PRICEACT
Updated 2024-02-28 21:30:54.260000
Syntax
SELECT [westclintech].[wct].[PRICEACT](
<@Settlement, datetime,>
,<@Maturity, datetime,>
,<@Rate, float,>
,<@Par, float,>
,<@Yield, float,>
,<@Frequency, float,>
,<@Basis, nvarchar(4000),>
,<@Repayments, nvarchar(max),>)
Description
Use the scalar function PRICEACT to calculate the price from yield of a bond where the coupon amounts are calculated as the actual number of days in the coupon period divided by the number of days in the year. This means that the coupon amounts will vary from period. The number of days in the year is either 360, 365, or 366 based upon the day-count convention. PRICEACT also allows the entry of a forced redemption schedule.
The price of the bond is the discounted cash flow value of all the remaining payments minus the accrued interest.
The formula for the price of a bond with more than one coupon period to redemption using the actual number of days in each coupon period is:
\rm{PRICE=DF_1\times\left(CF_1+\dots\left(DF_{n-2}\times\left(CF_{n-2}+DF_{n-1}\times\left(CF_{n-1}+\left(CF_n*DF_n\right)\right)\right)\right)\right)-R\times{P}\times\frac{A}{DIY}}
Where:
A = Actual number of days from the previous coupon date to the settlement dateCFn = Cash Flow for period nDFn = Discount factor for period nDIY = Number of days in the year in which the coupon payment occursn = Number of coupons from settlement date to maturity dateP = Par value of the securityR = Coupon rate
and
\rm{DF_n={1}/{\left({\left((1+\frac{Y}{F}\right)}^{t_n}\right)}}
WhereF = The number of coupon payments per yeart1 = Time, in years, from the settlement date to the first coupon datetn = Time, in years, of the coupon periodY = Annual yield
and
\rm{CF_n=\begin{cases}\text{When }N=n\text{ then }P\times\left(1+R\times{t_n}\right)\\\text{Else }P\times{R}\times{t_n}\end{cases}}
Where
P = Par value of the securityR = Coupon ratetn = Time, in years, of the coupon period
In the case where there are forced redemptions (i.e. partial repayments of principal prior to the maturity date of security), then the formula needs to be adjusted to reflect those redemptions in the cash flows (CFn) and the price calculation then becomes:
\rm{PRICE=\frac{DF_1\times\left(CF_1+\dots\left(DF_{n-2}\times\left(CF_{n-2}+DF_{n-1}\times\left(CF_{n-1}+\left(CF_n*DF_n\right)\right)\right)\right)\right)\times{P}}{Prin}-R\times{P}\times\frac{A}{DIY}}
Where P/Prin is the par value divided by the outstanding principal balance as of the coupon date immediately prior to the settlement date.
In the case where the settlement date is in the final coupon then the formula for the price of the bond is the same as the formula used in the PRICE function.
Arguments
@Basis
is the type of day count to use. @Basis is an expression of the character string data type category.
{"columns":[{"field":"@Basis","width":305},{"field":"Day count basis","width":270}],"rows":[{"@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":"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"}]}
@Frequency
the number of coupon payments per year. For annual payments, @Frequency = 1; for semi-annual, @Frequency = 2; for quarterly, @Frequency = 4; for bi-monthly, @Frequency = 6, for monthly, @Frequency = 12. @Frequency is an expression of type float or of a type that can be implicitly converted to float.
@Repayments
a SELECT statement, as a string, which identifies the coupon dates and the forced redemption amounts to be used in the price calculation.
@Rate
the security’s annual coupon rate. @Rate is an expression of type float or of a type that can be implicitly converted to float.
@Yield
the security’s annual yield. @Yield is an expression of type float or of a type that can be implicitly converted to float.
@Par
the par value of the security. Any forced redemptions are subtracted from the par value on the redemption date and the adjusted balance is used in calculating the subsequent coupon interest. @Par 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.
Return Type
float
Remarks
If @Basis is invalid then PRICEACT returns an error.
If @Frequency is invalid then PRICEACT returns an error.
