FixedBond

FixedBond instrument object

Since R2020a

Description

Create and price a FixedBond instrument object for one of more Fixed Bond instruments using this workflow:

1. Use fininstrument to create a FixedBond instrument object for one of more Fixed Bond instruments.

2. Use ratecurve to specify a curve model for the FixedBond instrument object or use a HullWhite, BlackKarasinski, BlackDermanToy, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model.

3. Choose a pricing method.

   • When using a ratecurve use finpricer to specify a Discount pricing method for one or more FixedBond instruments.

   • When using a HullWhite, BlackKarasinski, or BlackDermanToy model, use finpricer to specify an IRTree pricing method for one or more FixedBond instruments.

   • When using a HullWhite, BlackKarasinski, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model, use finpricer to specify an IRMonteCarlo pricing method for one or more FixedBond instruments.

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 for one of more Fixed Bond instruments 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" | string array with values of "Fixedbond" | character vector with value 'FixedBond' | cell array of character vectors with values of 'FixedBond'

Instrument type, specified as a string with the value of "FixedBond", a character vector with the value of 'FixedBond', an NINST-by-1 string array with values of "FixedBond", or an NINST-by-1 cell array of character vectors with values of 'FixedBond'.

Data Types: char | cell | string

Name-Value Arguments

Specify required and 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: 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

scalar decimal | vector of decimals | timetable

FixedBond coupon rate, specified as the comma-separated pair consisting of 'CouponRate' and a scalar decimal or an NINST-by-1 vector of decimals 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.

Note

If you are creating one or more FixedBond instruments and use a timetable, the timetable specification applies to all of the FixedBond instruments. CouponRate does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

Maturity — FixedBond maturity date

datetime array | string array | date character vector

FixedBond maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

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

Optional FixedBond Name-Value Pair Arguments

Period — Frequency of payments per year

2 (default) | scalar numeric value of 0, 1, 2, 3, 4, 6, or 12 | numeric vector with values 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 or an NINST-by-1 vector of integers. Values for Period are 1, 2, 3, 4, 6, or 12.

Data Types: double

Basis — Day count basis

0 (actual/actual) (default) | scalar integer from 0 to 13 | vector of integers from 0 to 13

Day count basis, specified as the comma-separated pair consisting of 'Basis' and scalar integer or an NINST-by-1 vector of integers using 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 | numeric vector | timetable

Principal amount or principal value schedule, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric or an NINST-by-1 numeric vector or a 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.

Note

If you are creating one or more FixedBond instruments and use a timetable, the timetable specification applies to all of the FixedBond instruments. Principal does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

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

false (default) | scalar logical value of true or false | vector of logical values 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 or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

BusinessDayConvention — Business day conventions for cash flow dates

"actual" (default) | string | string array | character vector | cell array of character vectors

Business day conventions for cash flow dates, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array. 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 | cell | string

Holidays — Holidays used in computing business days

NaT (default) | datetime array | string array | date character vector

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using an NINST-by-1 vector of a datetime array, string array, or date character vectors. For example:

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

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

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) | scalar logical value of true or false | vector of logical values 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 or an NINST-by-1 vector of logicals with values 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 array | string array | date character vector

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

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

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

FirstCouponDate — Irregular first coupon date

NaT (default) | datetime array | string array | date character vector

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

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

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 date character vectors or strings, the format must be recognizable by datetime because the FirstCouponDate property is stored as a datetime.

LastCouponDate — Irregular last coupon date

NaT (default) | datetime array | string array | date character vector

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

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

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 date character vectors or strings, the format must be recognizable by datetime because the LastCouponDate property is stored as a datetime.

StartDate — Forward starting date of payments

NaT (default) | 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 an NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

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

Name — User-defined name for instrument

" " (default) | string | string array | character vector | cell array of character vectors

User-defined name for one of more instruments, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: char | cell | string

Properties

CouponRate — FixedBond coupon annual rate

scalar decimal | vector of decimals | timetable

FixedBond coupon annual rate, returned as a scalar decimal or an NINST-by-1 vector of decimals or a timetable.

Data Types: double | timetable

Maturity — FixedBond maturity date

scalar datetime | vector of datetimes

FixedBond maturity date, returned as a scalar datetime or NINST-by-1 vector of datetimes.

Data Types: datetime

Period — Frequency of payments per year

2 (default) | scalar integer | vector of integers

Frequency of payments per year, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

Basis — Day count basis

0 (actual/actual) (default) | scalar integer from 0 to 13 | vector of integers from 0 to 13

Day count basis, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

Principal — Principal amount or principal value schedules

100 (default) | scalar numeric | numeric vector | timetable

Principal amount or principal value schedules, returned as a scalar numeric or an NINST-by-1 numeric vector or a timetable.

