Groundlearn / Calculators / Swap valuation
Swap valuation calculator
Value a plain-vanilla interest rate swap from a zero curve: both legs, the value to either side, and the par rate.
Calculator
Zero rates (annual compounding)
- Swap value to you
- −$3,285
- Par swap rate
- 3.9882%
- Floating leg PV
- $1,110,036
- Fixed leg PV
- $1,113,321
- Annuity factor (Σ DF)
- 2.783302
- Value of 1 bp on the fixed rate
- $2,783
Floating leg $1,110,036 − fixed leg $1,113,321 = −$3,285 to the fixed payer. Side: payer (pay fixed, receive floating).
| Year | Zero rate | Discount factor | PV of fixed payment |
|---|---|---|---|
| 1 | 3.50% | 0.966184 | $386,473 |
| 2 | 3.80% | 0.928122 | $371,249 |
| 3 | 4.00% | 0.888996 | $355,599 |
How it works
A plain-vanilla interest rate swap is valued as two legs. On a reset date the floating leg is worth par, so its present value is the notional times one minus the final discount factor. The fixed leg is a strip of coupons, each discounted with the zero rate for its date.
DFt = 1 ÷ (1 + zt)t
Floating PV = N × (1 − DFn)
Fixed PV = N × K × Σ DFt
Par rate = (1 − DFn) ÷ Σ DFt
The payer of fixed is long the floating leg and short the fixed leg, so a fixed rate above the par rate makes the swap worth less than zero to the payer. The par rate is the fixed rate that sets the value to zero, which is how a new swap is quoted.
Simplifications: annual payments on both legs, valuation on a reset date, a single curve for projection and discounting, and no day-count, credit or funding adjustments. Real desks discount with an overnight curve (SOFR, €STR) and add CVA and FVA on top.
Worked example
A three-year $10 million swap paying 4% fixed, with zero rates of 3.5%, 3.8% and 4.0%. The discount factors sum to 2.783302, the floating leg is worth $1,110,036 and the fixed leg $1,113,321, so the payer's position is worth −$3,285. The par rate is 3.9882%, just under the 4% being paid. The swap valuation guide goes through each step.
Related
- Interest rate swap valuationThe full guide with each step.
- Credit valuation adjustmentWhat a swap is worth after counterparty risk.
- Funding valuation adjustmentThe cost of funding uncollateralised swaps.
- SwapGlossary definition with the exam angle.
- OTC Learn82 OTC derivative products explained, free on Android.
- All calculatorsVaR scaling, duration and convexity.
Educational content only. This is not financial, investment, legal or regulatory advice. Results are illustrations under the stated assumptions, not a valuation of any real trade.
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