The interest rate swap: par rate and valuation
In a vanilla IRS the fixed payer K on notional N pays against a floating leg (e.g., SOFR), with both legs netted each period. At inception the value is zero and the fixed rate that achieves it is the par rate: K* = (DF₀ − DFₙ)/A + s, where A = Σ αᵢ·DFᵢ is the discounted annuity and s a floating spread. After inception, value moves with the curve: for the fixed payer, PV = A·(K* − K)·N. PV01 — the value change for a one-basis-point parallel shift — is the standard rate-risk yardstick.
Cross-currency swaps and TRS
A cross-currency swap exchanges principal at start and end plus periodic interest in two currencies — the standard tool for funding in a foreign currency with both rate and FX fully covered. A total return swap pays the total return of an equity or index (price + income) against funding + spread: the holder gets market exposure without taking delivery, the prime broker holds the physical book — the institutional standard for fast, capital-light exposure.
Worked example: 3-year IRS on 100m notional
- Discount factors: DF(1)=0.960, DF(2)=0.922, DF(3)=0.885; annual payments, no spread.
- A = 0.960 + 0.922 + 0.885 = 2.767.
- Par rate: K* = (1 − 0.885)/2.767 = 4.16%.
- A fixed payer at K = 4.50% holds value = 100M × (4.50% − 4.16%) × 2.767 ≈ +0.94M for the fixed receiver.
- Rates rise 25bp: PV01 ≈ 2.767 × 10⁻⁴ × 100M ≈ $27,670 in favor of the fixed payer.
نتیجه: A swap struck at par is worth zero at inception; every deviation from par and every curve move thereafter transfers value between the parties — and PV01 is the language of that transfer.
OTC swaps carry counterparty risk: positive value to you is a receivable that can burn in a default. Real markets mitigate with collateral (CSA); the platform's educational models exclude it explicitly and say so.