# PV of floating rate payments

Discussion in 'SP5' started by dimitris13, Jan 14, 2020.

1. Hi there,

i am reading some past papers and i see two "methods" for calculating the pv of floating payments in a swap.
Within the "quicker" method if the principal is L it says that we can say that it is L-L*Sumof Discount factors. Question 1: is this always the case irrespective of whether "I " pay the fixed or the floating leg?

Within an asset discussion (oct 2016 q5) it mentions
(Part 1)
that the swap value can be viewed as a FRN and fixed bond (so sth like Vswap=Vfixed-Vfloating)
and the pv of floating can be carried out more quickly if we use this info. there is some description ie about adding a notional payment at the end so we end up with a FRN
(part 2)
And it says: the value at any payment date will be equal to the nominal value. and if we deduct the value of the imaginary npominal payment from the nominal value we get the value of the interest payments alone.

I have two questions: 2. where we use the 1st sentence of Part 1
3. why if we do L-L*Sumof Discount factors equals the PV of floating payments ?

thanks

2. ### Colin McKeeActEd TutorStaff Member

I am reading some past papers and i see two "methods" for calculating the pv of floating payments in a swap.
Within the "quicker" method if the principal is L it says that we can say that it is L-L*Sumof Discount factors. Question 1: is this always the case irrespective of whether "I " pay the fixed or the floating leg?

I think the formula you refer to in ASET is slightly different. It has an "i" interest rate in it as well. The "sum of the discount rates" is the annuity used to price the future interest payments. The "i" is the percentage of those payments using the fixed swap rate, and the L is used to multiply the "i" to get the cash amount of those payments. I dont see any place in the solution where the formula you refer to is used.

The core reading refers to a swap being viewed as a fixed and a floating bond (one long and one short) in situations where the chance of default can be ignored. This essentially means that this method can be used when the rates used to estimate the floating coupons (probably LIBOR) are also the rates used to discount those coupons (ie the spot discount factors used in the ASET solution). This will often be the case in SP5, but if the discount rate is a different rate (for example a WACC or some other arbitrary rate) you would not be able to use that method and each cashflow would have to be discounted separately.