Par Swap Rate Calculation

Par Swap Rate Calculator

Annual (1/yr) Semi-Annual (2/yr) Quarterly (4/yr) Monthly (12/yr)

Note: This simplified calculator assumes a flat yield curve for the given zero rate.

Results

Par Swap Rate

0.00%

Total Periods

0

Final Discount Factor

0.0000

function calculateParSwap() { var tenor = parseFloat(document.getElementById('swapTenor').value); var freq = parseInt(document.getElementById('payFrequency').value); var zeroRate = parseFloat(document.getElementById('zeroRate').value) / 100; if (isNaN(tenor) || isNaN(zeroRate) || tenor <= 0) { alert("Please enter valid positive numbers."); return; } var totalPeriods = Math.ceil(tenor * freq); var delta = 1 / freq; var sumDF = 0; var lastDF = 0; // Using Discrete Compounding: DF = 1 / (1 + r/f)^(f*t) // For Par Swap: S = [1 – P(0,T)] / [Sum of (delta * P(0,ti))] for (var i = 1; i <= totalPeriods; i++) { var time = i * delta; var df = 1 / Math.pow((1 + zeroRate / freq), (freq * time)); sumDF += (delta * df); if (i === totalPeriods) { lastDF = df; } } var parSwapRate = ((1 – lastDF) / sumDF) * 100; document.getElementById('parRateDisplay').innerText = parSwapRate.toFixed(4) + "%"; document.getElementById('totalPeriodsDisplay').innerText = totalPeriods; document.getElementById('finalDFDisplay').innerText = lastDF.toFixed(6); document.getElementById('swapResult').style.display = 'block'; }

Understanding the Par Swap Rate

In financial engineering, the Par Swap Rate is the fixed interest rate that makes the present value of a swap's fixed leg exactly equal to the present value of its floating leg. When a swap is initiated "at par," no upfront payment is required from either party because the net market value of the contract is zero.

How the Calculation Works

The par swap rate is derived from the zero-coupon yield curve. To find the par rate, we use the following mathematical relationship:

R = (1 – P_n) / ∑( Δ_i × P_i )

• R: The Par Swap Rate.
• P_n: The discount factor for the final maturity date.
• P_i: The discount factor for each payment period i.
• Δ_i: The day count fraction or period length (e.g., 0.5 for semi-annual).

Example Calculation

Imagine a 2-year interest rate swap with semi-annual payments. If the annualized zero rate is 4%, we first calculate the discount factors (DF) for each 6-month interval:

1. 6 Months (0.5y): DF = 1 / (1 + 0.04/2)^1 = 0.9804
2. 12 Months (1.0y): DF = 1 / (1 + 0.04/2)^2 = 0.9612
3. 18 Months (1.5y): DF = 1 / (1 + 0.04/2)^3 = 0.9423
4. 24 Months (2.0y): DF = 1 / (1 + 0.04/2)^4 = 0.9238

The numerator would be (1 – 0.9238) = 0.0762. The denominator is the sum of (0.5 × each DF), which equals 1.9038. Dividing the two results in a semi-annual par rate that, when annualized, matches our zero rate input in a flat curve environment.

Why is it Important?

Par swap rates are the industry standard for quoting interest rate swaps. Banks and hedge funds use these rates to hedge against interest rate fluctuations. If market rates rise above the par swap rate, the party receiving the fixed rate loses value, while the party paying fixed (and receiving floating) gains value.