermediary.
The QSD looks like the final gain, so the deduction is skipped.
Fix: Always write: gain to parties = QSD − bank margin. Then check that the three gains add back to QSD.
Applying the gain to the wrong rate.
Students subtract the gain from the rate at which the firm borrowed, not from the rate it would have paid in the market it wanted.
Fix: Target cost = direct cost in the wanted market − share of gain. Then design the swap legs to reach it.
Valuing the floating leg as a stream of the current floating rate for all years.
Students copy today's rate forward and treat it as the same as a forecast.
Fix: Use the bond shortcut (par at the reset date) or forward rates from the zero curve. Do not use the spot rate for all periods.
Giving the sign of the swap value from the wrong party's viewpoint.
Fixed payer and fixed receiver have opposite values, and the question wording is skimmed.
Fix: Write the formula for the party asked. If market rates fall below your fixed rate, the fixed payer loses value and the fixed receiver gains.
Using annual rates for half-yearly payments without conversion.
The period length is overlooked.
Fix: Divide the annual rate by the number of periods per year for coupons, and use period discount rates. Then annualise the final swap rate.

Worked examples

Example 1

Company X and Company Y can borrow as follows. X: fixed 9.0%, floating MIBOR + 0.5%. Y: fixed 10.5%, floating MIBOR + 1.5%. X wants floating-rate funds and Y wants fixed-rate funds. A bank arranges the swap and takes 0.1% as its fee. The remaining gain is shared equally by X and Y. Show the swap terms and each party's net cost.

Show the solution

Fixed-rate spread difference = 10.5% − 9.0% = 1.5%. Floating-rate spread difference = 1.5% − 0.5% = 1.0%.
QSD = 1.5% − 1.0% = 0.5%. This is the total gain.
X has the bigger advantage in the fixed market (1.5% against 1.0%), so X borrows fixed at 9.0%. Y borrows floating at MIBOR + 1.5%.
Gain after bank fee = 0.5% − 0.1% = 0.4%. Each of X and Y gets 0.2%.
Target cost for X (wants floating) = MIBOR + 0.5% − 0.2% = MIBOR + 0.3%. Target cost for Y (wants fixed) = 10.5% − 0.2% = 10.3%.
Design the cash flows with the bank's floating leg flat. X receives a fixed rate a from the bank and pays MIBOR to the bank. X's cost = 9.0% − a + MIBOR = MIBOR + 0.3%, so a = 8.7%.
Y pays a fixed rate c to the bank and receives MIBOR. Y's cost = MIBOR + 1.5% + c − MIBOR = 10.3%, so c = 8.8%.
Bank gain = 8.8% − 8.7% = 0.1%, which matches its fee. Check: 0.2% + 0.2% + 0.1% = 0.5% = QSD.

Answer: X borrows fixed at 9.0%, receives 8.7% fixed from the bank and pays MIBOR to the bank, so its net cost is MIBOR + 0.3%. Y borrows floating at MIBOR + 1.5%, pays 8.8% fixed to the bank and receives MIBOR, so its net cost is 10.3%. X and Y each gain 0.2% and the bank earns 0.1%.

Example 2

A ₹10,00,00,000 (₹10 crore) swap has two years left. Annual payments are made on the notional. You pay a fixed rate of 8% and receive the floating rate, which has just reset. Zero rates are 7.0% for one year and 7.5% for two years. Find the swap rate for a new two-year swap and the value of your swap.

Show the solution

DF1 = 1 ÷ 1.07 = 0.934579. DF2 = 1 ÷ (1.075)² = 1 ÷ 1.155625 = 0.865333.
Sum of DFs = 0.934579 + 0.865333 = 1.799912.
Swap rate = (1 − 0.865333) ÷ 1.799912 = 0.134667 ÷ 1.799912 = 7.48% (approximately).
Bond approach, fixed leg: B_fixed = 0.08 × 0.934579 + 1.08 × 0.865333 = 0.074766 + 0.934560 = 1.009326 per ₹1 of notional.
Floating leg just reset, so B_float = 1.000000 per ₹1 of notional.
Value to fixed payer = B_float − B_fixed = 1.000000 − 1.009326 = −0.009326.
In rupees = −0.009326 × ₹10,00,00,000 = −₹9,32,600 (approximately).
Check: (8% − 7.4815%) × 1.799912 = 0.009326, which gives the same answer.

Answer: The current two-year swap rate is about 7.48%. Your swap pays 8%, which is above the market rate, so its value to you as fixed payer is about −₹9.33 lakh (a liability of about ₹9,32,600).

Exam tips

Write the QSD line first. Marks are usually given for the spread differences and the QSD, even if the later cash flows have an error.
State your sharing assumption (equal sharing) if the question does not give one. Do not leave it unstated.
Show the check that gains add up to the QSD. It proves your swap terms are right and costs one line.
In valuation questions, write the discount factors in a small table and show the fixed leg and floating leg separately. Then give the sign from the asked party's side.
Section A MCQs often test who borrows where and the size of the QSD. Do these in under a minute from the two spread differences.

Practice questions from Swaps

Swap Valuation and Pricing in other exams

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

Swap Valuation and Pricing: frequently asked questions

What is quality spread differential in a swap?

It is the difference between the fixed-rate spread gap and the floating-rate spread gap of two borrowers. It equals the total gain that can be created through a swap. After deducting any bank fee, the balance is shared between the parties.

How do I decide who borrows in which market?

Compare the spread difference in each market. Each borrower raises funds in the market where its relative advantage is greater, which means the lower-rated borrower borrows where its disadvantage is smaller. Then the swap changes the funds to the form each party wants.

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

Convert the given zero rates to discount factors. Value the fixed leg as a bond with coupons and notional. Value the floating leg as par at the last reset, or discount forward-rate payments. The value to the fixed payer is floating leg minus fixed leg.

What is the swap rate?

It is the fixed rate that makes the present value of the fixed leg equal to the present value of the floating leg at the start, so the swap has zero value. For annual payments it equals (1 − last discount factor) divided by the sum of discount factors.