# SQL Server price function for odd- first and last coupon bonds

OFLPRICE

Updated: 30 June 2014

Use OFLPRICE to calculate the price from yield per 100 face value of a bond with an odd first period and an odd last period. The OFLFPRICE formula for a bond with an odd short first coupon is:

Where

 A = C * accrued days / E C = 100 * coupon rate / frequency DFC = the number of days from the issue date to the first coupon date DLCi = the number of days from the previous coupon date to the lesser of the next coupon date and the maturity date in the ith last quasi-coupon period DSC = number of days from settlement to coupon E = the normal length of the first quasi-coupon period N = the number of coupons between the first coupon date and the last coupon date NCL = the number of quasi-coupons from the last coupon date to the quasi-maturity date NLLi = the normal length in days of the full ith quasi-coupon period in the odd last period RV = redemption value Y = yield / frequency

The OFLPRICE formula for a bond with an odd long first coupon is:

Where

 Ai = number of accrued days for the ith quasi-coupon period C = 100 * coupon rate / frequency DFCi = number of days from the issue date to the first quasi-coupon date or the number of days in the quasi-coupon period
 DLCi = the number of days from the previous coupon date to the lesser of the next coupon date and the maturity date in the ith last quasi-coupon period DSC = number of days from settlement date to the next quasi-coupon date or first coupon date. E = number of days in the quasi-coupon period in which settlement occurs N = the number of coupons between the first coupon date and the maturity date NCF = number of quasi-coupon periods that fit in the odd first period NCL = the number of quasi-coupons from the last coupon date to the quasi-maturity date NLFi = normal length in days of the full ith quasi-coupon period within the odd period. NLLi = the normal length in days of the full ith quasi-coupon period in the odd last period Nqf = the number of whole quasi-coupon periods between the settlement date and the first coupon. RV = redemption value Y = yield / frequency

