bndprice

Price fixed-income security from yield to maturity

In R2017b, the specification of optional input arguments has changed. While the previous ordered inputs syntax is still supported, it may no longer be supported in a future release. Use the optional name-value pair inputs: Period, Basis, EndMonthRule, IssueDate,FirstCouponDate, LastCouponDate, StartDate,Face, CompoundingFrequency, DiscountBasis, and LastCouponInterest.

Syntax

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

[Price,AccruedInt] = bndprice(___,Name,Value)

Description

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

In addition, you can use the Financial Instruments Toolbox™ object framework with a FixedBond (Financial Instruments Toolbox) instrument to price a fixed bond.

[Price,AccruedInt] = bndprice(___,Name,Value) adds optional name-value pair arguments.

Examples

Price a Treasury Bond from Yield to Maturity

This example shows how to 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)

Price = 3×1

  104.8106
   99.9951
   95.4384

AccruedInt = 3×1

    0.4945
    0.4945
    0.4945

Price a Treasury Bond from Yield to Maturity Using datetime Inputs

This example shows how to use datetime inputs to price a treasury bond at three different yield values.

Yield = [0.04; 0.05; 0.06];
CouponRate = 0.05;
Settle = datetime('20-Jan-1997','Locale','en_US');
Maturity = datetime('15-Jun-2002','Locale','en_US');
Period = 2;
Basis = 0;
[Price, AccruedInt] = bndprice(Yield, CouponRate, Settle,...
Maturity, Period, Basis)

Price = 3×1

  104.8106
   99.9951
   95.4384

AccruedInt = 3×1

    0.4945
    0.4945
    0.4945

Price a Treasury Bond with Different Yield Values

This example shows how to price a Treasury bond at two different yield values that include parameter/value pairs for CompoundingFrequency, DiscountBasis, and LastCouponPeriodInterest.

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

ans = 103.4743

Input Arguments

Yield — Bond yield to maturity

numeric

Bond yield to maturity is specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. Yield is on a semiannual basis for Basis values 0 through 7 and 13 and an annual basis for Basis values 8 through 12.

Data Types: double

CouponRate — Annual percentage rate used to determine coupons payable on a bond

decimal

Annual percentage rate used to determine the coupons payable on a bond, specified as decimal using a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

Settle — Settlement date of bond

datetime array | string array | date character vector

Settlement date of the bond, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors. The Settle date must be before the Maturity date.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Maturity — Maturity date of bond

datetime array | string array | date character vector

Maturity date of the bond, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [Price,AccruedInt] = bndprice(Yield,CouponRate,Settle,Maturity, 'Period',4,'Basis',9)

Period — Number of coupon payments per year

2 (default) | numeric with values 0, 1, 2, 3, 4, 6 or 12

Number of coupon payments per year, specified as the comma-separated pair consisting of 'Period' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using the values: 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Basis — Day-count basis of instrument

0 (default) | numeric values: 0,1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13

Day-count of the instrument, specified as the comma-separated pair consisting of 'Basis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a supported value:

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

EndMonthRule — End-of-month rule flag

1 (in effect) (default) | nonnegative integer 0 or 1

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS 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.

Data Types: logical

IssueDate — Bond issue date

datetime array | string array | date character vector

Bond Issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors.

If you do not specify an IssueDate, the cash flow payment dates are determined from other inputs.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

FirstCouponDate — Irregular or normal first coupon date

datetime array | string array | date character vector

Irregular or normal first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors.

If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

LastCouponDate — Irregular or normal last coupon date

datetime array | string array | date character vector

Irregular or normal last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors.

If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

StartDate — Forward starting date of payments

datetime array | string array | date character vector

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a datetime array, string array, or date character vectors.

If you do not specify a StartDate, the effective start date is the Settle date.

To support existing code, bndprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Face — Face value of bond

100 (default) | numeric

Face value of the bond, specified as the comma-separated pair consisting of 'Face' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

CompoundingFrequency — Compounding frequency for yield calculation

SIA bases uses2, ICMA bases uses 1 (default) | integer with value of 1, 2, 3, 4, 6, or 12

Compounding frequency for yield calculation, specified as the comma-separated pair consisting of 'CompoundingFrequency' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

• 1 — Annual compounding

• 2 — Semiannual compounding

• 3 — Compounding three times per year

• 4 — Quarterly compounding

• 6 — Bimonthly compounding

• 12 — Monthly compounding

Note

By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ICMA bases (8-12) use an annual compounding convention.

Data Types: double

DiscountBasis — Basis used to compute the discount factors for computing the yield

SIA bases uses 0 (default) | integers of the set [0...13] | vector of integers of the set [0...13]

Basis used to compute the discount factors for computing the yield, specified as the comma-separated pair consisting of 'DiscountBasis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. Values are:

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Note

If a SIA day-count basis is defined in the Basis input argument and there is no value assigned for DiscountBasis, the default behavior is for SIA bases to use the actual/actual day count to compute discount factors.

If an ICMA day-count basis or BUS/252 is defined in the Basis input argument and there is no value assigned for DiscountBasis, the specified bases from the Basis input argument are used.

Data Types: double

LastCouponInterest — Compounding convention for computing yield of a bond in last coupon period

compound (default) | values are simple or compound

Compounding convention for computing the yield of a bond in the last coupon period, specified as the comma-separated pair consisting of 'LastCouponInterest' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. LastCouponInterest is based on only the last coupon and the face value to be repaid. Acceptable values are:

• simple

• compound

Data Types: char | cell

Output Arguments

Price — Clean price of bond

numeric

Clean price of bond, returned as a NUMBONDS-by-1 vector. 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 — Accrued interest payable at settlement

numeric

accrued interest payable at settlement, returned as a NUMBONDS-by-1 vector.

More About

Price and Yield Conventions

The Price and Yield are related to different formulae for SIA and ICMA conventions.

For SIA conventions, Price and Yield are related by the formula:

 Price + Accrued Interest = sum(Cash_Flow*(1+Yield/2)^(-Time)) 

where the sum is over the bond's cash flows and corresponding times in units of semiannual coupon periods.

For ICMA conventions, the Price and Yield are related by the formula:

 Price + Accrued Interest = sum(Cash_Flow*(1+Yield)^(-Time))

Algorithms

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

$$PV={\displaystyle \sum _{i=1}^n\left(\frac{CF}{{(1+\frac{z}{f})}^{TF}}\right)},$$

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

References

[1] Krgin, D. Handbook of Global Fixed Income Calculations. Wiley, 2002.

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

[3] Stigum, M., Robinson, F. Money Market and Bond Calculation. McGraw-Hill, 1996.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although bndprice supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.