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Complete characterization of an interest rate requires a few elements:

  1. day count

  2. compounding frequency

  3. the rate itself

  4. start date and end date

That said, I notice that day counts are never displayed on yield curves found in textbooks or bloomberg. I would like to ask if there is a convention here widely used in the industry.

This has practical applications. The pricing of a vanilla interest rate swap requires the matching of the present value of the fix leg and the floating leg. The floating leg has to be calculated from the yield curve. Typical swap contracts specify the daycount of the floating leg. Pricers in bloomberg calculate different PV for different specifications of the floating leg daycount which seems to imply that the yield curve used does not have a daycount associated with it and the floating leg daycount is needed to completely specify the float leg cash flows.

Nevertheless, the yield curve is constructed using instruments with daycount conventions. So by extension, the rates presented on a yield curve should have a daycount associated with it.

Can anyone explain what is going on here? daycount or no daycount?

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    $\begingroup$ Yield curves are usually bootstrapped/stored as zero coupon prices curves $D(T)$ = time 0 price of 1 unit of numeraire paid on time $T$, and do not require any associated daycount convention. Rates are simply recomputed off it according to the rate convention. For instance if $D$ is a forward libor curve, fwd libor spanning $T_1$ to $T_2$ = $(D(T_1)/D(T_2) - 1)/\text{libordaycount}(T_1, T_2)$ $\endgroup$ – Antoine Conze Jun 25 at 17:07
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Please read the Interest Rates Instruments and Market Conventions paper from OpenGamma (https://developers.opengamma.com/quantitative-research/Interest-Rate-Instruments-and-Market-Conventions.pdf).

The conventions are implied but it is also worth checking with the counter party/vendor when in doubt.

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