CFA Level I Exam · Pricing and Valuation of Interest Rate and Other Swaps

How to Value an Interest Rate Swap After Initiation

Updated 7 October 2026 · Fact-checked

After initiation, a swap's value is the present value of the remaining fixed payments compared with the present value of the floating payments, both using current discount factors. The pay-fixed party's value is PV(floating) − PV(fixed). The receive-fixed party's value is the opposite. A new swap starts at zero value.

Understand Valuation of Interest Rate Swaps After Initiation

A plain vanilla interest rate swap is set up so its value is zero at initiation. The fixed rate is chosen so that the present value of the fixed payments equals the present value of the expected floating payments. Nobody pays anything upfront.

Once market rates move, that balance breaks. The fixed rate is locked in, but the floating leg now follows the new forward curve and the discount factors change. One side gains and the other loses. The value of the swap to a party is its mark-to-market value.

The cleanest way to see this is the bond view. The receive-fixed party is long a fixed-rate bond and short a floating-rate bond. The floating-rate bond is worth par (the notional) right after a reset date, because it pays current market rates. So the receive-fixed value is PV of the fixed bond minus the notional, when you stand on a reset date.

The second way is the forward rate view. Use the current discount factors to get the forward rates. Then compare each fixed payment with the expected floating payment for each period, and discount the net amount. Both methods give the same answer on a reset date.

Remember the direction. If rates rise after initiation, the fixed rate you locked in looks better to the pay-fixed party, so the pay-fixed side gains and the receive-fixed side loses. If rates fall, the reverse happens.

Key formulas to remember

Discount factor from a spot rate: Z = 1 ÷ (1 + r × days/360); Use the same day-count basis as the swap. For a multi-period case, Z_n is the discount factor to payment date n.
Forward rate from discount factors: FR(i-1, i) = (Z_(i-1) ÷ Z_i − 1) × (360 ÷ days in period); This is the expected floating rate for the period, from the current curve.
Fixed-leg PV per unit of notional: PV(fixed) = [Fixed rate × (days/360) × Σ Z_i] + Z_n; Z_n is the discounted principal, so the fixed leg is valued as a bond. On a reset date, compare this with 1, the value of the floating bond at par. The difference is the receive-fixed value per unit of notional.
Swap fixed rate at the current market: Current swap rate = (1 − Z_n) ÷ [Σ (days/360) × Z_i]; This is the rate that gives a new swap a zero value today. For annual periods the period fraction is 1, so it reduces to (1 − Z_n) ÷ ΣZ_i. Use it for the quick method.
Value to the receive-fixed party (on a reset date): V(receive-fixed) = Notional × Σ [(Old fixed rate − Current swap rate) × period fraction × Z_i]; Valid on a reset date, when the floating leg is worth par. Between reset dates the floating leg is not at par, so you must adjust for the next floating coupon already set. Pay-fixed value is the negative of this.
Value to the pay-fixed party: V(pay-fixed) = PV(floating) − PV(fixed) = −V(receive-fixed); The two sides of the swap always sum to zero, ignoring credit risk.

How to solve Valuation of Interest Rate Swaps After Initiation questions

Use this order for any question that asks for the value of an existing swap. Check first whether you are asked for the pay-fixed or receive-fixed party.

1Identify which party you are valuing and the remaining payment dates, notional and original fixed rate.
2Convert the current rates given (spot rates or discount factors) into a discount factor Z for each remaining payment date.
3Find the current market swap rate for the remaining term: (1 − Z_n) ÷ ΣZ_i, adjusted for period length if not annual.
4Compute the difference between the original fixed rate and the current swap rate.
5Multiply the difference by the notional, the period fraction, and the sum of the discount factors to get the value for the receive-fixed party.
6Flip the sign if you are valuing the pay-fixed party.
7Sanity check: if market rates rose, the receive-fixed party should show a negative value, and the pay-fixed party a positive value.

Quickest way: Rate-difference annuity shortcut

When to use it: Use it when the question gives discount factors or spot rates for all remaining dates and wants the swap value on a reset date. It avoids computing each forward rate.

Sum the discount factors for all remaining payment dates to get the annuity factor A.
Compute the current swap rate = (1 − Z_n) ÷ A.
Take (old fixed rate − current swap rate).
Value for receive-fixed = difference × A × notional (for annual periods).
Reverse the sign for pay-fixed.
Eliminate options: check the sign first. A wrong sign removes at least one option on the answer list.

