Solution
= Solution
With $P_0^0=1$, the time-zero value of payment $r_t-s$ is
$$
P_0^{t-1}-(1+s)P_0^t.
$$
Summing over $t$ telescopes, so the swap value is
$$
1-P_0^T-s\sum_{t=1}^TP_0^t.
$$
The par swap rate is therefore
$$
s=\frac{1-P_0^T}{\sum_{t=1}^TP_0^t}.
$$