Par swap rate ($s=(1-P_0(T))/{\sum }_{t=1}^T{P}_0(t)$)

The fixed rate making an interest rate swap have zero initial value. For unit accrual periods, unit notional and payments $r_t-s$, the floating-leg value is $1-P_0(T)$ and the fixed-leg annuity is ${\sum }_{t=1}^T{P}_0(t)$. The formula changes when accrual lengths or payment schedules differ.