1. The bank fee as a sum of three components

A bank charges a fee when it sells an interest rate derivative to a client. Examples are an interest rate swap, a cap, a floor or a collar. The fee on a derivative is not one number. It has three components:

• The trading margin, also called the hedging cost. It pays for hedging the risk that the bank takes from the client.
• The value adjustment fee, if it applies. It covers the credit valuation adjustment (CVA) and the funding valuation adjustment (FVA).
• The sales margin. It is the margin that sales adds on top.

The total fee is the sum of the three components:

The minimum fee is usually the trading margin plus the value adjustment fee. These two are costs that the bank expects to pay simply by entering the transaction. So their sum is the minimum price that the bank can quote and still cover these costs:

A bank goes below this minimum only if it really wants to attract the client. The sales margin comes on top of it.

A basis point (bp) is 0.01%. A margin is an extra rate, quoted in basis points a year. The basis point value (BPV), also called PV01, is the value today of a margin of 1bp paid every period. It is the common unit: it turns a margin in basis points into an amount in euros, and back.

This chapter builds on Net present value & basis point value. It shows what each component covers and how the three components add up in euros.

This chapter covers derivatives, not loans. A derivative is sold and priced by specialised desks of the bank. Sales and traders build the price from the cost of hedging in the market. A loan is priced on a bigger scale. Several departments of the bank take part, for example credit risk, treasury and capital management. Each brings its own models. It is a different mechanism, and this chapter does not cover it.

Caps and floors are options on interest rates. A collar combines a bought cap and a sold floor. The upcoming chapter Introduction to options explains them. The upcoming chapter xVA: value adjustments explains the value adjustments. The numbers in this chapter are invented. They are not market levels.

2. From a margin to euros

The chapter Net present value & basis point value showed two ways to charge a fee. On a swap, a margin is built into the fixed rate, and the client pays it in every period. A spot premium is the net present value (NPV) of that margin, paid on the spot date. The NPV is the value today of all the payments of the margin. In the euro market the spot date is usually two business days after the trade date. The BPV converts between the two:

Take a margin of 5bp on a €10 million leg. A leg is a series of interest payments on a notional, the amount on which interest is calculated. It runs for five years with annual payments, and the curve is flat at 3.00%. The BPV of the leg is €4,579.71. The spot premium is 5 × €4,579.71, which is about €22,899. Use the BPV of the leg that carries the margin. Section 7 shows which leg that is on a swap. The conversion holds while the contract runs to maturity.

The notional profile matters. Suppose, purely as an illustration, that a bank takes a margin of 5bp or 7bp. In euros, 5bp is 5 times the BPV of the leg, and 7bp is 7 times the BPV. A bullet leg keeps its notional of €10 million until the end. On an amortising leg the notional falls by €2 million a year. For the bullet leg and for the amortising leg:

The same 7bp is worth €32,058 on a bullet leg and €19,614 on an amortising one. Less notional is left on the amortising leg.

3. The trading margin

3.1 The trader hedges the risk

When a client trades with a bank, the bank takes the opposite side of the client’s risk. The job of the trader is to hedge this risk. The trader buys or sells several instruments with opposite effects. The net effect is more or less zero.

3.2 Every hedge has a bid and an ask

Each hedging instrument has a bid and an ask. The trader buys at the ask and sells at the bid. The mid is halfway between the two. So hedging has a cost, which comes from the bid/ask. This cost is the trading margin, also called the hedging cost. It is the bid/ask, or part of it, multiplied by the size of the risk.

For an interest rate swap, the bid/ask is quoted in basis points of the swap rate. Suppose the bid/ask is 1bp wide. The trader can decide to take the full bid/ask as a trading margin. On a five-year swap of €10 million, 1 times the BPV is €4,580.

3.3 Products with options have more risks

A swap has one main risk, the level of interest rates. The BPV measures it. A cap or a floor has other important risks. The main one is volatility. The market quotes it as a normal volatility, in basis points. Volatility is the size of the yearly rate moves that the market expects, in either direction, for example 70bp. This is a very simplified explanation. Implied volatility is an advanced topic.

The hedge for volatility has its own bid/ask, quoted in basis points of volatility. So for a cap or a floor, the trader combines the BPV with other measures. This chapter does not go into the details.

3.4 From the bid/ask of each risk to one margin

The trader calculates the margin from the bid/ask of each risk factor. For each factor, the trader decides how much of the bid/ask to take, for example the full bid/ask. The margin for that factor is this amount times the size of the risk. The trading margin is the sum of the margins of all the risk factors.

The trader then communicates the margin in one of three ways:

• As a spot premium, if the client pays a premium. This is usual when the client buys a cap on a rate.
• As a margin in basis points, if the client pays the fee in every period. The margin times the BPV is the cost in euros. This is usual on a swap.
• Built into a strike, if the client pays no premium. A zero-premium collar is an example. Section 8.3 shows it.

4. The value adjustment fee

The trader of section 3 only looks at the risk of the product itself. A second trader, the xVA trader, looks at the other risk factors. xVA is the family name of the value adjustments. The upcoming chapter xVA: value adjustments explains them. The risk factors are the credit risk of the client, the bank’s own credit risk and the funding of the bank.

