Day Count and Business Day Rules for Interest Rates
Summary
The note distinguishes day count conventions from business day conventions using an FRA example. A day count rule determines the accrual fraction used to calculate interest over the dates of a contract. Under ACT/360, the numerator is the actual number of calendar days between dates, including weekends and holidays, and the denominator is 360. Thus the elapsed calendar days determine the fraction; moving the valuation date does not itself alter the fraction between unchanged contract dates.
Business day rules instead determine which dates apply when generating coupon or maturity schedules. A rule such as following rolls a date that falls on a non-business day to a suitable business day under the relevant calendar. In practice, date generation and accrual calculation are both needed: first establish the applicable dates, then compute the interest fraction between them. The explanation is introductory and neglects calendar complications in the original question; it does not survey other day count methods or jurisdiction-specific adjustments.
Key ideas
- ACT/360 divides the actual calendar days in an accrual period by 360.
- Calendar days include weekends and holidays when counting actual days.
- Business day conventions adjust scheduled payment or maturity dates around non-business days.
- Date generation and interest accrual are separate steps in contract calculations.
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Full text
# Day Count conventions # Day Count conventions I have a general question concerning day count conventions. Let's say I have a 6M FRA with a start day 2017-02-09 and a end date 2017-08-09. The day count convention (DCC) would be e.g. Act/360. Today would be the 2017-02-09. (neglecting calendars). My DCC(Act/360) would be for the 6M FRA today 0.502777778. How would be the DCC(ACT/360) when moving one day further (2017-02-10)? Will it be the same value? The other question is how would holidays plays a role ## Answer by Phil H (score 2) https://quant.stackexchange.com/a/37758 ## Day count Day count conventions are a way to agree between parties how interest is calculated for an instrument. It is, therefore, as simple as possible given some constraints. An Act/360 convention is ActualDays/360, where 'actual' means days on the calendar, including counting weekend days, holidays etc. So 181 days is always 0.502777.. in Act/360. Other conventions like Bond basis are more complex, but satisfy other requirements like calendar 3 or 6m periods always having even fractions like 1/4 or 1/2 and thus making coupons equal (and generally round numbers) throughout the regular portion of a bond. ## Business day convention The convention for determining the coupon dates or maturity dates for a given tenor are not the same thing. This is a calendar function in which we find suitable dates given some rules about weekends, holidays and so on. So this time, we might use a simple rule like 'following' where we just roll forward from a natural calendar end for the 11th (2017-08-11) to the next available business day (2017-08-13). Essentially you always need both, first to generate the correct dates, then to calculate the correct interest amount given those dates. Oh and beware Brazil.
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