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
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.