PRICE
Updated: 05 May 2014
Use PRICE to calculate the price for a security that pays periodic interest and has a par value of 100. The formula for price with more than one coupon period to redemption is:
Where
C = 100 * coupon rate / frequency
Y = yield / frequency
RV = redemption value
DSC = number of days from settlement to coupon
N = the number of coupons between the settlement date and the maturity date
E = the number of days in the current coupon period
A = C * accrued days / E
When the settlement date is greater than or equal to the last coupon date, the formula for price is:
Where
C = 100 * coupon rate / frequency
Y = yield / frequency
RV = redemption value
DSR = number of days from settlement to redemption
E = the number of days in the current coupon period
A = C * accrued days / E
Syntax
SELECT [westclintech].[wct].[PRICE] (
<@Settlement, datetime,>
,<@Maturity, 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.
@Rate
the securityâ€™s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yld
the securityâ€™s annual yield. @Yld is an expression of type float or of a type that can be implicitly converted to float.
@Redemption
the securityâ€™s redemption value per 100 face value. @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 @Settlement is NULL then @Settlement = GETDATE().
Â· If @Maturity is NULL then @Maturity = GETDATE().
Â· If @Rate is NULL then @Rate = 0.
Â· If @Yield is NULL then @Yield = 0.
Â· If @Redemption is NULL then @Redemption = 100.
Â· If @Frequency is NULL then @Frequency = 2.
Â· If @Basis is NULL then @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 PRICE returns an error.
Â· If @Basis is invalid (see above list), PRICE returns an error.
Examples
In this example we calculate the price 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 basis code is 1.
SELECT wct.PRICE(
'20140501', @Settlement
'20340615', @Maturity
0.025, @Rate
0.0276, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as PRICE
This produces the following result.
PRICE

96.0043799057024
In this example, we calculate the price of a zerocoupon bond.
SELECT wct.PRICE(
'20140501', @Settlement
'20440615', @Maturity
0.00, @Rate
0.0301, @Yield
100, @Redemption
2, @Frequency
1 @Basis
) as PRICE
This produces the following result.
PRICE

40.6583576113141
In this example we calculate the price of a bond settling in the final coupon period.
SELECT wct.PRICE(
'20140501', @Settlement
'20140715', @Maturity
0.0190, @Rate
0.0005, @Yield
100, @Redemption
2, @Frequency
0 @Basis
) as PRICE
This produces the following result.
PRICE

100.380181205142
Here we calculate the price of a bond maturing on the 30^{th} of September 2034, with semiannual coupons payable on March 30^{th} and September 30^{th}.
SELECT wct.PRICE(
'20140501', @Settlement
'20340930', @Maturity
0.0257, @Rate
0.0269, @Yield
100, @Redemption
2, @Frequency
11 @Basis
) as PRICE
This produces the following result.
PRICE

98.1232907936385
Here's an example of the price calculation with a negative yield.
SELECT wct.PRICE(
'20140501', @Settlement
'20140930', @Maturity
0.0257, @Rate
0.046219, @Yield
98, @Redemption
2, @Frequency
0 @Basis
) as PRICE
This produces the following result.
PRICE

101.000010706758
This is an example of a bond paying interest every 26 weeks.
SELECT wct.PRICE(
'20141001', @Settlement
'20230313', @Maturity
0.1250, @Rate
0.1100, @Yield
100, @Redemption
182, @Frequency
9 @Basis
) as PRICE
This produces the following result.
PRICE

108.126105929164
See Also