The Par Swap Rate - Interest-Rate Swaps Step by Step

The par rate makes the swap worth zero at inception.

highlighted = computed this step

Rate that makes value zero

The par swap rate is the fixed rate that makes the swap value zero. It equals one minus the final discount factor, divided by the sum of discount factors.

K^*=\frac{1-d_n}{\sum_{t=1}^n d_t}

Par-rate value

Here one minus the final discount factor is 4/25, the discount factors sum to 27/10, and the par swap rate is 8/135, shown rounded as 5.93%.

K^*=\frac{4/25}{27/10}=8/135

Fixed and floating match

At the par swap rate, the floating-leg present value is $16.00 and the fixed-leg present value is $16.00, so the par swap value is $0.00.

\text{PV}_{\text{float}}=\text{PV}_{\text{fixed}}\Rightarrow V=\$0.00