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XLeratorDB/financial Documentation

SQL Server bond convexity function


RPICONVEXITY

Updated: 05 May 2014


Use RPICONVEXITY to calculate the convexity for a bond that pays regular periodic interest. Convexity is defined as the second derivative of price with respect to yield divided by the dirty price of the bond multiplied by 100.

XLeratorDB regular periodic interest convexity formula for RPICONVEXITY function for SQL Server
Syntax
SELECT [wctFinancial].[wct].[RPICONVEXITY](
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@Rate, float,>
 ,<@Yld, float,>
 ,<@Redemption, float,>
 ,<@Frequency, float,>
 ,<@Basis, nvarchar(4000),>)
Arguments
@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.
@Maturity
the maturity date of the bond. @Settlement 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 @Maturity <= @Settlement 0 is returned.
·         If @Settlement is NULL, @Settlement = GETDATE()
·         If @Rate is NULL, @Rate = 0
·         If @Yld is NULL, @Yld = 0
·         If @Frequency is NULL, @Frequency = 2
·         If @Basis is NULL, @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 RPICONVEXITY returns an error.
·         If @Basis is invalid (see above list), RPICONVEXITY returns an error.
·         @Rate is entered as a decimal value; 1.0% = 0.01
·         @Yld is entered as a decimal value; 1.0% = 0.01
Examples
In this example we calculate the convexity for a bond maturing on 2034-06-15. The settlement date is 2014-05-01, the yield is 2.76%, the coupon rate is 2.50%, the redemption value is 100, the coupon is paid twice-yearly, and the bais code is 1.
SELECT wct.RPICONVEXITY(
   '2014-05-01', --@Settlement
   '2034-06-15', --@Maturity
   0.025,         --@Rate
   0.0276,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as CONVEXITY
This produces the following result
             CONVEXITY
----------------------
      2.88538118059157


In this example, we calculate the convexity of a zero-coupon bond.
SELECT wct.RPICONVEXITY(
   '2014-05-01', --@Settlement
   '2044-06-15', --@Maturity
   0.00,          --@Rate
   0.0301,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as CONVEXITY
This produces the following result.
             CONVEXITY
----------------------
      8.95342799177463


In this example we know the price of the bond (99.9875), but not the yield.
SELECT wct.RPICONVEXITY(
   '2014-05-01', --@Settlement
   '2024-09-15', --@Maturity
   0.0190,        --@Rate
   wct.YIELD(
      '2014-05-01',
      '2024-09-15',
      0.0190,
      99.9875,
      100,
      2,
      1
      ),          --@Yield
   100,           --@Redemption
   2,             --@Frequency
   1              --@Basis
   ) as CONVEXITY

This produces the following result.
             CONVEXITY
----------------------
     0.975803209795089


In this example we calculate the convexity of a bond settling in the final coupon period.
SELECT wct.RPICONVEXITY(
   '2014-05-01', --@Settlement
   '2014-07-15', --@Maturity
   0.0190,        --@Rate
   0.0005,        --@Yield
   100,           --@Redemption
   2,             --@Frequency
   0              --@Basis
   ) as CONVEXITY

This produces the following result.
             CONVEXITY
----------------------
 0.000844887861799598


This is an example of a bond paying interest every 26 weeks.
SELECT wct.RPICONVEXITY(
      '2014-10-01',     --@Settlement
      '2023-03-13',     --@Maturity
      0.1250,           --@Rate
      0.1100,           --@Yield
      100,              --@Redemption
      182,              --@Frequency
      9                 --@Basis
      ) as CONVEXITY
This produces the following result.
             CONVEXITY
----------------------
     0.380890754107744

 

See Also

 



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