FixedBond

FixedBond instrument object

Description

Create and price a FixedBond instrument object using this workflow:

1. Use fininstrument to create a FixedBond instrument object.

2. Use ratecurve to specify a curve model for the FixedBond instrument.

3. Use finpricer to specify a Discount pricing method for the FixedBond instrument.

For more detailed information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

For more information on the available models and pricing methods for a FixedBond instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

FixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date)

FixedBondObj = fininstrument(___,Name,Value)

Description

FixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date) creates a FixedBond object by specifying InstrumentType and sets the properties for the required name-value pair arguments CouponRate and Maturity.

The FixedBond instrument supports a vanilla bond, a stepped coupon bond, and an amortizing bond. For more information, see More About.

FixedBondObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, FixedBondObj = fininstrument("FixedBond",'CouponRate',0.034,'Maturity',datetime(2019,1,30),'Period',4,'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"fixedbond_instrument") creates a FixedBond option with a coupon rate of 0.34 and a maturity of January 30, 2019. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

string with value "Fixedbond" | character vector with value 'FixedBond'

Instrument type, specified as a string with the value of "FixedBond" or a character vector with a value of 'FixedBond'.

Data Types: char | string

FixedBond Name-Value Pair Arguments

Specify required and optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: FixedBondObj = fininstrument("FixedBond",'CouponRate',0.034,'Maturity',datetime(2019,1,30),'Period',4,'Basis',1,'Principal',100,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',true,'Name',"fixedbond_instrument")

Required FixedBond Name-Value Pair Arguments

'CouponRate' — FixedBond coupon rate

decimal | timetable

FixedBond coupon rate, specified as the comma-separated pair consisting of 'CouponRate' and a scalar decimal for an annual rate or a timetable where the first column is dates and the second column is associated rates. The date indicates the last day that the coupon rate is valid.

Data Types: double | timetable

'Maturity' — FixedBond maturity date

datetime | serial date number | date character vector | date string

FixedBond maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, serial date number, date character vector, or date string.

If you use a date character vector or date string, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

Data Types: char | double | string | datetime

Optional FixedBond Name-Value Pair Arguments

'Period' — Frequency of payments per year

2 (default) | numeric value of 0, 1, 2, 3, 4, 6, or 12

Frequency of payments, specified as the comma-separated pair consisting of 'Period' and a scalar integer. Values for Period are: 1, 2, 3, 4, 6, or 12.

Data Types: double

'Basis' — Day count basis

0 (actual/actual) (default) | integer from 0 to 13

Day count basis, specified as the comma-separated pair consisting of 'Basis' and scalar integer using one of the following values:

• 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

'Principal' — Principal amount or principal value schedule

100 (default) | scalar numeric | timetable

Principal amount or principal value schedule, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric or timetable.

Principal accepts a timetable, where the first column is dates and the second column is the associated notional principal value. The date indicates the last day that the principal value is valid.

Data Types: double | timetable

'DaycountAdjustedCashFlow' — Flag indicating whether cash flow adjusts for day count convention

false (default) | value of true or false

Flag indicating whether cash flow is adjusted by day count convention, specified as the comma-separated pair consisting of 'DaycountAdjustedCashFlow' and a scalar logical with a value of true or false.

Data Types: logical

'BusinessDayConvention' — Business day conventions for cash flow dates

"actual" (default) | string | character vector

Business day conventions for cash flow dates, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

• "actual" — Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness days are assumed to be distributed on the actual date.

• "follow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.

• "modifiedfollow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.

• "previous" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.

• "modifiedprevious" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types: char | string

'Holidays' — Holidays used in computing business days

NaT (default) | datetime | cell array of character vectors | date string array | serial date numbers

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using datetimes, serial date numbers, cell array of date character vectors, or date string array. For example:

H = holidays(datetime('today'),datetime(2025,12,15));
FixedBondObj = fininstrument("FixedBond",'CouponRate',0.34,'Maturity',datetime(2025,12,15),'Holidays',H)

Data Types: double | cell | datetime | string

'EndMonthRule' — End-of-month rule flag for generating dates when Maturity is end-of-month date for month with 30 or fewer days

true (in effect) (default) | value of true or false

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month with 30 or fewer days, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar logical value of true or false.

