STEPDURATION
Updated 2024-02-29 14:56:29.280000
Syntax
SELECT [westclintech].[wct].[STEPDURATION](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@Yld, float,>
,<@Redemption, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>
,<@Coupons, nvarchar(max),>
Description
Use the scalar function STEPDURATION to calculate the duration for a stepped-coupon bond. The duration is calculated as the first derivative of the price of the bond with respect to yield multiplied by -1 divided by the dirty price of the bond multiplied by 1 plus the yield divided by the frequency.
DURATION=\frac{-\frac{\partial{P}}{\partial{y}}}{P_{dirty}}\left(1+\frac{Y}{F}\right)
Arguments
@Redemption
the redemption value of the bond assuming a 100 par value. @Redemption is an expression of type float or of a type that can be implicitly converted to float.
@Coupons
a SELECT statement, as a string, which identifies the coupon dates and rates to be used in the duration calculation. The coupon rate is assumed to be in effect from the associated coupon date to the next greater coupon date returned by the SELECT statement. The last rate is assumed to be in effect from the last date until the maturity date of the bond.
@Yld
the yield for the maturity date passed into the function. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Frequency
the number of coupon payments per year. For annual payments, @Frequency = 1; for semi-annual, @Frequency = 2; for quarterly, @Frequency = 4; for monthly @Frequency = 12. @Frequency is an expression of type float or of a type that can be implicitly converted to float.
@Maturity
the maturity date of the bond. @Maturity is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Basis
is the type of day count to use. @Basis is an expression of the character string data type category.
{"columns":[{"field":"Basis","width":114},{"field":"Day count basis","width":132}],"rows":[{"Basis":"0 or omitted","Day count basis":"US (NASD) 30/360"},{"Basis":"1","Day count basis":"Actual/Actual"},{"Basis":"2","Day count basis":"Actual/360"},{"Basis":"3","Day count basis":"Actual/365"},{"Basis":"4","Day count basis":"European 30/360"}]}
@Settlement
the settlement date occurring within a coupon period of the bond. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
Return Type
float
Remarks
If @Basis < 0 or @Basis > 4, STEPDURATION returns an error.
If @Maturity < @Settlement 0 is returned.
If @Settlement is NULL, @Settlement = GETDATE().
If @Frequency is NULL, @Frequency = 2.
If @Basis is NULL, @Basis = 0.
If @Coupons is empty or NULL then coupon rate is assumed to be zero.
Accrued interest is calculated from the previous coupon date to the settlement date.
Previous coupon date is calculated backwards from the maturity date. If the maturity date is the last day of the month, all the previous coupon dates are assumed to occur on the last day of the month.
Previous coupon date <= @Settlement < next coupon date.
Examples
In this example we calculate the duration for a bond maturing on 2019-01-15 with the following step-up schedule.
{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"column 2"}],"rows":[{"column 1":"2010-01-15","column 2":"5.0%"},{"column 1":"2013-01-15","column 2":"5.5%"},{"column 1":"2016-01-15","column 2":"6.0%"}]}
The settlement date is April 21, 2014, the yield is 4.0% and the redemption value is 100.
SELECT wct.STEPDURATION(
'2014-04-21', --@Settlement
'2019-01-15', --@Maturity
.04, --@Yld
100, --@Redemption
2, --@Frequency
0, --@Basis
'SELECT wct.CALCDATE(2010,1,15),0.05 UNION ALL
SELECT wct.CALCDATE(2013,1,15),0.055 UNION ALL
SELECT wct.CALCDATE(2016,1,15),0.06' --@Coupons
) as DURATION;
This produces the following result.
{"columns":[{"field":"DURATION","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"DURATION":"4.18487140205481"}]}
The SELECT statement in @Coupons can make reference to another table, as in the following example.
SELECT *
INTO #coups
FROM
(
SELECT '2010-1-15',
0.05
UNION ALL
SELECT '2013-1-15',
0.055
UNION ALL
SELECT '2016-1,15',
0.06
) n(coupdate, couprate);
SELECT wct.STEPDURATION( '2014-04-21', --@Settlement
'2019-01-15', --@Maturity
.04, --@Yld
100, --@Redemption
2, --@Frequency
0, --@Basis
'SELECT *FROM #coups' --@Coupons
) as DURATION;
This produces the following result.
{"columns":[{"field":"DURATION","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"DURATION":"4.18487140205481"}]}
In this example we have multiple securities with different step-up schedules and we only have the prices which need to be converted to yields for input into the duration calculation. For purposes of this example, the coupon schedules are stored in a temporary table, #coups.
SELECT *
INTO #coups
FROM
(
SELECT 'ABC',
'2010-01-15',
0.050
UNION ALL
SELECT 'ABC',
'2013-01-15',
0.055
UNION ALL
SELECT 'ABC',
'2016-01-15',
0.060
UNION ALL
SELECT 'GHI',
'2031-07-22',
0.070
UNION ALL
SELECT 'GHI',
'2026-07-22',
0.0675
UNION ALL
SELECT 'GHI',
'2021-07-22',
0.0650
UNION ALL
SELECT 'GHI',
'2016-07-22',
0.0625
UNION ALL
SELECT 'GHI',
'2011-07-22',
0.0600
UNION ALL
SELECT 'XYZ',
'2023-03-01',
0.0600
UNION ALL
SELECT 'XYZ',
'2019-03-01',
0.0575
UNION ALL
SELECT 'XYZ',
'2015-03-1',
0.0550
UNION ALL
SELECT 'XYZ',
'2011-03-1',
0.0
) c(secid, coupdate, couprate);
SELECT secid,
wct.STEPDURATION(
'2014-04-21',
n.maturity,
wct.YIELDSTEP(
'2014-04-21',
n.maturity,
n.price,
n.redemption,
n.frequency,
n.basis,
'SELECT
coupdate,
couprate
FROM
#coups
WHERE
secid = ' + '''' + n.secid + ''''
),
n.redemption,
n.frequency,
n.basis,
'SELECT
coupdate,
couprate
FROM
#coups
WHERE
secid = ' + '''' + n.secid + ''''
) as DURATION
FROM
(
SELECT 'ABC',
'2019-01-15',
103.670988,
100,
2,
0
UNION ALL
SELECT 'GHI',
'2036-07-22',
120.467994,
103,
2,
1
UNION ALL
SELECT 'XYZ',
'2027-03-01',
97.478325,
101,
1,
0
) n(secid, maturity, price, redemption, frequency, basis);
This produces the following result.
{"columns":[{"field":"secid"},{"field":"DURATION","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"secid":"ABC","DURATION":"4.17171497362109"},{"secid":"GHI","DURATION":"13.1030222345025"},{"secid":"XYZ","DURATION":"9.96086919797441"}]}
See Also
DURATION - Duration of a bond paying regular, periodic interest
PRICESTEP - Calculate the Price of a security with step-up rates
STEPACCINT - Accrued interest of a stepped-coupon bond
STEPCONVEXITY - Convexity of a stepped-coupon bond
STEPMDURATION - Modified duration of a stepped coupon bond
YIELDSTEP - Calculate the Yield of a security with step-up rates