Data Types: double

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

false (default) | scalar logical value of true or false | vector of logicals with values of true or false

Flag indicating whether cash flow adjusts for day count convention, returned as scalar logical or an NINST-by-1 vector of logicals with values of true or false.

Data Types: logical

BusinessDayConvention — Business day conventions

"actual" (default) | string | string array

Business day conventions, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Holidays — Holidays used in computing business days

NaT (default) | datetimes

Holidays used in computing business days, returned as an NINST-by-1 vector of 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) | scalar logical value of true or false | vector of logicals with values 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 or an NINST-by-1 vector of logical values.

Data Types: logical

IssueDate — Bond issue date

NaT (default) | datetime | vector of datetimes

Bond issue date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

FirstCouponDate — Irregular first coupon date

NaT (default) | datetime | vector of datetimes

Irregular first coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

LastCouponDate — Irregular last coupon date

NaT (default) | datetime | vector of datetimes

Irregular last coupon date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

StartDate — Forward starting date of payments

NaT (default) | datetime | vector of datetimes

Forward starting date of payments, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Name — User-defined name for instrument

" " (default) | string | string array

User-defined name for the instrument, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Object Functions

cashflows

Compute cash flow for FixedBond, FloatBond, Swap, FRA, STIRFuture, OISFuture, OvernightIndexedSwap, 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 Vanilla Fixed Bond Instrument Using ratecurve and Discount Pricer and Perform Bond Analytics

This example shows how to create a FixedBond instrument and then use any of the following Financial Toolbox™ functions to perform bond analytics: bnddurp, bnddury, bndconvp, bndconvy, bndkrdur, cfdur, and cfconv.

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object.

MaturityDate = datetime(2027,12,16);
CouponRate = 0.01;

FixedBondObj = fininstrument('FixedBond','CouponRate',CouponRate,'Maturity',MaturityDate); 

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2022,10,10);   
MarketDates = datetime([2023,9,15 ; 2024,9,15 ; 2025,9,15 ; 2026,9,15 ; 2027,9,15 ; 2028,9,15]);
ZeroDates = datetime([2023,10,15 ; 2024,10,15 ; 2025,10,15 ; 2026,10,15 ; 2027,10,15 ; 2028,10,15]);
ZeroRates = [4.2520 4.1081 3.8801 3.7170 3.6060 3.5250]'/100;
MarketSpreads = [97.9825 97.9825 97.9825 97.9825 97.9825 97.9825]';

RateObjB = ratecurve('zero',Settle,ZeroDates,ZeroRates+MarketSpreads(1)/10000); 

Create Discount Pricer Object

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

Pricer1 = finpricer("Discount",'DiscountCurve',RateObjB); 

Price FixedBond Instrument

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

[Price1, outPR] = price(Pricer1, FixedBondObj,["all"])

Price1 = 83.4210

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

Compute Bond Durations for FixedBond Instrument

Use bnddurp to compute the bond durations given the bond price.

[ModDuration, YearDuration, PerDuration] = bnddurp(Price1,FixedBondObj.CouponRate, Settle, FixedBondObj.Maturity,Period=FixedBondObj.Period) 

ModDuration = 4.9169

YearDuration = 5.0308

PerDuration = 10.0616

Compute Key Rate Durations for FixedBond Instrument

Use bndkrdur to compute the FixedBond instrument key rate duration given a zero curve.

ZeroData1 = [datenum(RateObjB.Dates) RateObjB.Rates]; 
KeyRateDuration = bndkrdur(ZeroData1,FixedBondObj.CouponRate,Settle,FixedBondObj.Maturity) 

KeyRateDuration = 1×6

    0.0133    0.0212    0.0304    0.0389    4.0226    0.8164

Price Multiple Vanilla Fixed Bond Instruments Using ratecurve and Discount Pricer

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

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object for three Fixed Bond instruments.

FixB = fininstrument("FixedBond",'Maturity',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'CouponRate',0.021,'Period',2,'Basis',1,'Principal',[100 ; 250 ; 500],'Name',"fixed_bond_instrument")

FixB=3×1 object
  3x1 FixedBond array with properties:

    CouponRate
    Period
    Basis
    EndMonthRule
    Principal
    DaycountAdjustedCashFlow
    BusinessDayConvention
    Holidays
    IssueDate
    FirstCouponDate
    LastCouponDate
    StartDate
    Maturity
    Name

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 Instruments

Use price to compute the prices and sensitivities for the FixedBond instruments.