• If you set EndMonthRule to false, the software ignores the rule, meaning that a payment date is always the same numerical day of the month.

• If you set EndMonthRule to true, the software sets the rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

'IssueDate' — Bond issue date

NaT (default) | datetime | serial date number | date character vector | date string

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar datetime, serial date number, date character vector, or date string.

If you use a date character vector or date string, the format must be recognizable by datetime because the IssueDate property is stored as a datetime.

Data Types: double | char | string | datetime

'FirstCouponDate' — Irregular first coupon date

NaT (default) | datetime | serial date number | date character vector | date string

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar datetime, serial date number, date character vector, or date string.

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify FirstCouponDate, the cash flow payment dates are determined from other inputs.

If you use a date character vector or date string, the format must be recognizable by datetime because the FirstCouponDate property is stored as a datetime.

Data Types: double | char | string | datetime

'LastCouponDate' — Irregular last coupon date

NaT (default) | datetime | serial date number | date character vector | date string

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar datetime, serial date number, date character vector, or date string.

If you specify LastCouponDate but not FirstCouponDate, LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify LastCouponDate, the cash flow payment dates are determined from other inputs.

If you use a date character vector or date string, the format must be recognizable by datetime because the LastCouponDate property is stored as a datetime.

Data Types: double | char | string | datetime

'StartDate' — Forward starting date of payments

NaT (default) | datetime | serial date number | date character vector | date string

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, serial date number, date character vector, or date string.

If you use a date character vector or date string, the format must be recognizable by datetime because the StartDate property is stored as a datetime.

Data Types: char | double | string | datetime

'Name' — User-defined name for instrument

" " (default) | string | character vector

User-defined name for the instrument, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector.

Data Types: char | string

Properties

CouponRate — FixedBond coupon annual rate

scalar decimal | timetable

FixedBond coupon annual rate, returned as a scalar decimal or timetable.

Data Types: double | timetable

Maturity — FixedBond maturity date

datetime

FixedBond maturity date, returned as a datetime.

Data Types: datetime

Period — Frequency of payments per year

2 (default) | integer

Frequency of payments per year, returned as a scalar integer.

Data Types: double

Basis — Day count basis

0 (actual/actual) (default) | integer from 0 to 13

Day count basis, returned as a scalar integer.

Data Types: double

Principal — Principal amount or principal value schedules

100 (default) | scalar numeric | timetable

Principal amount or principal value schedules, returned as a scalar numeric or timetable.

Data Types: double

DaycountAdjustedCashFlow — Flag indicating whether cash flow adjusts for day count convention

false (default) | value of true or false

Flag indicating whether cash flow adjusts for day count convention, returned as scalar logical with a value of true or false.

Data Types: logical

BusinessDayConvention — Business day conventions

"actual" (default) | string

Business day conventions, returned as a string

Data Types: string

Holidays — Holidays used in computing business days

NaT (default) | datetime

Holidays used in computing business days, returned as datetimes.

Data Types: datetime

EndMonthRule — End-of-month rule flag for generating dates when Maturity is end-of-month date for month with 30 or fewer days

true (in effect) (default) | value of true or false

End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month having 30 or fewer days, returned as a scalar logical.

Data Types: logical

IssueDate — Bond issue date

NaT (default) | datetime

Bond issue date, returned as a datetime.

Data Types: datetime

FirstCouponDate — Irregular first coupon date

NaT (default) | datetime

Irregular first coupon date, returned as a datetime.

Data Types: datetime

LastCouponDate — Irregular last coupon date

NaT (default) | datetime

Irregular last coupon date, returned as a datetime.

Data Types: datetime

StartDate — Forward starting date of payments

NaT (default) | datetime

Forward starting date of payments, returned as a datetime.

Data Types: datetime

Name — User-defined name for instrument

" " (default) | string

User-defined name for the instrument, returned as a string.

Data Types: string

Object Functions

cashflows

Computes cash flow for FixedBond, FloatBond, Swap, FRA, or Deposit instrument

Examples

Price Vanilla Fixed Bond Instrument Using ratecurve and Discount Pricer

This example shows the workflow to price a vanilla FixedBond instrument when you use a ratecurve and a Discount pricing method.

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object.

