Date Generation Functions
Formulas & Technical Details
Description of Supported Business Day Conventions
Non End-of-Month Conventions
When generating a sequence of dates (for example, when
generating the coupon payment dates for a swap or a bond), it may be necessary
to adjust the dates for weekends and holidays.
Weekends can be defined to include Saturdays and Sundays, or just
Sundays. Several adjustment methods are
provided.
|
Business Day Convention |
Description |
|
no date adjustment |
Dates are not adjusted. |
|
next good business day |
If a date falls on a weekend or a holiday, the next good
business day is used. |
|
previous good business day |
If a date falls on a weekend or a holiday, the previous
good business day is used. |
|
modified following business day |
If a date falls on a weekend or a holiday, the next good
business day is used. If the next good
business day falls in the next month, the previous good business day is used. |
End-of-Month Conventions
When generating a sequence of dates, there are different
conventions regarding how dates are generated at the end of the month. The preceding non end-of-month conventions
will generate cash flow dates that fall on the same day of the month, and then
possibly adjust the date to a business day.
End-of-month conventions will generate dates in the same way, except
when the base date (or cycle date) falls on the last day of the month. In this case, the end-of-month convention
will generate subsequent cash flow dates that fall on the last day of each cash
flow month (and then possibly adjust to a business day. For example, suppose today is
|
Business Day Convention |
Description |
|
end of month no date adjustment |
Dates are generated according to the end-of-month rule
described above. Generated dates are
not adjusted for business days. |
|
end of month next good business day |
Dates are generated according to the end-of-month rule
described above. If a generated date
falls on a weekend or a holiday, the next good business day is used. |
|
end of month previous good business day |
Dates are generated according to the end-of-month rule
described above. If a generated date
falls on a weekend or a holiday, the previous good business day is used. |
|
end of month modified following business day |
Dates are generated according to the end-of-month rule
described above. If a generated date
falls on a weekend or a holiday, the next good business day is used. If the next good business day falls in the
next month, the previous good business day is used. |
|
end of month ignore leap years |
Dates are generated according to the end of month rule
described above. Generated dates are
not adjusted for business days. In a
leap year, the end of month for February will be February 28. |
Third Wednesday Conventions
Two other date adjustment methods are provided, both
relating to exchange traded contracts where trading stops two business days
prior to the third Wednesday of the month, or on the third Wednesday of the
month.
|
Business Day Convention |
Description |
|
two business days prior to third Wednesday |
For annual, semi-annual, quarterly, or monthly
frequencies, generated dates are adjusted to fall 2 business days prior to
the third Wednesday of the month. For
all other frequencies, dates are generated as usual, with no adjustment for
weekends or holidays. Note: The
maturity date is not adjusted. |
|
third Wednesday |
For annual, semi-annual, quarterly, or monthly
frequencies, generated dates are adjusted to fall on the third Wednesday of
the month. For all other frequencies,
dates are generated as usual, with no adjustment for weekends or
holidays. Note: The maturity date is
not adjusted. |
Odd First and/or Last Coupon Periods
For bonds (and swaps), the coupon payment dates generally
follow a regular payment schedule (e.g. every 6 months). If there is any irregularity, generally, it
is either an odd first coupon period and / or an odd last coupon period.
Case 1 no odd coupons:
In this case d_l_cpn = d_f_cpn =
0. If d_e
is prior to d_s, it is ignored. Note that if d_e
< d_s, d_e
can be set to 0, in which case the function will calculate the previous regular
coupon date.
Case 2 odd first coupon:
In this case d_l_cpn =
0, d_e < d_f_cpn
< d_t.
By assumption, d_f_cpn and d_t will be on the same cycle (e.g. if the
frequency is semi-annual, d_t =
Case 3 odd last coupon:
In this case d_f_cpn =
0, d_e < d_l_cpn
< d_t.
Note that by assumption, d_l_cpn and d_e will be on the same cycle (e.g. if the
frequency is annual, d_l_cpn =
Case 4 odd first and odd last coupons:
In this case, d_e < d_f_cpn < d_l_cpn
< d_t.
Note that by assumption, d_l_cpn and d_f_cpn will be on the same cycle (e.g. if the
frequency is annual, d_l_cpn =
FINCAD Functions
The first class of functions generates a date which is a
specified number of adjustment units (days, weeks, months, etc.) forward or
backwards from a given base date.
