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DavidJN
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Joined: July 14th, 2002, 3:00 am

Converting a swap spread to a different day count

November 30th, 2020, 6:33 pm

I have an applied question for any swap traders out there. Scientists are please encouraged to not hijack the thread. 
 
Say you have a bespoke single currency interest rate swap that pays X BPS on the fixed side semi-annual 30/360, against 3M LIBOR plus a Y BPS spread act/360 on the floating side. To avoid the complexities of counterparty credit risk and collateralization, pretend we are in the single curve LIBOR world.
 
For risk purposes, a not uncommon shortcut is to treat this swap as paying X – Y BPS on the fixed side against a LIBOR flat floating side (whereupon valuing the floating side becomes trivial). What if, as is likely, the day counts of the fixed and floating sides are different? Strictly speaking, subtracting an act/360 spread from a 30/360 rate is not correct. 
 
I haven’t spent much time with swaps since leaving front office twelve years ago, so I want to confirm I remember the technique for converting a spread from one day count to another. Presumably, one starts by finding what the present value of Y BPS is on the floating side using its conventions, and then solves for the equivalent spread on the fixed side using its conventions. To do this efficiently, I was thinking of calculating a CDF (cumulative discount factor) from the zero curve for each leg using their respective conventions. The PV of the spread income on the floating side is the notional principal times the spread times the floating side CDF. Divide that amount by the fixed CDF to get the fixed side BPS equivalent.
 
Just wanted to verify the procedure, because it may eventually show up in a book.
 
Does it mean anything practically? Simple numerical experiments suggest the impact could be approaching a basis point on a 5-year deal, so yes it is useful to get it right.
 
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DavidJN
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Posts: 242
Joined: July 14th, 2002, 3:00 am

Re: Converting a swap spread to a different day count

December 1st, 2020, 4:21 pm

Yes, that is the procedure, for those who might want to know