Deriving the formula for determining the swap rate

Can anyone help explain that when we pirce a plain vanilla (fixed-for-floating) interest rate swap,

  1. why are we discounting all the coupons and the par value for the fixed rate bond, but take this value to equal to the par value of the floating rate bond? What is the rationale behind this?

  2. why don’t we discount the floating rate coupons and par value accordingly as well?


You may recall from Level I that when a bond’s coupon rate equals its YTM, the bond sells at par.

For the floating-rate bond in the swap equivalence, the bond’s coupon rate resets to LIBOR at every settlement date; therefore, the coupon rate equals the YTM, so the bond sells at par.

Thank you very much!

You’re welcome.