The most general functions are:
aaDateAdjust2(d_to_adj,
num_units, adj_units, d_rul, weekend, hl)
Adjusts a base date a specified number of market days,
calendar days, weeks, months, years, Mondays,
Sundays. Weekends can be defined to include Saturdays
and Sundays, or Sundays only.
aaDateAdjust(d_to_adj,
num_units, adj_units, d_rul, hl)
Adjusts a base date a specified number of market days,
calendar days, weeks, months, years, Mondays,
Sundays.
Other functions are:
aaMaturity_date2(d_to_adj,
jump_by, jump_fwd, d_rul, hl)
Adjusts a base date a specified number of days or months
using the specified business day convention.
aaDateSettle(d_to_adj,
days_adj, hl)
Adjusts a base date by a specified number of business
days.
The second type of function generates tables of
dates. The most general functions are:
aaDateGen2(d_s,
d_t, d_e, d_f_cpn, d_l_cpn, freq, hl, d_rul, weekend, table_type)
Generates a one or two column table of dates (for example
bond or swap coupon dates). Weekends can
be defined to include Saturdays and Sundays, or Sundays only. The sequence may have odd first and / or odd
last periods, and the frequency may be annual, semi-annual, quarterly, monthly,
biweekly, weekly, 35 day, 28 day, 21 day, 42 day, market days, calendar days.
aaDateGen(d_s,
d_t, d_e, d_f_cpn, d_l_cpn, freq, hl, d_rul, table_type)
Generates a one or two column table of dates (for example
bond or swap coupon dates). The sequence
may have odd first or / and odd last periods, and the frequency may be annual,
semi-annual, quarterly, monthly, biweekly, weekly, 35 day, 28 day, 21 day, 42
day.
aaDateGen_daily(d_e,
d_t, freq, hl, table_type)
Generates a one (or two) column table of market of
calendar dates.
aaSamplingDates2(sam_freq, d_exp, d_e, hl)
Generates the sampling dates for a given frequency. This function exposes the internal sampling
dates used in many path dependent option functions (e.g. Super Asian option).
aaSamplingDates(sam_freq,
d_exp, d_aver)
Generates the sampling dates for a given frequency. This function exposes the internal sampling
dates used in many path dependent option functions (e.g. Asian, discrete
lookback, average strike, double average).
aaDates1(d_e,
d_t, freq, hl, orientation, d_rul, odd, d_dir)
Generates a one column date list using a specified
frequency and business day convention.
aaDates2(d_e,
d_t, freq, hl, orientation, d_rul, odd, d_dir)
Generates a two column date list using a specified
frequency and business day convention.
Description of Inputs
|
Input Argument |
Description |
|
d_to_adj |
date to be adjusted |
|
num_units |
number of units to adjust the base date by |
|
adj_units |
date adjustment method |
|
d_rul |
business day convention |
|
weekend |
weekend definition |
|
hl |
holiday list |
|
jump_by |
adjust by days or months |
|
jump_fwd |
adjustment period |
|
days_adj |
number of days to adjust the base date |
|
d_s |
settlement date |
|
d_t |
terminating date |
|
d_e |
effective date |
|
d_f_cpn |
date of first coupon.
This is an optional argument and a
value of 0 means that it will be ignored.
A date should only be entered if the structure has an odd first coupon
period. If d_f_cpn < d_s, the odd
coupon period has expired and this input has no effect. |
|
d_l_cpn |
date of last coupon.
This is an optional argument and a
value of 0 means that it will be ignored.
A date should only be entered if the structure has an odd last coupon
period. |
|
freq |
cash flow frequency |
|
table_type |
output table selection |
|
sam_freq |
sampling frequency |
|
d_exp |
expiry date |
|
d_aver |
date when averaging starts |
|
orientation |
orientation of output table |
|
odd |
odd date list |
|
d_dir |
direction for date generation |
Description of Outputs
aaDateAdjust and aaDateAdjust2
|
Output |
Description |
|
d_adj |
date adjusted for weekends and holidays |
aaMaturity_date2 and aaDateSettle
|
Output |
Description |
|
d_adj |
date adjusted for business day convention |
aaDateGen,
aaDateGen2, aaDateGen_daily, and aaDates2
|
Output |
Description |
|
d_tbl |
date table - two column - effective date, terminating date |
aaSamplingDates, aaSamplingDates2 and aaDates1
|
Output |
Description |
|
d_list |
date list - one column |
Examples
Example 1
Using the function aaDateGen2() (with
adjustment to the next good business day).