FixB = fininstrument("FixedBond",'Maturity',datetime(2022,9,15),'CouponRate',0.021,'Period',2,'Basis',1,'Principal',100,'Name',"fixed_bond_instrument")

FixB = 
  FixedBond with properties:

                  CouponRate: 0.0210
                      Period: 2
                       Basis: 1
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2022
                        Name: "fixed_bond_instrument"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Type = 'zero';
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Discount Pricer Object

Use finpricer to create a Discount pricer object and use the ratecurve object with the 'DiscountCurve' name-value pair argument.

outPricer = finpricer("Discount",'DiscountCurve',myRC)

outPricer = 
  Discount with properties:

    DiscountCurve: [1x1 ratecurve]

Price FixedBond Instrument

Use price to compute the price and sensitivities for the FixedBond instrument.

[Price, outPR] = price(outPricer, FixB,["all"])

Price = 104.5679

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    104.57    0.040397

Price Stepped Fixed Bond Instrument Using ratecurve and Discount Pricer

This example shows the workflow to price a stepped FixedBond instrument when you use a ratecurve and a Discount pricing method.

Create FixedBond Instrument Object

Use fininstrument to create a stepped FixedBond instrument object.

Maturity = datetime(2024,1,1);
Period = 1;
CDates = datetime([2020,1,1 ; 2024,1,1]);
CRates = [.025; .03];
CouponRate = timetable(CDates,CRates);

SBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period) 

SBond = 
  FixedBond with properties:

                  CouponRate: [2x1 timetable]
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 01-Jan-2024
                        Name: ""

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
ZeroTimes = calyears(1:10)';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
Compounding = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: 1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 01-Jan-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Discount Pricer Object

Use finpricer to create a Discount pricer object and use the ratecurve object with the 'DiscountCurve' name-value pair argument.

outPricer = finpricer("Discount",'DiscountCurve',ZeroCurve)

outPricer = 
  Discount with properties:

    DiscountCurve: [1x1 ratecurve]

Price FixedBond Instrument

Use price to compute the price and sensitivities for the vanilla FixedBond instrument.

[Price, outPR] = price(outPricer, SBond,["all"])

Price = 109.6218

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    109.62    0.061108

Price Amortizing Fixed Bond Instrument Using ratecurve and Discount Pricer

This example shows the workflow to price a amortizing FixedBond instrument when you use a ratecurve and a Discount pricing method.

Create FixedBond Instrument Object

Use fininstrument to create a amortizing FixedBond instrument object.

Maturity = datetime(2024,1,1);
Period = 1;
ADates = datetime([2020,1,1 ; 2024,1,1]);
APrincipal = [100; 85];
Principal = timetable(ADates,APrincipal);
Bondamort = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',0.025,'Period',Period,'Principal',Principal)  

Bondamort = 
  FixedBond with properties:

                  CouponRate: 0.0250
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: [2x1 timetable]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 01-Jan-2024
                        Name: ""

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
ZeroTimes = calyears(1:10)';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
Compounding = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding);

Create Discount Pricer Object

Use finpricer to create a Discount pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

outPricer = finpricer("Discount",'DiscountCurve',ZeroCurve)

outPricer = 
  Discount with properties:

    DiscountCurve: [1x1 ratecurve]

Price FixedBond Instrument

Use price to compute the price and sensitivities for the vanilla FixedBond instrument.

[Price, outPR] = price(outPricer,Bondamort,["all"])

Price = 107.1273

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    107.13    0.054279

More About

Fixed-Rate Note

A fixed-rate note is a long-term debt security with a preset interest rate and maturity, by which the interest must be paid.

The principal might or might not be paid at maturity. In Financial Instruments Toolbox™, the principal is always paid at maturity. For more information, see Fixed-Rate Note.

Vanilla Bond

A vanilla coupon bond is a security representing an obligation to repay a borrowed amount at a designated time and to make periodic interest payments until that time.

The issuer of a bond makes the periodic interest payments until the bond matures. At maturity, the issuer pays to the holder of the bond the principal amount owed (face value) and the last interest payment.

Stepped Coupon Bond

A step-up bond and a step-down bond are debt securities with a predetermined coupon structure over time.

With these instruments, coupons increase (step up) or decrease (step down) at specific times during the life of the bond.

Bond with an Amortization Schedule

An amortized bond is treated as an asset, with the discount amount being amortized to interest expense over the life of the bond.