PRICEFR

Updated 2024-02-29 14:17:56.857000

Syntax

SELECT [westclintech][wct].[PRICEFR](
  <@Settlement, datetime,>
 ,<@Maturity, datetime,>
 ,<@Rate, float,>
 ,<@Par, float,>
 ,<@Yield, float,>
 ,<@Frequency, float,>
 ,<@Basis, nvarchar(4000),>
 ,<@Repayments, nvarchar(max),>)

Description

Use the scalar function PRICEFR to calculate the price from yield of a bond with a forced redemption schedule where the coupon payment dates occur at regular periods and the redemptions can occur on any coupon date. The formula for the price of a bond with a forced redemption schedule with more than one period to maturity is:

\rm{PRICE=\frac{P}{P-\Sigma_{j=1}^MFR_j}\times\left[\sum_{k=1}^N\frac{C_k+FR_k}{\left(1+\frac{Y}{F}\right)^{k-1+\frac{DSC}{E}}}-\left(P-\sum_{j=1}^MFR_j\right)\times\frac{R}{F}\times\frac{A}{E}\right]}

Where:A = Number of days from previous coupon date to settlement dateC = Coupon AmountDSC = Number of days from settlement date to the next coupon dateE = Number of days in the current coupon periodF = Number of coupon payments per yearFR = Forced Redemption amountM = Number of forced redemptions on or before the previous coupon dateN = Number of coupons from the settlement to the maturity dateP = Par ValueR = Annual interest rate in decimal terms (10% = 0.10)Y = Annual yield in decimal terms (10% = 0.10)

The coupon payments can vary over the life of the bond as they are affected by the forced redemption schedule. Coupon payments are calculated as

\rm{C_k=\left(P-\sum_{j=1}^{k-1}FR_j\right)\times\frac{R}{F}}

Where:Ck = Coupon payment number kF = Number of coupon payments per yearFR = Forced redemption amountP = Par valueR = Annual rate of interest in decimal terms

If the settlement date is in the final coupon period, then the formula for the calculation of price is:

\rm{PRICE=P\times\left[\frac{1+\frac{R}{F}}{1+\left(\frac{DSR}{E}\times\frac{Y}{F}\right)}-\left(\frac{A}{E}\times\frac{R}{F}\right)\right]}

Where:A = Number of days from previous coupon date to settlement dateDSR = Number of days from settlement date to maturity dateE = Number of days in the current coupon periodF = Number of coupon payments per yearR = Annual interest rate in decimal terms (10% = 0.10)P = Par ValueY = Annual yield in decimal terms (10% = 0.10)

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":313},{"field":"Day count basis","width":277}],"rows":[{"@Basis":"0 , 'BOND'","Day count basis":"US (NASD) 30/360"},{"@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":"4 , '30E/360 (ISDA)' , '30E/360' , 'ISDA' , '30E/360 ISDA' , 'EBOND'","Day count basis":"European 30/360"},{"@Basis":"5 , '30/360' , '30/360 ISDA' , 'GERMAN'","Day count basis":"30/360 ISDA"},{"@Basis":"6 , 'NL/ACT'","Day count basis":"No Leap Year/ACT"},{"@Basis":"7 , 'NL/365'","Day count basis":"No Leap Year /365"},{"@Basis":"8 , 'NL/360'","Day count basis":"No Leap Year /360"},{"@Basis":"9 , 'A/364'","Day count basis":"Actual/364"},{"@Basis":"10 , 'BOND NON-EOM'","Day count basis":"US (NASD) 30/360 non-end-of-month"},{"@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"},{"@Basis":"14 , '30E/360 NON-EOM' , '30E/360 ICMA NON-EOM' , 'EBOND NON-EOM'","Day count basis":"European 30/360 non-end-of-month"},{"@Basis":"15 , '30/360 NON-EOM' , '30/360 ISDA NON-EOM' , 'GERMAN NON-EOM'","Day count basis":"30/360 ISDA non-end-of-month"},{"@Basis":"16 , 'NL/ACT NON-EOM'","Day count basis":"No Leap Year/ACT non-end-of-month"},{"@Basis":"17 , 'NL/365 NON-EOM'","Day count basis":"No Leap Year/365 non-end-of-month"},{"@Basis":"18 , 'NL/360 NON-EOM'","Day count basis":"No Leap Year/360 non-end-of-month"},{"@Basis":"19 , 'A/364 NON-EOM'","Day count basis":"Actual/364 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 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.

@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. All 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 PRICEFR returns an error.

If @Frequency is invalid then PRICEFR returns an error.

If @Maturity < @Settlement then NULL is returned.

If @Repayments returns no rows then NULL is returned.

If @Settlement is NULL, @Settlement = GETDATE().

If @Frequency is NULL, @Frequency = 2.

If @Basis is NULL, @Basis = 0.

PRICEFR 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 PRICEFR returns NULL.

Examples

In this example we calculate the price of a bond maturing on 2029-09-15 with the following redemption schedule:

2017-09-25 28.0742021-09-20 32.291896962024-09-15 39.63410304

The bond has an 11.0% coupon rate, pays interest every 182 days using the Actual/364 day-count convention and has a par value or 100. The bond is being purchased at a yield of 10.75% for settlement on 2014-10-16.

SELECT wct.PRICEFR(

                      '2014-10-16', --@Settlement

                      '2025-09-15', --@Maturity

                      0.1100,       --@Rate

                      100,          --@Par

                      0.1075,       --@Yield

                      182,          --@Frequency

                      9,            --@Basis

                      'SELECT

          *

       FROM (VALUES

          (''2017,09,25'', 28.074),

          (''2021,09,20'', 32.29189696),

          (''2025,09,15'', 39.63410304)

          )n(date_cf, amt_cf)'      --@Repayments

                  ) as [PRICE];