The value adjustment fee charges two of them. The CVA is the price of the risk that the client does not pay what it owes. The FVA is the cost of funding the collateral that the bank posts on its hedges, when the client posts none. The second trader manages and, where possible, hedges these risks. The cost is charged in the same three ways as the trading margin. Other value adjustments exist. One covers the credit risk of the bank itself, and another the cost of the capital the bank must hold.

The fee applies when the cash flows of the product itself can go from the client to the bank. The trade can then have a positive value for the bank, and the bank is exposed to the client. A swap without collateral is an example. Its payments go in both directions, so the client can owe the bank money.

A cap is different. A cap pays the client when the rate is above its strike, the rate level fixed in the contract. Take a cap that the client pays for on the spot date. After that date, its only cash flows are payments from the bank to the client. The client owes nothing, so the bank is never exposed to the client. The bank hedges by buying a cap. A bought cap never has a negative value, so the bank posts no collateral. Such a cap has no CVA and no FVA. This holds only if the client pays the full premium on the spot date. A premium paid later, or in instalments, makes the client a debtor, and the fee applies.

5. The sales margin

Sales adds its own margin on top of the trading margin and the value adjustment fee. Sales typically takes a certain number of times the BPV. It does so to keep the fee in proportion with the risk that the client exchanges with the bank. On a swap, the BPV measures this rate risk, so a multiple of the BPV follows it. On a cap or a collar, the BPV of the leg measures the size of the deal. A multiple of the BPV is also used when the client pays a premium.

The multiple is the bank’s choice. A bank can use a different multiple for each type of instrument.

6. Comparing bank quotes in euros

6.1 A margin is the NPV of yearly payments

A bank quotes its margin in basis points a year. This looks small. But the client pays the margin every year, on the notional.

Take the margin of 5bp from section 2, on the same leg of €10 million. The client pays 5bp of €10 million, which is €5,000, every year for five years. In total that is €25,000.

The spot premium is the NPV of the yearly margins that the client is going to pay. It is €22,899, which is €2,101 less than €25,000. A payment in year 5 is worth less today than a payment in year 1. So each yearly margin is discounted back to the spot date, here on the flat 3.00% curve.

Change the margin in the simulator below to see what the yearly payments are worth today.

What the yearly margins are worth today

The client pays the margin every year. The spot premium is the NPV of these yearly payments.

Notional

€10m

Maturity

5 years

Flat market rateRate

3.00%

Notional profileProfile

BulletAmortising (equal steps)

Margin (bp a year)

• Margin paid in each year
• Worth today
• Lost to discounting

Paid every year

€5,000

Total paid over 5 years

€25,000

NPV of the yearly margins = the spot premium

€22,899

Same as 5.0 × €4,579.71, the BPV

Lost to discounting

€2,101

Show data

The numbers are invented. One flat rate, annual payments, held to maturity.

To compare the quotes of several banks, convert each margin into euros with the same BPV. This does not change the ranking of the quotes, but it shows what a difference between two banks is worth. Compare quotes only if they cover the same dates, notional profile, curve, payment conventions and collateral terms. The simplest check is to ask every bank for its mid market rate at the same time. Compare it with one independent mid. Then multiply each margin in bp by the BPV.

6.2 Questions to ask your bank

Ask the bank four questions about a quote:

• Which mid market rate do you see for these dates?
• How much BPV do you see on the leg?
• How much margin did you take, in BPV? For example, 5 times the BPV.
• How does the margin split into the trading margin, the value adjustment fee and the sales margin?

7. Interest rate swaps: which BPV?

An interest rate swap has two legs. The fixed leg pays a fixed rate. The floating leg pays a floating rate. Each leg has its own BPV. Market practice uses the BPV of the fixed leg, because the margin is added to the fixed rate.

The choice does not matter much. Take a five-year swap of €10 million. The fixed leg pays once a year and counts days as 30/360. The floating leg pays every three months and counts days as ACT/360. The curve is flat at 3.00%. Weekends and holidays are ignored.

The floating leg is 2.6% higher. Day count adds 1.44%, because ACT/360 divides the actual days by 360. Earlier payments add 1.12%, because quarterly payments are discounted less. On a margin of 5bp, the gap is about €591. A margin of 5bp on the fixed leg equals 4.87bp on the floating leg.

8. Practical examples

All examples use a €10 million notional and five years. The trade date is Wednesday 7 October 2026. The spot date is Friday 9 October 2026, and amounts are values on that date. The curve of the examples is fictive. It is flat at 3.00% with annual compounding, and it is not a market curve. The same fictive curve projects the floating rates and discounts the payments. The floating rate of the examples is the 3-month EURIBOR. Rows in the tables are rounded, so they may not add up exactly.

