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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

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  • $\begingroup$ Holidays and dcc are two distinct issues. Use holidays and an adjustment convention (following, modified following, no adjustment, etc.) to adjust the period start and end dates. Then apply the dcc to compute the year fraction between the start and end dates. See for instance en.wikipedia.org/wiki/Day_count_convention for an overview of various dcc. $\endgroup$ – Antoine Conze Jan 15 '18 at 11:04
  • $\begingroup$ Thanks. But the question is now, are the DCC static means every day I am using the same DCC or do I have to adjust the actual days numerator every day? $\endgroup$ – JonDoe Jan 15 '18 at 11:50
  • $\begingroup$ The latter. It is not static. $\endgroup$ – dm63 Jan 15 '18 at 12:08
  • $\begingroup$ The year frac depends on the start date and the end date. If these change the year frac has to be recomputed. If you trade a 6x6 FRA today then the start and end dates are not the same than for a 6x6 FRA that was traded yesterday. $\endgroup$ – Antoine Conze Jan 15 '18 at 12:12
  • $\begingroup$ Thanks. That means starting today I would get a DCC and that stay through the whole lifetime of the trade until it matures. either way which evaluation day it is for that trade the DCC e.g. stays at 0.55 evey day. $\endgroup$ – JonDoe Jan 15 '18 at 13:16
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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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