Common mistakes in Valuation of Interest Rate Swaps After Initiation

Getting the sign wrong for the party being valued
Students remember that rising rates help one side but forget which side.
Fix: Pay-fixed gains when rates rise. Receive-fixed gains when rates fall. Check the sign against this before you choose an answer.
Using the original swap rate to discount the remaining cash flows
The original rate feels like the swap's own rate.
Fix: Always discount with current discount factors from today's curve. The original fixed rate only sets the size of the fixed payments.
Forgetting to add the final principal in the bond approach
Swaps have no principal exchange, so students leave it out of both legs.
Fix: In the bond approach, treat both legs as bonds with notional returned at the end. The floating bond is worth par on a reset date, so compare PV of the fixed bond with the notional. The quick method already builds this in through the 1 − Z_n term.
Valuing the floating leg as if it were zero or at its original rate
Students assume the floating leg does not change.
Fix: The floating leg changes with the forward curve. On a reset date the floating bond is worth the notional. Between reset dates, the floating bond is worth (notional + the next coupon already set) discounted from the next reset date.
Ignoring period length in the rate comparison
Quarterly swaps are quoted in annual rates.
Fix: Multiply the annual rate by days/360 (or 1/4 for quarterly) before applying it to the notional.
Treating the swap as having a nonzero value at initiation
Students confuse initiation with a later date.
Fix: At initiation the fixed rate is set so the value is zero (ignoring dealer spread). A value only appears after rates change.

Worked examples

Example 1

A 3-year annual-pay swap has a notional of $10,000,000 and a fixed rate of 3.00%. One year has passed, so two payments remain. Current discount factors are Z1 = 0.9804 and Z2 = 0.9524. Value the swap for the receive-fixed party on the reset date. Options: A. −$103,840, B. $0, C. +$103,840.

Show the solution

Annuity factor A = 0.9804 + 0.9524 = 1.9328.
Current 2-year swap rate = (1 − 0.9524) ÷ 1.9328 = 0.0476 ÷ 1.9328 ≈ 2.4627%.
Rate difference = 3.00% − 2.4627% ≈ 0.5373%. Because these rates are rounded, do not use them for the final figure.
Value without rounding the rate: (0.03 × 1.9328) − (1 − 0.9524) = 0.057984 − 0.0476 = 0.010384. Times $10,000,000 = $103,840.
Check by bond approach: fixed bond PV = 0.03 × 1.9328 + 0.9524 = 0.057984 + 0.9524 = 1.010384. Minus par 1 = 0.010384, so $103,840 on $10,000,000.
Both methods give $103,840. Rates fell, so receive-fixed gains and the value is positive.

Answer: C. +$103,840 for the receive-fixed party. The sign is positive because rates fell, so the 3.00% fixed rate is above the current market swap rate.

Example 2

A pay-fixed party holds a swap with two annual payments left, notional €5,000,000, and fixed rate 2.50%. Discount factors are Z1 = 0.9709 and Z2 = 0.9246. What is the value to the pay-fixed party on the reset date? Options: A. −€140,063, B. €0, C. €140,063.

Show the solution

A = 0.9709 + 0.9246 = 1.8955.
Current swap rate = (1 − 0.9246) ÷ 1.8955 = 0.0754 ÷ 1.8955 ≈ 3.9778% (rounded).
Rate difference (old fixed − current) = 2.50% − 3.9778% ≈ −1.4778% (rounded).
Receive-fixed value per unit ≈ −0.02801 (rounded rates give about −0.028012). Check with the bond approach, which avoids the rounded rate: 0.025 × 1.8955 + 0.9246 − 1 = 0.0473875 + 0.9246 − 1 = −0.0280125.
Receive-fixed value = −0.0280125 × 5,000,000 = −€140,062.50, about −€140,063.
Pay-fixed value is the negative of this: about +€140,063.
Rates rose, so pay-fixed gains and the sign is positive.

Answer: C. About +€140,063 to the pay-fixed party. The sign is positive because the fixed rate is below the current market swap rate.

Exam tips

Decide the sign first. Rates up means pay-fixed gains. This often removes one or two options before any calculation.
Compute the current swap rate from discount factors, then multiply the rate gap by the annuity factor and notional. It is faster than building forward rates.
Check whether the question is asking about a reset date. If it is between dates, you need to include accrued floating interest.
Use your calculator's memory to hold the sum of the discount factors. On the BA II Plus, add the discount factors on the display, press STO 1 to store the sum, then press RCL 1 to recall it.
Remember that the two parties' values are equal and opposite, so a question may ask for one while giving data on the other.

Practice questions from Pricing and Valuation of Interest Rate and Other Swaps

Valuation of Interest Rate Swaps After Initiation in other exams

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

Valuation of Interest Rate Swaps After Initiation: frequently asked questions

What is the value of an interest rate swap at initiation?

It is zero, ignoring dealer spreads. The fixed rate is set so the PV of the fixed payments equals the PV of the expected floating payments. Value only appears after market rates change.

Why is a floating-rate bond worth par on a reset date?

Its next coupon is set at the current market rate, so discounting at that same rate gives par. This is why the bond approach compares the fixed bond with the notional. Between reset dates, the value is not exactly par.

How do I know which party gains when rates change?

If market swap rates rise above your locked fixed rate, the pay-fixed party gains. If they fall, the receive-fixed party gains. The gain of one party equals the loss of the other.

Do I need forward rates to value a swap?

You can use them, but you do not have to. The discount factor method gives the same answer faster. You compute the current swap rate from the discount factors and compare it with the old fixed rate.