OFCCONVEXITY
Updated: 31 May 2014
Use OFCCONVEXITY to calculate the convexity for a bond that has an odd first 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.
Syntax
SELECT [wctFinancial].[wct].[OFCCONVEXITY](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@IssueDate, datetime,>
,<@FirstCouponDate, datetime,>
,<@Rate, float,>
,<@Yld, float,>
,<@Redemption, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>)
Arguments
@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.
@IssueDate
the issue date of the security; the date from which the security 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 security. 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.
@Rate
the bondâ€™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 semiannual, @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 NONEOM'

US (NASD) 30/360 nonendofmonth

11, 'ACTUAL NONEOM'

Actual/Actual nonendofmonth

12, 'A360 NONEOM'

Actual/360 nonendofmonth

13, 'A365 NONEOM'

Actual/365 nonendofmonth

14, '30E/360 NONEOM', '30E/360 ICMA NONEOM', 'EBOND NONEOM'

European 30/360 nonendofmonth

15, '30/360 NONEOM', '30/360 ISDA NONEOM', 'GERMAN NONEOM'

30/360 ISDA nonendofmonth

16, 'NL/ACT NONEOM'

No Leap Year/ACT nonendofmonth

17, 'NL/365 NONEOM'

No Leap Year/365 nonendofmonth

18, 'NL/360 NONEOM'

No Leap Year/360 nonendofmonth

19, 'A/364 NONEOM'

Actual/364 nonendofmonth

Return Type
float
Remarks
Â· If @Maturity <= @Settlement 0 is returned.
Â· If @Settlement is NULL, @Settlement = GETDATE()
Â· If @Rate is NULL, @Rate = 0
Â· If @Yld is NULL, @Yld = 0
Â· If @Frequency is NULL, @Frequency = 2
Â· If @Basis is NULL, @Basis = 0.
Â· 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 OFCCONVEXITY returns an error.
Â· If @Basis is invalid (see above list), OFCCONVEXITY returns an error.
Â· @Rate is entered as a decimal value; 1.0% = 0.01
Â· @Yld is entered as a decimal value; 1.0% = 0.01
Â· If @Maturity is NULL an error will be returned.
Â· If @IssueDate is NULL an error will be returned.
Â· If @FirstCouponDate is NULL an error will be returned.
Examples
This bond has an odd short first coupon (meaning that the first coupon period is shorter than a normal coupon period) and settles on the issue date.
SELECT
wct.OFCCONVEXITY(
'20140501', @Settlement
'20340615', @Maturity
'20140501', @Issue
'20140615', @FirstCoupon
0.025, @Rate
0.0276, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as OFCCONVEXITY
This produces the following result
OFCCONVEXITY

2.91355672454477
This bond has odd long first coupon (meaning that the first coupon period is longer than a normal coupon period) and settles on the issue date.
SELECT
wct.OFCCONVEXITY(
'20140501', @Settlement
'20340615', @Maturity
'20140501', @Issue
'20141215', @FirstCoupon
0.025, @Rate
0.0276, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as OFCCONVEXITY
This produces the following result.
OFCCONVEXITY

2.91370314034075
Here we calculate the convexity of a bond with an odd short first coupon with semiannual coupons payable on March 30^{th} and September 30^{th}.
SELECT
wct.OFCCONVEXITY(
'20140315', @Settlement
'20340930', @Maturity
'20140301', @Issue
'20140330', @FirstCoupon
0.0257, @Rate
0.0269, @Yield
100, @Redemption
2, @Frequency
11 @Basis
) as OFCCONVEXITY
This produces the following result.
OFCCONVEXITY

3.00014574085169
In this example we know the price of the bond (99.9875), but not the yield.
SELECT
wct.OFCCONVEXITY(
'20140528', @Settlement
'20341130', @Maturity
'20140501', @Issue
'20141130', @FirstCoupon
0.0225, @Rate
wct.ODDFYIELD(
'20140528',
'20341130',
'20140501',
'20141130',
0.0225,
99.875,
100,
2,
5
), @Yield
100, @Redemption
2, @Frequency
5 @Basis
) as OFCCONVEXITY
This produces the following result.
OFCCONVEXITY

3.13822993960329
This is an example of a bond paying interest every 26 weeks.
SELECT
wct.OFCCONVEXITY(
'20141004', @Settlement
'20291212', @Maturity
'20140326', @Issue
'20141231', @FirstCoupon
0.1250, @Rate
0.1100, @Yield
100, @Redemption
182, @Frequency
9 @Basis
) as OFCCONVEXITY
This produces the following result.
OFCCONVEXITY

0.740865190925824
See Also