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    Calculates locally in your browser · bootstrapped curve
    Rates / swap curve

    Swap curve calculator

    A swap is priced off a curve, not a single rate. This calculator interpolates a par curve from three quoted tenors, bootstraps the discount factors, and prices a fixed-for-floating swap against it — so you can see the par rate and how far your fixed rate sits from it.

    Tenor10yCurveUpwardPositionLiability
    Swap NPV
    -$317,818
    Fixed 4.20% against the curve
    Par swap rate
    4.600%
    The rate that makes the swap worth zero
    Annuity factor
    7.945
    Sum of the discount factors
    10-year discount factor
    0.6345
    From 4.60% par
    Bootstrapped curve
    Par rates in, discount factors out.
    4.600%
    Bootstrapped curve
    YearPar rateDiscount factor
    14.000%0.96154
    24.000%0.92456
    34.100%0.88633
    44.200%0.84794
    54.300%0.80951
    64.360%0.77315
    74.420%0.73743
    84.480%0.70240
    94.540%0.66808
    104.600%0.63451

    Annual fixed-leg payments; the floating leg is valued as 1 − DF at maturity.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Discount factors by maturity
    Bootstrapped from the interpolated par curve.
    Discount factors by maturity0.0000.2150.4310.6460.8621.081y1y2y2y3y3y4y4y5y5y6y6y7y7y8y8y9y9y10y10yDF
    Swap NPV against the fixed rate
    It crosses zero at the par rate.
    Swap NPV against the fixed rate-$1812.8k-$1182.8k-$552.7k$77.3k$707.3k$1337.4k2.52%2.52%2.86%2.86%3.19%3.19%3.53%3.53%3.86%3.86%4.20%4.20%4.54%4.54%4.87%4.87%5.21%5.21%5.54%5.54%5.88%5.88%NPV
    Canonical equations
    The exact relationships implemented by this engine.

    DF_i = (1 − s_i ΣDF) / (1 + s_i) · Sequential from the shortest tenor.

    s = (1 − DF_n) / ΣDF · The coupon that prices the swap at par.

    N (fixed·ΣDF − (1 − DF_n)) · Fixed leg minus floating leg.

    finance methodology

    A clear path from inputs to results.

    A swap is priced off a curve, not a single rate. This calculator interpolates a par curve from three quoted tenors, bootstraps the discount factors, and prices a fixed-for-floating swap against it — so you can see the par rate and how far your fixed rate sits from it.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the notional and the fixed rate you pay.
    2. Set the 2, 5 and 10-year par swap rates.
    3. Read the bootstrapped discount factors.
    4. Compare the NPV with the par rate.

    The formula

    DFi=1−si∑j<iDFj1+si,NPV=N(S∑DF−(1−DFn))DF_i = \frac{1 - s_i \sum_{j<i} DF_j}{1 + s_i}, \qquad NPV = N\left(S\sum DF - (1 - DF_n)\right)

    Reference: Standard par-rate bootstrapping; single-curve swap valuation.

    Worked example

    $10M, pay 4.2%, curve 4.0 / 4.3 / 4.6

    Inputs
    • Notional $10,000,000.
    • Fixed 4.2%.
    • Par curve 4.0%, 4.3%, 4.6% at 2, 5 and 10 years.
    Calculation path
    1. 1

      Interpolate annual par rates between the three points.

    2. 2

      Bootstrap discount factors: DF₁ = 1/1.04 = 0.9615, and so on.

    3. 3

      10-year DF = 0.6345; annuity factor 7.945.

    4. 4

      Par swap rate: (1 − 0.6345)/7.945 = 4.60%.

    5. 5

      NPV at 4.2% fixed: 10M × (0.042 × 7.945 − 0.3655) = −$318k.

    Result

    Par 4.60% · paying 4.2% is worth −$318k.

    Interpreting the result

    Paying below the par rate is a liability, not a bargain: you have locked in a coupon the market thinks is too low for the risk, so the swap has negative value today. The NPV is the amount you would pay to exit it immediately.

    Assumptions & limitations

    • Annual fixed payments.
    • Linear interpolation of par rates between quoted tenors.
    • Single-curve discounting (no OIS/LIBOR split).
    • No collateral or credit adjustment.

    Frequently asked questions

    Why bootstrap instead of using bond yields?

    Swap par rates define the discount factors directly, without a bond basis.

    Does a negative NPV mean a bad trade?

    Not necessarily — it may be hedged against an asset that offsets it.

    What is the par rate?

    The fixed rate that makes the swap worth zero at inception.

    Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.