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How can I convert a 6M Libor rate e.g. 1Y Tenor to a 3M Libor rate using a basis swap 3M vs. 6M? I wanted to know the math and also an example would be great.

Update:

Example:

6M Swap 1Y Tenor: 1.925
3M Swap 1Y Tenor: 1.77109
3v6M Basis Swap 1Y Tenor = 15.625

When calculating now the 3N Swap 1Y Tenor based on the 6M Swap and the Basis Swap I receive the following value:

Calc 3M Swap 1Y Tenor: 1.76875

which is a relative differdnce og 0.13%.

The day count conventions are the same so I am not sure why I receive this kind of difference.

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Let's say 1yr semiannual rate versus 6m Libor is 2.00% and 1yr basis swap is 6m libor = 3m libor + 15bp. Then , to a first approximation 1yr rate versus 3m libor is 2.00-0.15= 1.85%.

More precisely , we have to take into account daycount conventions. So, we know that a swap consisting of 2.00% semiannual 30/360 daycount versus 3m libor +15 bp quarterly Act/360 is a fair swap, since both sides are equivalent to 6m libor. So the fixed rate equivalent of 3m libor is actually 2.00% minus the semiannual equivalent of 15bp quarterly Act/360. This conversion is not exactly solvable without having the discount factors for all the cash flows, but an approximation would be to first convert the 15bp to 30/360 daycount by calculating 15*365/360. Then you need to find the semiannual stream equivalent to the above quarterly stream. You might end up with 15.5bp instead of 15bp, so the answer would be 1.845%.

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    $\begingroup$ thanks. So that means when the day count conv is the same for 3M and 6M then it is simply subtract the basis spread from the 6M curve to receive the 3M quote. $\endgroup$ – JonDoe Dec 11 '17 at 12:34

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