bndprice - Price fixed income security from yield to maturity

Syntax

[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle, Maturity) [Price, AccruedInt] = bndprice(Yield, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face) [Price, AccruedInt] = bndprice(Yield, CouponRate, Settle, Maturity, 'ParameterName', 'ParameterValue ...)

Description

[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle,Maturity), given bonds with SIA date parameters and semiannual yields to maturity, returns the clean prices and accrued interest due.

[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle,Maturity, Period, Basis, EndMonthRule, IssueDate,FirstCouponDate, LastCouponDate, StartDate, Face) given bonds with SIA date parameters and semiannual yields to maturity and optional inputs, returns the clean prices and accrued interest due.

[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle,Maturity, 'ParameterName', 'ParameterValue ...) accepts optional inputs as one or more comma-separated parameter/value pairs. 'ParameterName' is the name of the parameter inside single quotes. ParameterValue is the value corresponding to 'ParameterName'. Specify parameter/value pairs in any order. Names are case-insensitive.

Input Arguments

`Yield`	Bond yield to maturity is on a semiannual basis for `basis` values `0` through `7` and an annual basis for `basis` values `8` through `12`.
`CouponRate`	Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.
`Settle`	Settlement date. A vector of serial date numbers or date strings. `Settle` must be earlier than `Maturity`.
`Maturity`	Maturity date. A vector of serial date numbers or date strings.

Ordered Input or Parameter–Value Pairs

Enter the following inputs using an ordered syntax or as parameter value pairs. You cannot mix ordered syntax with parameter value pairs.

`Period`	Coupons per year of the bond. A vector of integers. Values are 0, 1, 2 , 3, 4, 6, and 12. Default: 2
`Basis`	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA) 13 = BUS/252 For more information, see basis. Default: 0
`EndMonthRule`	End-of-month rule. A vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month. 1 = set rule on, meaning that a bond coupon payment date is always the last actual day of the month. Default: 1
`IssueDate`	Issue date for a bond. Default: If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.
`FirstCouponDate`	Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure. Default: If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.
`LastCouponDate`	Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. In the absence of a specified `FirstCouponDate`, a specified `LastCouponDate` determines the coupon structure of the bond. The coupon structure of a bond is truncated at the `LastCouponDate`, regardless of where it falls, and is followed only by the bond's maturity cash flow date. Default: If you do not specify a `LastCouponDate`, the cash flow payment dates are determined from other inputs.
`StartDate`	Date when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date. If you do not specify `StartDate`, the effective start date is the `Settle` date. Default: If you do not specify `StartDate`, the effective start date is the `Settle` date.
`Face`	Face or par value. Default: 100

Parameter–Value Pairs

Enter the following inputs only as parameter/value pairs.

CompoundingFrequency

Compounding frequency for yield calculation. By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ISMA bases (8-12) use an annual compounding convention.

Default: SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ISMA bases (8-12) use an annual compounding convention.

DiscountBasis

Basis used to compute the discount factors for computing the yield. The default behavior is for SIA bases to use the actual/actual day count to compute discount factors. If you use ISMA day counts and BUS/252, the specified bases are used.

Default: SIA bases use the actual/actual day count to compute discount factors.

LastCouponInterest

Compounding convention for computing the yield of a bond in the last coupon period. This is based on only the last coupon and the face value to be repaid. Acceptable values are simple or compound.

Default: compound

Output Arguments

`Price`	`NUMBONDS`-by-`1` vector for the clean price of the bond. The dirty price of the bond is the clean price plus the accrued interest. It equals the present value of the bond cash flows of the yield to maturity with semiannual compounding.
`AccruedInt`	`NUMBONDS`-by-`1` vector for the accrued interest payable at settlement.

Definitions

Given NBONDS with date parameters and yields to maturity, bndprice returns the clean prices and the accrued interest due.

All nonscalar or empty matrix input arguments must be either NUMBONDS-by-1 or 1-by-NUMBONDS conforming vectors. Fill in unspecified entries input vectors with NaNs. Dates can be serial date numbers or date strings.

Examples

Price a treasury bond at three different yield values:

Yield = [0.04; 0.05; 0.06]; 
CouponRate = 0.05; 
Settle = '20-Jan-1997'; 
Maturity = '15-Jun-2002'; 
Period = 2; 
Basis = 0; 

[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle,...
Maturity, Period, Basis)

This returns:

Price =

  104.8106
   99.9951
   95.4384

AccruedInt =

  0.4945
  0.4945
  0.4945

Price a Treasury bond at two different yield values that include parameter/value pairs for CompoundingFrequency, DiscountBasis, and LastCouponPeriodInterest:

bndprice(.04,0.08,'5/25/2004','4/21/2005','Period',1,'Basis',8, ...
'LastCouponInterest','simple')

This returns:

ans =

  103.4743

Algorithms

For SIA conventions, the following formula defines bond price and yield:

where:

PV =	Present value of a cash flow.
CF =	Cash flow amount.
z =	Risk-adjusted annualized rate or yield corresponding to a given cash flow. The yield is quoted on a semiannual basis.
f =	Frequency of quotes for the yield. Default is `2` for `Basis` values `0` to `7` and `13` and `1` for `Basis` values `8` to `12`. The default can be overridden by specifying the `CompoundingFrequency` name/value pair.
TF =	Time factor for a given cash flow. The time factor is computed using the compounding frequency and the discount basis. If these values are not specified, then the defaults are as follows: `CompoundingFrequency` default is `2` for `Basis` values `0` to `7` and `13` and `1` for `Basis` values `8` to `12`. `DiscountBasis` is `0` for `Basis` values `0` to `7` and `13` and the input `Basis` for `Basis` values `8` to `12`.

Note The Basis is always used to compute accrued interest.

For ISMA conventions, the frequency of annual coupon payments determines bond price and yield.

References

Krgin, Dragomir, Handbook of Global Fixed Income Calculations, John Wiley & Sons, 2002.

Mayle, Jan, "Standard Securities Calculations Methods: Fixed Income Securities Formulas for Analytic Measures", SIA, Vol 2, Jan 1994.

Stigum, Marcia, and Franklin Robinson, Money Market and Bond Calculations, McGraw-Hill, 1996.

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