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.
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 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 RPICONVEXITY returns an error.
Â· If @Basis is invalid (see above list), RPICONVEXITY 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
Examples
In this example we calculate the convexity for a bond maturing on 20340615. The settlement date is 20140501, the yield is 2.76%, the coupon rate is 2.50%, the redemption value is 100, the coupon is paid twiceyearly, and the bais code is 1.
SELECT wct.RPICONVEXITY(
'20140501', @Settlement
'20340615', @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 zerocoupon bond.
SELECT wct.RPICONVEXITY(
'20140501', @Settlement
'20440615', @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(
'20140501', @Settlement
'20240915', @Maturity
0.0190, @Rate
wct.YIELD(
'20140501',
'20240915',
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(
'20140501', @Settlement
'20140715', @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(
'20141001', @Settlement
'20230313', @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