360-day calendar
The 360-day calendar is a method of measuring durations used in financial markets, in computer models, in ancient literature, and in prophetic literary genres. It is based on merging the three major calendar systems into one complex clock, with the 360-day year as the average year of the lunar and the solar: [365.2425 (solar) + 354.3829 (lunar)] ÷ 2 = 719.61 ÷ 2 = 359.8 days rounded to 360. It is a simplification to a 360-day year, consisting of 12 months of 30 days each. To derive such a calendar from the standard Gregorian calendar, certain days are skipped.
A duration is calculated as an integral number of days between two dates A and B (where by convention A is earlier than B). There are two methods commonly available which differ in the way that they handle the cases where the months are not 30 days long:
- The European Method (30E/360)[1]
- If either date A or B falls on the 31st of the month, that date will be changed to the 30th;
- Where date B falls on the last day of February, the actual date B will be used.
- The US/NASD Method (30US/360)[2]
- If both date A and B fall on the last day of February, then date B will be changed to the 30th.
- If date A falls on the 31st of a month or last day of February, then date A will be changed to the 30th.
- If date A falls on the 30th of a month after applying (2) above and date B falls on the 31st of a month, then date B will be changed to the 30th.
In both cases the difference between the possibly-adjusted dates is then computed by treating all intervening months as being 30 days long.
Other methods include the ISDA 360-day calendar, and the PSA 360-day calendar.
Standard software implementations
The 360-day calendar is implemented by the following spreadsheet functions.
| Package | Function |
|---|---|
| Microsoft Excel | DAYS360 (not SIA-compliant)[3] |
| StarOffice/OpenOffice.org | DAYS360 (also not SIA-compliant, to maintain Excel compatibility)[4] |
| SQL Server 2000 Analysis Services | Days360 |
| Mathworks Financial Toolbox | days360 (US/NASD) |
| Mathworks Financial Toolbox | days360e (European) |
| Mathworks Financial Toolbox | days360isda (ISDA) |
| Mathworks Financial Toolbox | days360psa (PSA) |
| Gnumeric | DAYS360 |
See also
- 365-day calendar
- French Republican Calendar a calendar with twelve 30-day months and five or six appended holidays
- Iranian calendars where the Old Persian calendar had 360 days with an extra month added every 6 years
References
- ↑ ISMA book “Bond Markets: Structures and Yield Calculations”, ISBN 1-901912-02-7, and ISMA’s Circular 14 of 1997
- ↑ Standard Securities Calculation Methods, Fixed Income Securities Formulas for Price, Yield, and Accrued Interest: Volume 1, 1993, Jan Mayle, New York, NY: Securities Industry Association, ISBN 1882936019
- ↑ See Microsoft Kb Article 916004. This bug is present in Excel versions 97, 2000, 2002, 2003 and 2007. This can be demonstrated by evaluating DAYS360(DATE(2006,2,28),DATE(2007,2,28)); here years starting and ending on the last day in February only have 358 days.
- ↑ See Issue 84934 — ODFF: DAYS360 compliance