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

Price = 3×1

  104.5679
  261.4498
  522.9174

outPR=1×3 object
  1x3 priceresult array with properties:

    Results
    PricerData

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    104.57    0.040397

ans=1×2 table
    Price     DV01 
    ______    _____

    261.45    0.103

ans=1×2 table
    Price      DV01  
    ______    _______

    522.92    0.21013

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

Price Fixed Bond Instrument Using Hull-White Model and IRMonteCarlo Pricer

This example shows the workflow to price a FixedBond instrument when using a HullWhite model and an IRMonteCarlo pricing method.

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object.

FixB = fininstrument("FixedBond","Maturity",datetime(2022,9,15),"CouponRate",0.05,'Name',"fixed_bond")

FixB = 
  FixedBond with properties:

                  CouponRate: 0.0500
                      Period: 2
                       Basis: 0
                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"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.32,'Sigma',0.49)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.3200
    Sigma: 0.4900

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2019,1,1);
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: 01-Jan-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create IRMonteCarlo Pricer Object

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

outPricer = finpricer("IRMonteCarlo",'Model',HullWhiteModel,'DiscountCurve',myRC,'SimulationDates',ZeroDates)

outPricer = 
  HWMonteCarlo with properties:

          NumTrials: 1000
      RandomNumbers: []
      DiscountCurve: [1x1 ratecurve]
    SimulationDates: [01-Jul-2019    01-Jan-2020    01-Jan-2021    01-Jan-2022    01-Jan-2023    01-Jan-2024    01-Jan-2026    01-Jan-2029    01-Jan-2039    01-Jan-2049]
              Model: [1x1 finmodel.HullWhite]

Price FixedBond Instrument

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

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

Price = 115.0303

outPR = 
  priceresult with properties:

       Results: [1x4 table]
    PricerData: [1x1 struct]

outPR.Results

ans=1×4 table
    Price      Delta     Gamma     Vega
    ______    _______    ______    ____

    115.03    -397.13    1430.4     0  

Price FixedBond Instrument Using a Hull-White Model and IRTree Pricer

This example shows the workflow to price a FixedBond instrument when using a HullWhite model and a IRTree pricing method.

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object.

FixB = fininstrument("FixedBond","Maturity",datetime(2029,9,15),"CouponRate",.05,"Period",1,"Name","fixed_bond_instrument")

FixB = 
  FixedBond with properties:

                  CouponRate: 0.0500
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2029
                        Name: "fixed_bond_instrument"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2019,9,15);
Type = "zero";
ZeroTimes = [calyears([1:10])]';
ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]';
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-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("hullwhite",'Alpha',0.052,'Sigma',0.34)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0520
    Sigma: 0.3400

Create IRTree Pricer Object

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

HWTreePricer = finpricer("irtree","model",HullWhiteModel,"DiscountCurve",myRC,"TreeDates",ZeroDates)

HWTreePricer = 
  HWBKTree with properties:

             Tree: [1x1 struct]
        TreeDates: [10x1 datetime]
            Model: [1x1 finmodel.HullWhite]
    DiscountCurve: [1x1 ratecurve]

HWTreePricer.Tree

ans = struct with fields:
        tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
        dObs: [15-Sep-2019    15-Sep-2020    15-Sep-2021    15-Sep-2022    15-Sep-2023    15-Sep-2024    15-Sep-2025    15-Sep-2026    15-Sep-2027    15-Sep-2028]
      CFlowT: {[10x1 double]  [9x1 double]  [8x1 double]  [7x1 double]  [6x1 double]  [5x1 double]  [4x1 double]  [3x1 double]  [2x1 double]  [9.9809]}
       Probs: {[3x1 double]  [3x3 double]  [3x5 double]  [3x7 double]  [3x9 double]  [3x11 double]  [3x13 double]  [3x15 double]  [3x17 double]}
     Connect: {[2]  [2 3 4]  [2 3 4 5 6]  [2 3 4 5 6 7 8]  [2 3 4 5 6 7 8 9 10]  [2 3 4 5 6 7 8 9 10 11 12]  [2 3 4 5 6 7 8 9 10 11 12 13 14]  [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]  [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
     FwdTree: {1x10 cell}
    RateTree: {1x10 cell}

Price FixedBond Instrument

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

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

Price = 117.9440

outPR = 
  priceresult with properties:

       Results: [1x4 table]
    PricerData: [1x1 struct]

outPR.Results

ans=1×4 table
    Price      Delta     Gamma        Vega    
    ______    _______    ______    ___________

    117.94    -964.01    8868.6    -4.2633e-10

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.

Version History

Introduced in R2020a

R2022b: Serial date numbers not recommended

Although FixedBond 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.