How do you value an interest rate swap at initiation vs. during its life? The two approaches confuse me.

Question

AcadiFi · Accepted Answer

Swap valuation is one of the most tested topics in CFA Level II Derivatives. Let's separate the two stages clearly.

**At Initiation (Value = 0):**
The fixed rate on a new swap is set so that the present value of fixed payments exactly equals the present value of expected floating payments. No money changes hands, and neither party has an advantage — hence value = zero.

The swap fixed rate is determined by:

Swap Rate = (1 - PV of last discount factor) / (Sum of all discount factors)

**During the Swap's Life (Value != 0):**
Once rates move, the fixed payments are locked in but the floating side resets. If rates have risen since initiation, the fixed-rate payer benefits (paying below-market fixed, receiving higher floating). The swap now has positive value to the fixed-rate payer and negative value to the fixed-rate receiver.

**Method 1 — Bond Replication:**
Treat the swap as a long position in a floating-rate bond and a short position in a fixed-rate bond (for the pay-fixed side):

V_swap = PV(floating bond) - PV(fixed bond)

The floating-rate bond resets to par at each payment date, so between resets its value is simply the next floating payment plus par, discounted back.

**Method 2 — FRA Replication:**
Decompose the swap into a series of forward rate agreements. Each FRA locks in the difference between the original fixed rate and the current forward rate for that period. Sum the present values of all these differences.

```mermaid
flowchart TD
    A[Swap Valuation] --> B[At Initiation]
    A --> C[During Life]
    B --> D[Value = 0: Fixed rate set so PV fixed = PV floating]
    C --> E[Method 1: Bond Replication]
    C --> F[Method 2: FRA Replication]
    E --> G[V = PV Floating Bond - PV Fixed Bond]
    F --> H[V = Sum of PV of each FRA difference]
    G --> I[Both methods give same answer]
    H --> I
```

**Worked Example (Bond Method):**
A 2-year pay-fixed swap with annual payments, notional $10 million, fixed rate 3.5%. After 6 months, the new discount factors are:
- 0.5-year: 0.9804
- 1.5-year: 0.9426

Fixed bond value = $350,000 x 0.9804 + ($350,000 + $10,000,000) x 0.9426 = $343,140 + $9,756,930 = $10,100,070

Floating bond value (resets to par at next date) = ($10,000,000 + next floating payment) x 0.9804. If the next floating coupon is $380,000: = $10,380,000 x 0.9804 = $10,176,552

Swap value to fixed payer = $10,176,552 - $10,100,070 = **$76,482**

Both methods always produce the same result. Use whichever the exam question sets up. Practice both in our CFA Level II question bank.

How do you value an interest rate swap at initiation vs. during its life? The two approaches confuse me.

Master Level II with our CFA Course

Related Questions

Practice Questions