Interest Rate Swaps
Value a plain vanilla swap of a fixed rate for the market reference rate from a table of discount factors: the par swap rate, each leg as a bond, the value to each side, the FRA strip behind it, and the upfront payment for an off-market rate.
Learning focus: a payer swap is a long floating-rate note and a short fixed-rate bond, so the floating leg is worth par on a reset date and the swap's value is the gap between the par swap rate and the fixed rate, times the annuity.
One row per remaining payment, nearest first. Leave τ blank for 1 ÷ payments per year, or type a day-count fraction such as 92/360 (ACT/360) or 0.5 (30/360). Both legs use the same τ.
This panel treats the swap as new today; for a swap traded earlier, the value above is what it is worth, not an upfront. A new swap at the par rate is worth zero to both sides. At any other fixed rate it starts with value to one side, which pays that value upfront so the trade is fair. A payer who pays less than the par rate pays the upfront; one who pays more receives it.
| # | τ | DF | MRR | Fixed payment | Expected floating | Net to you | PV of net |
|---|---|---|---|---|---|---|---|
| 1 | 1.0000 | 0.966200 | 3.4982% | 1,500,000.00 | 1,749,120.26 | 249,120.26 | 240,700.00 |
| 2 | 1.0000 | 0.930200 | 3.8701% | 1,500,000.00 | 1,935,067.73 | 435,067.73 | 404,700.00 |
| 3 | 1.0000 | 0.892900 | 4.1774% | 1,500,000.00 | 2,088,699.74 | 588,699.74 | 525,650.00 |
| Sum = swap value to you | 1,171,050.00 | ||||||
Each period is an FRA: the MRR is the rate already set (marked) or the forward rate (DFᵢ₋₁ ÷ DFᵢ − 1) ÷ τᵢ implied by the curve. Discounting each net payment and adding them gives the same value as the two-bond view.
Each bar is one period's net payment discounted to today, and the line adds them up to the swap's value; on an upward-sloping curve a swap at par has negative early bars and positive later ones for the payer.