SQL Server OFLCONVEXITY Function
Updated 2024-02-28 16:34:07.947000
Description
Use the scalar function OFLCONVEXITY to calculate the convexity for a bond that has an odd first and 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{P}}{\partial{y}^2}}{P_{dirty}*100}
Syntax
Syntax
SELECT [westclintech].[wct].[OFLCONVEXITY](
<@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. @IssueDate 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 OFLCONVEXITY returns an error.
If @Basis is invalid (see above list), OFLCONVEXITY 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.
Examples
This is a bond with an odd short first coupon and an odd short last coupon.
SELECT wct.OFLCONVEXITY( '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 CONVEXITY;
This produces the following result.
| CONVEXITY |
|---|
| 0.715521292648933 |
This is a bond with an odd long first coupon and an odd long last coupon.
SELECT wct.OFLCONVEXITY( '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 CONVEXITY;
This produces the following result.
| CONVEXITY |
|---|
| 0.786624033875058 |
This is a bond with an odd long first coupon and an odd short last coupon.
SELECT wct.OFLCONVEXITY( '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 CONVEXITY;
This produces the following result.
| CONVEXITY |
|---|
| 0.70479358765673 |
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.OFLCONVEXITY( '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 CONVEXITY;
This produces the following result.
| CONVEXITY |
|---|
| 0.79858540584316 |
This is an example of a bond paying interest every 26 weeks.
SELECT wct.OFLCONVEXITY( '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 CONVEXITY;
This produces the following result.
| CONVEXITY |
|---|
| 0.769305489495315 |
See Also
ODDFINT - Accrued interest for a bond with an odd first coupon
OFCCONVEXITY - Convexity of a bond with and odd first coupon
OFLDURATION - Duration of a bond with an odd first and odd last coupon
OFLFACTORS - Returns the components of the OFLPRICE equation
OFLMDURATION - Modified duration of a bond with an odd first and odd last coupon
OFLPRICE - Price of a security with an odd last coupon.
OFLYIELD - Yield of a bond with an odd first and an odd last coupon
OLCCONVEXITY - Convexity of a bond with and odd last coupon
RPICONVEXITY - Convexity of a bond paying regular periodic interest