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I read the following definitions of day count rules

(ii) if “Actual/Actual (ISDA)” or “Act/Act (ISDA)” is specified, the actual number of days in the Interest Period divided by 365 (or, if any portion of that Interest Period falls in a leap year, the sum of (1) the actual number of days in that portion of the Interest Period falling in a leap year divided by 366 and (2) the number of days in that portion of the Interest Period falling in a non-leap year divided by 365);

(iii) if “Actual/Actual (ICMA)” is specified, the number of days in the Interest Period, including February 29 in a leap year, divided by the product of (1) the actual number of days in such Interest Period and (2) the number of Interest Periods in the calendar year;

(iv) if “Actual/Actual (Bond)” is specified, the number of calendar days in the Interest Period, divided by the number of calendar days in the Interest Period multiplied by the number of Interest Periods in the calendar year;

It seems very difficult to obtain precise calculations for these. In particular I think ii) is well defined but iii) and iv) might require a subjective assessment. In particular I read iii) and iv) as the same since a calendar day includes a leap, but the very fact of different presentation alludes to the fact they are different.

Has anyone specifically implemented these into their quant finance libraries, or can offer an opinion?

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Daycount rules can be daunting and I sometimes feel like "everyone" uses a different name for the same definition and names frequently change.

For short:

iii) and iv) are the same

Long answer:

You can check for example quantlib's where you can see

the ISDA convention, also known as "Actual/Actual (Historical)", "Actual/Actual", "Act/Act", and according to ISDA also "Actual/365", "Act/365", and "A/365";

the ISMA and US Treasury convention, also known as "Actual/Actual (Bond)";

the AFB convention, also known as "Actual/Actual (Euro)".

Now ISMA is the same as ICMA, you can see that on ISDA where Act/Act (Bond) is not even mentioned as an alternative name for ICMA.

However, ISDA mentions it here (with examples showing that there is no subjective assessment) where it is written that:

The existing ISDA approach will be retained, to be known as "Actual/Actual (Historical)", the AFB approach will be introduced, to be known as "Actual/Actual (Euro)". The ISMA approach will also be introduced, to be known as "Actual/Actual (Bond)". These changes will be taken forward when ISDA revises and consolidates its existing interest rate swap definition booklets in the course of 1999.

As you can see, back in 1999, ISDA called "Actual/Actual (Bond)" the ISMA approach, which is known as ICMA since 2011 🙃

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    $\begingroup$ Thanks, very nice, the ActActICMA is the last one I need to implement. Slightly more difficult because it relies on the frequency. $\endgroup$
    – Attack68
    Aug 11, 2022 at 20:42
  • $\begingroup$ Am I too invasive if I ask your help to answer quant.stackexchange.com/questions/76150/…? $\endgroup$ Jul 26, 2023 at 18:19

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