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.

Inputs

`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 or equal to `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 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.
`FirstCouponDate`	Irregular or normal first coupon date.
`LastCouponDate`	Irregular or normal last coupon date.
`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.
`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.
`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.
`LastCouponPeriodInterest`	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'`.

Outputs

`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

Algorithm

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

where:

PV =	Present value of a cash flow.
CF =	The cash flow amount.
z =	The risk-adjusted annualized rate or yield corresponding to a given cash flow. The yield is quoted on a semiannual basis.
f =	The frequency of quotes for the yield.
TF =	Time factor for a given cash flow. Time is measured in semiannual periods from the settlement date to the cash flow date. In computing time factors, use SIA actual/actual day count conventions for all time factor calculations.