Trading Days and Day Counts

Trading Days and Day Counts

Three related things: moving by trading days, rolling a date off a closed day, and measuring the fraction of a year between two instants. They come together because an option tenor is all three at once.

Weekday, business day, trading day

Three different words for three different things, used precisely throughout:

• Weekday. Monday to Friday. A calendar fact, no exchange involved. is_weekday(), weekdays_between().
• Trading day. A day the exchange's calendar says it is open. Weekends and holidays excluded. is_trading_day(ex).
• Business day. A trading day, used specifically in the ISDA sense of rolling a date that landed on a closed one.

weekdays_between is closed form: no loop, no calendar. It is exactly what trading_days_between degenerates to under a calendar with no holidays.

Moving

d.next_trading_day(ex)          // the next one, whatever d is
d.prev_trading_day(ex)
d.plus_trading_days(2, ex)      // T+2
d.minus_trading_days(5, ex)

plus_trading_days(0) returns the same date whether or not it trades. That is deliberate: moving zero days is not a request to fix the date. Use adjusted for that.

The walk is bounded at abs(n) * 2 + 30 calendar days and raises if it runs out, because roughly 1.45 calendar days per trading day is the worst real case and running out means the calendar data is wrong.

Rolling: the ISDA conventions

adjusted(conv, ex) moves a date off a non-trading day by the named rule:

Convention	Behaviour
UNADJUSTED	Leave it alone even if the market is shut
FOLLOWING	Move forward to the next trading day
MOD_FOLLOWING	Move forward, unless that crosses into the next month, then backward
PRECEDING	Move backward to the previous trading day
MOD_PRECEDING	Move backward, unless that crosses into the previous month, then forward

The two modified forms exist so a schedule of month-end payments stays inside its months. It returns a DateTime at midnight rather than preserving the receiver's time of day, because a business-day roll is a statement about which day settles.

A three-month forward, rolled the way a swap desk would:

d.plus_period(t.parse_tenor("3M")).adjusted(t.BusinessDay.MOD_FOLLOWING, ex)

Positions within a month

t.first_trading_day_of_month(2025, 6, ex)
t.last_trading_day_of_month(2025, 6, ex)
t.trading_days_in_month(2025, 6, ex)     // 19 to 23 on the equity calendars
d.trading_day_of_month(ex)               // which one this is, 1-based

trading_day_of_month returns na on a day the market is shut, not 0. Zero would be a real ordinal, so it cannot also mean "no answer". This is the in-band-number clause from the Error Model.

Counting a span

trading_days_between is half-open on the earlier of the two dates: the earlier date counts when it trades, the later never does, and the result is negated when the arguments come the other way round. Half-open so consecutive spans add up without double-counting the join.

It does not walk the calendar. See Performance and Limits for why that matters and how the proposal-and-filter approach works.

Day counts

The convention is the denominator of every rate and the tau of every option price. Per the ISDA 2006 Definitions:

Convention	Numerator over denominator
ACT_365F	Actual days over a fixed 365. The usual option tenor, and what crypto derivatives actually quote
ACT_360	Actual days over 360. Money-market convention
ACT_ACT_ISDA	Actual days, leap-year days over 366 and the rest over 365
D30_360	30/360 Bond Basis: a 31st becomes a 30th, and the end date flattens only when the start already has
D30E_360	30E/360 Eurobond: both ends flatten unconditionally
ACT_252	Trading days over 252. Business-day time in equity volatility

int   expiry = t.monthly_expiry(2025, 12)
float tau    = t.year_fraction(time, expiry, t.DayCount.ACT_365F)
int   n      = t.day_count_days(time, expiry, t.DayCount.D30_360)

day_count_days exposes the numerator separately because for the 30/360 family it is not recoverable from the fraction alone.

Two traps worth naming. ACT_252 needs an exchange, since it counts trading days, and under Exchange.CRYPTO every calendar day is a trading day, so it degenerates to actual days over 252, a denominator no crypto desk uses. Crypto tenors are ACT_365F.

The 30/360 and 30E/360 implementations reproduce 14 published ISDA worked examples, both as year fractions and as raw integer numerators.

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