If @Maturity < @Settlement then NULL is returned.
If @Repayments returns NULL then @Par is used for all interest calculations and as the redemption value.
If @Settlement is NULL, @Settlement = GETDATE().
If @Frequency is NULL, @Frequency = 2.
If @Basis is NULL, @Basis = 1.
PRICEACT forces the principal balance of the bond to zero at maturity.
If @Par is NULL then @Par = 100.
If @Rate is NULL then @Rate = 0.
If @Yield is NULL then @Yield = 0.
If @Maturity is NULL then PRICEACT returns NULL.
If @Basis = 3 or @Basis = 13 then the number of days in a year is always 365.
If @Basis =2 or @Basis = 12 then the number of days in a year is always 360.
If @Basis =1 or @Basis = 1 then the number of days in a year is determined by the actual number of days in the year of coupon period end date.
Examples
In this example we calculate the price of a bond maturity on 2034-11-01 with a coupon interest rate of 11.0% paying interest semi-annually. The bond is priced at a yield of 12.5% and is settling on 2014-10-29. The bond uses the actual/actual day-count convention.
SELECT wct.PRICEACT( '2014-10-29', --@Settlement
'2034-11-01', --@Maturity
0.11, --@Rate
100, --@Par
0.125, --@Yield
2, --@Frequency
1, --@Basis
NULL --@Repayments
) as PRICE;
This produces the following result.
{"columns":[{"field":"PRICE","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"PRICE":"89.0583463371609"}]}
Let's compare this to the result returned by the PRICE function.
SELECT wct.PRICEACT( '2014-10-29', --@Settlement
'2034-11-01', --@Maturity
0.11, --@Rate
100, --@Par
0.125, --@Yield
2, --@Frequency
1, --@Basis
NULL --@Repayments
) as PRICEACT,
wct.PRICE( '2014-10-29', --@Settlement
'2034-11-01', --@Maturity
0.11, --@Rate
0.125, --@Yield
100, --@Redemption
2, --@Frequency
1 --@Basis
) as PRICE;
This produces the following result.
{"columns":[{"field":"PRICEACT","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"PRICE","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"PRICEACT":"89.0583463371609","PRICE":"89.0580044972901"}]}
In this example we have a bond maturing on 2019-10-31 with a 12.5% coupon paid semi-annually. The bond has 16 equal forced redemptions starting with the 2012-04-30 coupon. The bond is priced at a yield of 12.5% settling on 2014-10-29.
SELECT wct.PRICEACT(
'2014-10-29', --@Settlement
'2019-10-31', --@Maturity
0.125, --@Rate
100, --@Par
0.125, --@Yield
2, --@Frequency
1, --@Basis
'SELECT
*
FROM (VALUES
(''2012-04-30'',6.25)
,(''2012-10-31'',6.25)
,(''2013-04-30'',6.25)
,(''2013-10-31'',6.25)
,(''2014-04-30'',6.25)
,(''2014-10-31'',6.25)
,(''2015-04-30'',6.25)
,(''2015-10-31'',6.25)
,(''2016-04-30'',6.25)
,(''2016-10-31'',6.25)
,(''2017-04-30'',6.25)
,(''2017-10-31'',6.25)
,(''2018-04-30'',6.25)
,(''2018-10-31'',6.25)
,(''2019-04-30'',6.25)
,(''2019-10-31'',6.25)
)n(dt_ppay, amt_ppay)' --@Repayments
) as PRICE;
This produces the following result.
{"columns":[{"field":"PRICE","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"PRICE":"99.9985011972914"}]}
See Also
ODDFPRICE - Price of a security with an odd first coupon
ODDLPRICE - Price of a bond with an odd last coupon
OFLPRICE - Price of a security with an odd last coupon.
PRICEFR - Price of a bond with forced redemptions
PRICE - Price of a bond paying regular periodic interest
PRICEDISC - Price of a discount security
PRICEMAT - Price of an interest-at-maturity security
PRICESTEP - Calculate the Price of a security with step-up rates