aaDateGen2
|
Argument |
Description |
Example Data |
Switch |
|
d_s |
settlement date |
1-Jun-1990 |
|
|
d_t |
terminating date |
30-Nov-1996 |
|
|
d_e |
effective date |
1-Apr-1988 |
|
|
d_f_cpn |
date of first coupon |
20-Feb-1991 |
|
|
d_l_cpn |
date of last coupon |
20-Feb-1995 |
|
|
freq |
cash flow frequency |
1 |
annual |
|
hl |
holiday list |
0 |
|
|
d_rul |
business day convention |
2 |
next business day |
|
weekend |
weekend definition |
1 |
Sat. and Sun. |
|
table_type |
output table type |
2 |
2 column |
Results
|
Output |
||
|
1-Apr-1988 Fri |
20-Feb-1991 Wed |
odd first |
|
20-Feb-1991 Wed |
20-Feb-1992 Thu |
|
|
20-Feb-1992 Thu |
22-Feb-1993 Mon |
|
|
22-Feb-1993 Mon |
21-Feb-1994 Mon |
|
|
21-Feb-1994 Mon |
20-Feb-1995 Mon |
|
|
20-Feb-1995 Mon |
2-Dec-1996 Mon |
odd last |
Example 2
Using the function aaDateGen2() (with
adjustment to the third Wednesday).
aaDateGen2
|
Argument |
Description |
Example Data |
Switch |
|
d_s |
settlement date |
24-Sep-2003 |
|
|
d_t |
terminating date |
12-Jan-2006 |
|
|
d_e |
effective date |
2-May-2003 |
|
|
d_f_cpn |
date of first coupon |
|
|
|
d_l_cpn |
date of last coupon |
|
|
|
freq |
cash flow frequency |
3 |
quarterly |
|
hl |
holiday list |
0 |
|
|
d_rul |
business day convention |
10 |
3rd Wed. |
|
weekend |
weekend definition |
1 |
Sat. and Sun. |
|
table_type |
output table type |
2 |
2 column |
Results
|
Output |
|
|
16-Jul-2003 Wed |
15-Oct-2003 Wed |
|
15-Oct-2003 Wed |
21-Jan-2004 Wed |
|
21-Jan-2004 Wed |
21-Apr-2004 Wed |
|
21-Apr-2004 Wed |
21-Jul-2004 Wed |
|
21-Jul-2004 Wed |
20-Oct-2004 Wed |
|
20-Oct-2004 Wed |
19-Jan-2005 Wed |
|
19-Jan-2005 Wed |
20-Apr-2005 Wed |
|
20-Apr-2005 Wed |
20-Jul-2005 Wed |
|
20-Jul-2005 Wed |
19-Oct-2005 Wed |
|
19-Oct-2005 Wed |
12-Jan-2006 Thu |
Note:
Maturity date is not adjusted to a Wednesday
Example 3
Using the function aaDateGen2() to
generate Market days (where Saturday is a market day)
aaDateGen2
|
Argument |
Description |
Example Data |
Switch |
|
d_s |
settlement date |
8-Jan-2003 |
|
|
d_t |
terminating date |
20-Jan-2003 |
|
|
d_e |
effective date |
1-Jan-2003 |
|
|
d_f_cpn |
date of first coupon |
|
|
|
d_l_cpn |
date of last coupon |
|
|
|
freq |
cash flow frequency |
11 |
market days |
|
hl |
holiday list |
0 |
|
|
d_rul |
business day convention |
1 |
no adjustment |
|
weekend |
weekend definition |
2 |
Sun. only |
|
table_type |
output table type |
2 |
2 column |
Results
|
Output |
|
|
08-Jan-2003 Wed |
09-Jan-2003 Thu |
|
09-Jan20-03 Thu |
10-Jan-2003 Fri |
|
10-Jan-2003 Fri |
11-Jan-2003 Sat |
|
11-Jan-2003 Sat |
13-Jan-2003 Mon |
|
13-Jan-2003 Mon |
14-Jan-2003 Tue |
|
14-Jan-2003 Tue |
15-Jan-2003 Wed |
|
15-Jan20-03 Wed |
16-Jan-2003 Thu |
|
16-Jan-2003 Thu |
17-Jan-2003 Fri |
|
17-Jan-2003 Fri |
18-Jan-2003 Sat |
|
18-Jan-2003 Sat |
20-Jan-2003 Mon |
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