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XLeratorDB/financial Documentation

SQL Server convexity function for odd last coupon bonds


OFLMDURATION

Updated: 30 June 2014


Use OFLMDURATION to calculate the modified duration for a bond that has an odd first and an odd last coupon. Modified duration is calculated as the first derivative of the price with respect to yield multiplied by -1 divided by the dirty price of the bond.

Syntax
SELECT [wctFinancial].[wct].[OFLMDURATION](
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@IssueDate, datetime,>
 ,<@FirstCouponDate, datetime,>
 ,<@LastCouponDate, 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. 
@IssueDate
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. 
@FirstCouponDate
the first coupon date of the bond. The period from the issue date until the first coupon date defines the odd interest period. All subsequent coupon dates are assumed to occur at regular periodic intervals as defined by @Frequency. @FirstCouponDate is an expression that returns a datetime or smalldatetime value, or a character string in date format. 
@LastCouponDate
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 @FirstCouponDate to @LastCouponDate are assumed to occur at regular periodic intervals as defined by @Frequency. @LastCouponDate 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 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.
@Redemption
the redemption value of the bond assuming a par value of 100. @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 OFLMDURATION returns an error.
·         If @Basis is invalid (see above list), OFLMDURATION returns an error.
·         If @Maturity is NULL then an error is returned.
·         If @LastCouponDate is NULL then an error is returned.
·         If @FirstCouponDate is NULL then an error is returned.
·         If @Issue is NULL then an error is returned.
·         If @Settlement >= @FirstCouponDate 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.OFLMDURATION(
       '2013-03-04'     --@Settlement
      ,'2022-04-28'     --@Maturity
      ,'2012-12-07'     --@Issue
      ,'2013-03-15'     --@FirstCouponDate
      ,'2022-03-15'     --@LastCouponDate
      ,.03125           --@Rate
      ,.02875           --@Yld
      ,100              --@Redemption
      ,2                --@Frequency
      ,1                --@Basis
   ) as MDURATION
This produces the following result.
             MDURATION
----------------------
      7.86952877685135


This is a bond with an odd long first coupon and an odd long last coupon.
SELECT
   wct.OFLMDURATION(
       '2013-03-04'     --@Settlement
      ,'2022-11-28'     --@Maturity
      ,'2012-06-07'     --@Issue
      ,'2013-03-15'     --@FirstCouponDate
      ,'2022-03-15'     --@LastCouponDate
      ,.03125           --@Rate
      ,.02875           --@Yld
      ,100              --@Redemption
      ,2                --@Frequency
      ,1                --@Basis
      ) as MDURATION
This produces the following result.
             MDURATION
----------------------
      8.18063795829975


This is a bond with an odd long first coupon and an odd short last coupon.
SELECT
   wct.OFLMDURATION(
       '2013-03-04'     --@Settlement
      ,'2022-04-28'     --@Maturity
      ,'2012-06-07'     --@Issue
      ,'2013-03-15'     --@FirstCouponDate
      ,'2022-03-15'     --@LastCouponDate
      ,.03125           --@Rate
      ,.02875           --@Yld
      ,100              --@Redemption
      ,2                --@Frequency
      ,1                --@Basis
      ) as MDURATION
This produces the following result.
             MDURATION
----------------------
      7.75196548444765


This is a bond with an odd short first coupon and an odd long last coupon. We know the price of the bond but not the yield.
SELECT
   wct.OFLMDURATION(
       '2013-03-04'     --@Settlement
      ,'2022-11-28'     --@Maturity
      ,'2012-12-07'     --@Issue
      ,'2013-03-15'     --@FirstCouponDate
      ,'2022-03-15'     --@LastCouponDate
      ,.03125           --@Rate
      ,wct.OFLYIELD(
          '2013-03-04'        --@Settlement
         ,'2022-11-28'        --@Maturity
         ,'2012-12-07'        --@Issue
         ,'2013-03-15'        --@First_coupon
         ,'2022-03-15'        --@Last_coupon
         ,.03125              --@Rate
         ,102.104790915433    --@Price
         ,100                 --@Redemption
         ,2                   --@Frequency
         ,1                   --@Basis
         )              --@Yld
      ,100              --@Redemption
      ,2                --@Frequency
      ,1                --@Basis
   ) as MDURATION
This produces the following result.
             MDURATION
----------------------
      8.30460156314822


This is an example of a bond paying interest every 26 weeks.
SELECT
   wct.OFLMDURATION(
       '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 MDURATION
This produces the following result.
             MDURATION
----------------------
      7.01255265314168

 

See Also

 



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