Syntax
SELECT [wctFinancial].[wct].[OFLPRICE](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@Issue, datetime,>
,<@First_coupon, datetime,>
,<@Last_coupon, datetime,>
,<@Rate, float,>
,<@Yld, float,>
,<@Redemption, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>)
Arguments
@Settlement
the settlement date of the bond. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@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.
@Issue
the issue date of the bond; the date from which the bond starts accruing interest. @Issue is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@First_coupon
the first coupon date of the bond. The period from the issue date until the first coupon date defines the odd interest period. All coupon dates from @First_coupon to @Last_coupon are assumed to occur at regular periodic intervals as defined by @Frequency@First_coupon is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Last_coupon
the last coupon date of the bond prior to the maturity. The period from the last interest date until the maturity date defines the odd interest period. All coupon dates from @First_coupon to @Last_coupon are assumed to occur at regular periodic intervals as defined by @Frequency. @Last_coupon is an expression that returns a datetime or smalldatetime value, or a character string in date format.
@Rate
the bond’s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yld
the bond’s annual yield. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the bond’s redemption value per 100 face value. @Redemption 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 bimonthly @Frequency = 6; for monthly @Frequency = 12. For bonds with @Basis = 'A/364' or 9, you can enter 364 for payments made every 52 weeks, 182 for payments made every 26 weeks, 91 for payments made every 13 weeks, 28 for payments made every 4 weeks, 14 for payments made every 2 weeks, and 7 for weekly payments. @Frequency is an expression of type float or of a type that can be implicitly converted to float.
@Basis
is the type of day count to use. @Basis is an expression of the character string data type category.
 @Basis Day count basis 0, 'BOND' US (NASD) 30/360 1, 'ACTUAL' Actual/Actual 2, 'A360' Actual/360 3, 'A365' Actual/365 4, '30E/360 (ISDA)', '30E/360', 'ISDA', '30E/360 ISDA', 'EBOND' European 30/360 5, '30/360', '30/360 ISDA', 'GERMAN' 30/360 ISDA 6, 'NL/ACT' No Leap Year/ACT 7, 'NL/365' No Leap Year /365 8, 'NL/360' No Leap Year /360 9, 'A/364' Actual/364 10, 'BOND NON-EOM' US (NASD) 30/360 non-end-of-month 11, 'ACTUAL NON-EOM' Actual/Actual non-end-of-month 12, 'A360 NON-EOM' Actual/360 non-end-of-month 13, 'A365 NON-EOM' Actual/365 non-end-of-month 14, '30E/360 NON-EOM', '30E/360 ICMA NON-EOM', 'EBOND NON-EOM' European 30/360 non-end-of-month 15, '30/360 NON-EOM', '30/360 ISDA NON-EOM', 'GERMAN NON-EOM' 30/360 ISDA non-end-of-month 16, 'NL/ACT NON-EOM' No Leap Year/ACT non-end-of-month 17, 'NL/365 NON-EOM' No Leap Year/365 non-end-of-month 18, 'NL/360 NON-EOM' No Leap Year/360 non-end-of-month 19, 'A/364 NON-EOM' Actual/364 non-end-of-month
Return Type
float
Remarks
·         If @Settlement is NULL then @Settlement = GETDATE().
·         If @Rate is NULL then @Rate = 0.
·         If @Yield is NULL then @Yield = 0.
·         If @Redemption is NULL then @Redemption = 100.
·         If @Frequency is NULL then @Frequency = 2.
·         If @Basis is NULL then @Basis = 0.
·         If @Frequency is any number other than 1, 2, 4, 6 or 12, or for @Basis = 'A/364' any number other than 1, 2, 4, 6, or 12 as well as 7, 14, 28, 91, 182, or 364 OFLPRICE returns an error.
·         If @Basis is invalid (see above list), OFLPRICE returns an error.
·         If @Maturity is NULL then an error is returned.
·         If @Last_coupon is NULL then an error is returned.
·         If @First_coupon is NULL then an error is returned.
·         If @Issue is NULL then an error is returned.
·         If @Settlement >= @First_coupon then the price is calculated using ODDLPRICE.
Example
This is a bond with an odd short first coupon and an odd short last coupon.
SELECT
wct.OFLPRICE(
'2013-03-04'     --@Settlement
,'2022-04-28'     --@Maturity
,'2012-12-07'     --@Issue
,'2013-03-15'     --@First_coupon
,'2022-03-15'     --@Last_coupon
,.03125           --@Rate
,.02875           --@Yld
,100              --@Redemption
,2                --@Frequency
,1                --@Basis
) as PRICE
This produces the following result.
PRICE
----------------------
102.00036224598
This is a bond with an odd long first coupon and an odd long last coupon.
SELECT
wct.OFLPRICE(
'2013-03-04'     --@Settlement
,'2022-11-28'     --@Maturity
,'2012-06-07'     --@Issue
,'2013-03-15'     --@First_coupon
,'2022-03-15'     --@Last_coupon
,.03125           --@Rate
,.02875           --@Yld
,100              --@Redemption
,2                --@Frequency
,1                --@Basis
) as PRICE
This produces the following result.
PRICE
----------------------
102.103433425767
This is a bond with an odd long first coupon and an odd short last coupon.
SELECT
wct.OFLPRICE(
'2013-03-04'     --@Settlement
,'2022-04-28'     --@Maturity
,'2012-06-07'     --@Issue
,'2013-03-15'     --@First_coupon
,'2022-03-15'     --@Last_coupon
,.03125           --@Rate
,.02875           --@Yld
,100              --@Redemption
,2                --@Frequency
,1                --@Basis
) as PRICE
This produces the following result.
PRICE
----------------------
101.999004756314
This is a bond with an odd short first coupon and an odd long last coupon.
SELECT
wct.OFLPRICE(
'2013-03-04'     --@Settlement
,'2022-11-28'     --@Maturity
,'2012-12-07'     --@Issue
,'2013-03-15'     --@First_coupon
,'2022-03-15'     --@Last_coupon
,.03125           --@Rate
,.02875           --@Yld
,100              --@Redemption
,2                --@Frequency
,1                --@Basis
) as PRICE
This produces the following result.
PRICE
----------------------
102.104790915433

This is an example of a bond paying interest every 26 weeks.
SELECT
wct.OFLPRICE(
'2014-10-04'     --@Settlement
,'2029-12-12'     --@Maturity
,'2014-07-30'     --@Issue
,'2015-03-18'     --@First_coupon
,'2029-02-28'     --@Last_coupon
,.1250            --@Rate
,.1100            --@Yld
,100              --@Redemption
,182              --@Frequency
,9                --@Basis
) as PRICE
This produces the following result.
PRICE
----------------------
110.846098828263