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mekornilol
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Posts: 22
Joined: April 13th, 2013, 5:29 pm

Converting swap rates (or any rate) between different day counts

January 21st, 2017, 1:42 pm

Recently I got a lot of cr*p from a trader when discussing some calculations concerning the zero curve, he wouldn't be willing to explain why I made a mistake in my calculations, so let's see if you can shed some light.

Assume I have a yield curve (in ACT/365) built using depo rates up to 12M and then swap rates from 2Y on. For the purpose of checking that the yield curve had been built properly, the trader asked me to imply the original 2Y Swap rate market raw input (quoted in 30/360 ) from the 1Y and 2Y point of the zero curve. This was easy, I did all my calculations in ACT/365 but then I converted my result into 30/360 by multiplying by the year fraction between spot and 2Y in 30/360 and dividing by the same time bracket but in ACT/365. The trader claimed this was wrong and that I should have done all my calculations in 30/360 from the beginning. 

Why was my rate conversion conceptually wrong as he claims?
 
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DavidJN
Posts: 242
Joined: July 14th, 2002, 3:00 am

Re: Converting swap rates (or any rate) between different day counts

January 23rd, 2017, 7:30 pm

Your best bet in doing such conversions is to work with discount factors since they are invariant to how rates are quoted - the price of a dollar payoff in the future is the same regardless of how you quote it as a rate, it it isn't so you can get rich quickly. Compute the discount factor from your starting rate using its conventions. Then solve for the rate using the new conventions that give you the same discount factor. This logic works for annuities as well as single points in time.
 
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harkinsi
Posts: 3
Joined: July 9th, 2007, 12:40 pm

Re: Converting swap rates (or any rate) between different day counts

May 21st, 2017, 4:03 pm

agree with DavidJN.
If i've understood what you've done correctly, then your trader is wrong but you can always use what DavidJN suggested to check your calcs as this is the foolproof way.
 
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Martinghoul
Posts: 188
Joined: July 18th, 2006, 5:49 am

Re: Converting swap rates (or any rate) between different day counts

May 22nd, 2017, 8:16 am

Do what David suggested and you can't go wrong...