RPICONVEXITY

Updated 2024-02-29 14:28:24.047000

Syntax

SELECT [westclintech].[wct].[RPICONVEXITY](
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@Rate, float,>
 ,<@Yld, float,>
 ,<@Redemption, float,>
 ,<@Frequency, float,>
 ,<@Basis, nvarchar(4000),>)

Description

Use the scalar function 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.

CONVEXITY=\frac{\frac{\partial^2P}{\partial{y}^2}}{P_{dirty}*100}

Arguments

@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 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.

{"columns":[{"field":"@Basis","width":313},{"field":"Day count basis","width":277}],"rows":[{"@Basis":"0 , 'BOND'","Day count basis":"US (NASD) 30/360"},{"@Basis":"1 , 'ACTUAL'","Day count basis":"Actual/Actual"},{"@Basis":"2 , 'A360'","Day count basis":"Actual/360"},{"@Basis":"3 , 'A365'","Day count basis":"Actual/365"},{"@Basis":"4 , '30E/360 (ISDA)' , '30E/360' , 'ISDA' , '30E/360 ISDA' , 'EBOND'","Day count basis":"European 30/360"},{"@Basis":"5 , '30/360' , '30/360 ISDA' , 'GERMAN'","Day count basis":"30/360 ISDA"},{"@Basis":"6 , 'NL/ACT'","Day count basis":"No Leap Year/ACT"},{"@Basis":"7 , 'NL/365'","Day count basis":"No Leap Year /365"},{"@Basis":"8 , 'NL/360'","Day count basis":"No Leap Year /360"},{"@Basis":"9 , 'A/364'","Day count basis":"Actual/364"},{"@Basis":"10 , 'BOND NON-EOM'","Day count basis":"US (NASD) 30/360 non-end-of-month"},{"@Basis":"11 , 'ACTUAL NON-EOM'","Day count basis":"Actual/Actual non-end-of-month"},{"@Basis":"12 , 'A360 NON-EOM'","Day count basis":"Actual/360 non-end-of-month"},{"@Basis":"13 , 'A365 NON-EOM'","Day count basis":"Actual/365 non-end-of-month"},{"@Basis":"14 , '30E/360 NON-EOM' , '30E/360 ICMA NON-EOM' , 'EBOND NON-EOM'","Day count basis":"European 30/360 non-end-of-month"},{"@Basis":"15 , '30/360 NON-EOM' , '30/360 ISDA NON-EOM' , 'GERMAN NON-EOM'","Day count basis":"30/360 ISDA non-end-of-month"},{"@Basis":"16 , 'NL/ACT NON-EOM'","Day count basis":"No Leap Year/ACT non-end-of-month"},{"@Basis":"17 , 'NL/365 NON-EOM'","Day count basis":"No Leap Year/365 non-end-of-month"},{"@Basis":"18 , 'NL/360 NON-EOM'","Day count basis":"No Leap Year/360 non-end-of-month"},{"@Basis":"19 , 'A/364 NON-EOM'","Day count basis":"Actual/364 non-end-of-month"}]}

@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.

@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.

@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.

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 basis 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;