8.1 A swap with the margin in the fixed rate

A client pays the fixed rate on a five-year swap. The mid swap rate, which is the par rate, is 3.000%. The swap has no collateral, so the value adjustment fee applies. The trader takes the full bid/ask of 1bp from section 3.2. The other two components of the margin are invented:

The bank adds the 7.5bp to the fixed rate. The client pays 3.075% instead of 3.000%. That is €7,500 more interest every year on €10 million. The NPV of this margin is €34,348.

8.2 A cap with a spot premium

A client that pays a floating rate buys a five-year cap with a strike of 3.50%. The strike is the rate level above which the cap pays. The client pays a premium on the spot date, two business days after the trade date. The cap covers 19 quarters, because the first rate is already known. A cap has no fixed leg, so the BPV of the quarterly floating leg is used. It counts all 20 quarters, for simplicity.

The diagram shows the payoff to the client for one quarterly period on €10 million, against the 3-month EURIBOR at the fixing.

What a 3.50% cap on €10 million pays the client in one quarter

3-month EURIBOR at the fixing

4.50%

Show data

The client paid the premium on the spot date. The cap pays only when the rate is above the strike. This holds in each of the 19 quarters that count.

The mid market price of this cap is €87,728. To keep it simple, the trader estimates the hedging cost, volatility included, at 2bp, which is 2 times the BPV. The parts of the premium are:

The premium paid on the spot date is the price of the cap at the mid plus the fee. The fee alone, €32,885, is the spot premium of section 2. It is 7.0 times the BPV of the leg. Sales takes its multiple of the BPV even though the client pays a premium. Section 4 explains why the value adjustment fee is zero.

8.3 A collar that costs no premium

The client prefers to pay no premium. The client buys the cap at 3.50% and sells a floor. A floor pays when the rate falls below its strike. The client sold it, so the client pays the bank in that case. The combination is called a collar. At the mid, a floor with a strike of 2.349% is worth exactly the same as the cap. That collar has an NPV of zero at the mid.

The diagram shows the payoff to the client for one quarterly period on €10 million, against the 3-month EURIBOR at the fixing. It shows the collar without the fee and with the fee, as the next paragraphs explain.

What the collar on €10 million pays the client in one quarter, with and without the fee

• Collar without the fee, floor strike 2.349%
• Collar with the fee, floor strike 2.617%

3-month EURIBOR at the fixing

2.50%

Show data

The collar costs no premium. The client gives up the benefit of low rates below the floor strike. With the fee the floor strike is 26.8bp higher, so the client pays in more situations. The shaded band shows the difference.

The bank also needs its fee. The trader again estimates the hedging cost at 2bp. The client can owe the bank money on the floor, so the collar can have a positive value for the bank. The bank is exposed to the client, and the value adjustment fee applies. The bank sets the floor strike higher, so that the floor pays for the cap and for the fee. A floor with a higher strike is worth more to the bank. The extra €37,583 pays the fee.

The collar still costs no cash. But the floor strike is 26.8bp higher, and the NPV at the mid is negative for the client. The negative amount is the fee of the bank. It is 8.0 times the BPV of the leg. The 26.8bp is a difference in strike, not a margin.

9. Key takeaways

• A derivative fee has three components. They are the trading margin, also called the hedging cost, the value adjustment fee if it applies, and the sales margin. Total fee = trading margin + value adjustment fee + sales margin.
• The trading margin and the value adjustment fee are costs that the bank expects to pay by entering the transaction. Their sum is usually the minimum fee. A bank goes below it only to attract a client.
• The BPV is the common unit. Spot premium = margin in bp × BPV, and the reverse also holds.
• A margin of a few basis points looks small, but the client pays it every year. The spot premium is the NPV of these yearly margins, so it is a little less than their sum.
• The trader hedges the risk taken from the client with instruments that have opposite effects. Each hedge is done at the bid or the ask. For each risk factor, the trader decides how much of the bid/ask to take, for example the full bid/ask. The margin is this amount times the size of the risk.
• On a swap, the bid/ask is quoted in basis points, so the cost is a multiple of the BPV. On a product with options, volatility is another risk and has its own bid/ask.
• The trader communicates the margin as a spot premium, as a margin in basis points or built into a strike. The BPV links the first two.
• A second trader looks at other risk factors: the credit risk of both counterparties and the funding of the bank. This gives the CVA and the FVA.
• The value adjustment fee applies when the cash flows of the product itself can go from the client to the bank. The bank is then exposed to the client. A cap paid in full on the spot date only pays the client, so it has no CVA and no FVA.
• Sales adds a certain number of times the BPV, also when the client pays a premium. On a swap, the BPV measures the risk that the client exchanges with the bank. So the sales fee stays in proportion with that risk. On a cap or a collar, the BPV of the leg measures the size of the deal.
• On a swap, the BPV of the fixed leg converts the margin. The floating leg gives a similar number. In the example it is 2.6% higher.
• In a collar with no premium, the floor strike includes the fee. The NPV at the mid is then negative for the client instead of zero.
• To compare quotes, ask each bank for the mid market rate, the BPV on the leg and the margin in BPV. Ask how the margin splits into the three components. Then convert each margin into euros with the same BPV.
• The numbers in this chapter are invented. They are not market levels.