Interest rate swap

An agreement to exchange interest cash flows according to fixed and floating schedules. For unit accrual periods and unit notional, floating-minus-fixed payments are $r_t-s$ at the specified dates. Zero-coupon bonds value the fixed leg and a rolling floating leg supplies the telescoping floating-leg value.

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.