I clearly understand that the value of the plain vanilla swap can be calculated as the different in value of the floating rate bond and a fixed rate bond, which you can easily calculate.
However, when the benchmark rates for the floating rate bond is LIBOR + x%, the calculation seems messed up for me. The value of the floating rate bond will equal to the par value at settlement date. The value of the fixed rate bond should be calculated by discounting the remaining coupons and principal, but which rates are we using, the LIBOR or the LIBOR + x%?
It seems intuitive to me that the LIBOR should be use? I have encountered one practice problems that used the LIBOR + x% to value the fixed rate bond. Can anyone help me?
Unless there’s a credit quality issue that would lead you to discount the payments at a rate higher than straight LIBOR (and I’ve never seen such a scenario presented), you should discount all of the payments using the LIBOR spot rates.
So . . . how do you handle the fact that the floating-rate leg won’t reset to par at each coupon date?
In a nutshell: you cheat.
If the swap fixed rate is SFR, and the floating rate is LIBOR + x% (x being a constant), then the net payment is:
SFR – (LIBOR + x%)
A little algebra:
SFR – (LIBOR + x%)
= SFR – LIBOR – x%
= (SFR – x%) – LIBOR
So, the payments are equivalent to a swap having a fixed rate of (SFR – x%) and a floating rate of LIBOR, and – here’s the cool part – the floating leg of this swap resets to par at each coupon date.
So, you value the original swap by treating the fixed rate as (SFR – x%) and the floating rate as LIBOR.
It’s just that I saw an item set from the third party in which they discounted the payment of fixed coupon bond using the LIBOR + x%. Everything is clear now.
