The Par Swap Rate

Par Rate Equals Par Yield

The swap par rate is the curve par yield from the same discount factors.

highlighted = computed this step

Same as the curve par yield

The par swap rate is 8/135. The curve's three-year par yield is also 8/135. They are the same because both divide one minus the final discount factor by the same discount-factor sum.

K∗=cpar=1−dn∑t=1ndtK^*=c_{\text{par}}=\frac{1-d_n}{\sum_{t=1}^n d_t}
Par swap reconciliationThe par swap rate equates fixed and floating leg PVs.Par swap reconciliationItemExactDisplayΣ discount factors27/1027/101 - d_n4/254/25Par swap rate8/1358/135 (5.93%)Floating-leg PV1600$16.00Fixed-leg PV at par1600$16.00Swap value at par0$+0.00

Swap rate and par bond

A par bond uses that rate as its coupon rate to price to face. A par swap uses that rate as its fixed rate to make fixed and floating legs equal.

par bond coupon rate=par swap fixed rate\text{par bond coupon rate}=\text{par swap fixed rate}

Model scope

This is a model valuation off a stated curve under frictionless assumptions: one set of discount factors, no transaction costs or fees, and no credit, counterparty, collateral, or day-count subtleties. The floating leg uses curve-implied forwards, not a forecast. This is descriptive, not investment advice.

par swap rate reconciles to the curve par yield\text{par swap rate reconciles to the curve par yield}