If we calculate the par rate for n periods, why does the nth swap rate equal the par rate? A mathematical formulation would be helpful apart from an intuitive answer.
Edit: Example:- A 2 year bond pays semiannual coupons and has a par value of $100.
Swap Rates- 0.65% (0.5year), 0.8% (1year), 1.02% (1.5 years), 1.16% (2years).
Computing discount rates from this gives- 0.9968, 0.9920, 0.9848, 0.977 respectively.
Now the par rate would be -
$Par/2 * [(d(0.5)+d(1.0)+d(1.5)+d(1.5)+d(2.0)] + 100 * d(2.0) = 100$
Gives par = 1.16%