Learning Module 7
Pricing and Valuation of Interest Rates and Other Swaps
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Describe how swap contracts are similar to but different from a series of forward contracts.
Contrast the value and price of swaps.
1 · Swaps vs. a Series of FRAs
Feature | Series of FRAs | Standard Interest Rate Swap |
|---|---|---|
Fixed rate per period | Different rate for each period (= each period's IFR) | One constant fixed rate (the swap rate) across all periods |
Initial value | Zero for each FRA | Zero for the swap as a whole |
Payoff profile | Symmetric per FRA | Symmetric per period |
Administrative burden | Higher — multiple separate contracts | Lower — one contract for the whole period |
Both are firm commitments with symmetric payoffs and zero value at inception, and both carry counterparty credit risk.
A fixed-rate payer on either instrument gains if MRR sets above the agreed fixed rate.
FRAs settle at the start of each rate period; swaps settle at the end of each period.
2 · The Par Swap Rate
The par swap rate (sN) is the single fixed rate that equates the present value of all expected floating payments (using each period's IFR) to the present value of all fixed payments.
It can be interpreted as the internal rate of return on the strip of implied forward rates through the swap's maturity.
Even though the swap's combined value is zero at inception, individual implied periods may show positive or negative present value relative to the constant swap rate — only the sum is zero.
Σ PV(IFRi) = Σ PV(sN) → solve for sN using the zero-rate curve as discount factors
3 · Swap as Combination of Long/Short Bond Positions
Swap Position | Bond-Market Equivalent | Rates Rise | Rates Fall |
|---|---|---|---|
Pay fixed / receive floating | Long FRN + short fixed-rate bond | Gain | Loss |
Receive fixed / pay floating | Long fixed-rate bond + short FRN | Loss | Gain |
Receive-fixed swap ≈ long a fixed-coupon bond → behaves like adding duration; benefits when rates fall (just like a bond price rising as yields drop).
Pay-fixed swap ≈ short a fixed-coupon bond / long an FRN → reduces duration; benefits when rates rise.
Active fixed-income managers often prefer swaps over trading bonds directly because of greater liquidity and lower transaction cost.
4 · Swap Valuation During the Contract's Life
Settlement value (fixed-rate payer) = (MRR − sN) × Notional × Period
The swap's MTM value at any point = current period's settlement value + PV of all remaining future settlements.
A rise in expected forward rates after inception raises the PV of floating payments → MTM gain to the fixed-rate payer (floating-rate receiver) / MTM loss to the fixed-rate receiver.
A fall in expected forward rates → the opposite: MTM gain to the fixed-rate receiver, loss to the fixed-rate payer.
Without information on how the forward curve has moved since inception, you cannot determine whether a swap's current MTM value is positive or negative — knowing only that a payment was just made or received is insufficient on its own.