OLCCONVEXITY

Updated 2024-02-28 20:23:47.060000

Syntax

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

Description

Use the scalar function OLCCONVEXITY to calculate the convexity for a bond that has an odd last coupon. 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.

@LastCouponDate

the last coupon date of the security. The period from the last coupon date until the maturity date defines the odd interest period. The quasi-maturity date is assumed to occur at a regular periodic interval as defined by @Frequency and @Basis. @LastCouponDate 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":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 of the security. @Settlement is an expression that returns a datetime or smalldatetime value, or a character string in date format.

@Maturity

the maturity date of the security. @Maturity 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 OLCCONVEXITY returns an error.

If @Basis is invalid (see above list), OLCCONVEXITY 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.

If @Maturity is NULL an error will be returned.

If @IssueDate is NULL an error will be returned.

If @LastCouponDate is NULL an error will be returned.

Examples

This is a bond with an odd short last coupon period where the settlement date in the last coupon period.

SELECT wct.OLCCONVEXITY(   '2014-10-01', --@Settlement

                           '2014-12-15', --@Maturity

                           '2014-09-15', --@Last_interest

                           0.0225,       --@Rate

                           0.0010,       --@Yield

                           100,          --@Redemption

                           2,            --@Frequency

                           1             --@Basis

                       ) as Convexity;