OptionEmbeddedFixedBond

OptionEmbeddedFixedBond instrument object

Description

Create and price a OptionEmbeddedFixedBond instrument object for one or more Option Embedded Fixed Bond instruments using this workflow:

1. Use fininstrument to create an OptionEmbeddedFixedBond instrument object for one or more Option Embedded Fixed Bond instruments.

2. use finmodel to specify a HullWhite, BlackKarasinski, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model for the OptionEmbeddedFixedBond instrument object.

3. Choose a pricing method.

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

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

For more 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 an OptionEmbeddedFixedBond instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

OptionEmbeddedFixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date,'CallSchedule',call_schedule_value)

OptionEmbeddedFixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date,'PutSchedule',put_schedule_value)

OptionEmbeddedFixedBondObj = fininstrument(___,Name,Value)

Description

OptionEmbeddedFixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date,'CallSchedule',call_schedule_value) creates a OptionEmbeddedFixedBond object for one or more Option Embedded Fixed Bond instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments CouponRate, Maturity, and CallSchedule.

The OptionEmbeddedFixedBond instrument supports a vanilla bond with embedded option, stepped coupon bond with embedded option, and an amortizing bond with embedded option. For more information, see More About.

OptionEmbeddedFixedBondObj = fininstrument(InstrumentType,'CouponRate',couponrate_value,'Maturity',maturity_date,'PutSchedule',put_schedule_value) creates a OptionEmbeddedFixedBond object for one or more Option Embedded Fixed Bond instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments CouponRate, Maturity, and PutSchedule.

OptionEmbeddedFixedBondObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, OptionEmbeddedFixedBondObj = fininstrument("OptionEmbeddedFixedBond",'CouponRate',0.034,'Maturity',datetime(2019,1,30),'Period',2,'Basis',1,'Principal',100,'CallSchedule',schedule,'CallExerciseStyle',"American",'Name',"optionembeddedfixedbond_instrument") creates an OptionEmbeddedFixedBond instrument with an American exercise and a call schedule. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

string with value "OptionEmbeddedFixedBond" | string array with values of "OptionEmbeddedFixedBond" | character vector with value 'OptionEmbeddedFixedBond' | cell array of character vectors with values of 'OptionEmbeddedFixedBond'

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

Data Types: char | cell | string

OptionEmbeddedFixedBond 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: OptionEmbeddedFixedBondObj = fininstrument("OptionEmbeddedFixedBond",'CouponRate',0.034,'Maturity',datetime(2019,1,30),'Period',2,'Basis',1,'Principal',100,'CallSchedule',schedule,'CallExerciseStyle',"American",'Name',"optionembeddedfixedbond_instrument")

Required OptionEmbeddedFixedBond Name-Value Pair Arguments

CouponRate — Coupon rate for OptionEmbeddedFixedBond

scalar decimal | vector of decimals | timetable

Coupon rate for OptionEmbeddedFixedBond, specified as the comma-separated pair consisting of 'CouponRate' as 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 OptionEmbeddedFixedBond instruments and use a timetable, the timetable specification applies to all of the OptionEmbeddedFixedBond instruments. CouponRate does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

Maturity — Maturity date for OptionEmbeddedFixedBond

datetime | serial date number | date character vector | date string | vector of datetimes | vector of serial date numbers | cell array of date character vectors | date string array

Maturity date for OptionEmbeddedFixedBond, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, serial date number, date character vector, date string or an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

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

Data Types: char | cell | double | string | datetime

CallSchedule — Call schedule

timetable

Call schedule, specified as the comma-separated pair consisting of 'CallSchedule' and a timetable of call dates and strikes.

If you use a date character vector or date string for the dates in this timetable, the format must be recognizable by datetime because the CallSchedule property is stored as a datetime.

Note

The OptionEmbeddedFixedBond instrument supports either CallSchedule and CallExerciseStyle or PutSchedule and PutExerciseStyle, but not both.

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

Data Types: timetable

PutSchedule — Call schedule

timetable

Put schedule, specified as the comma-separated pair consisting of 'PutSchedule' and a timetable of call dates and strikes.

If you use a date character vector or date string for dates in this timetable, the format must be recognizable by datetime because the PutSchedule property is stored as a datetime.

Note

The OptionEmbeddedFixedBond instrument supports either CallSchedule and CallExerciseStyle or PutSchedule and PutExerciseStyle, but not both.

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

Data Types: timetable

Optional OptionEmbeddedFixedBond Name-Value Pair Arguments

Period — Frequency of payments per year

2 (default) | scalar integer | vector of integers

Frequency of payments per year, 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, and 12.

Data Types: double

CallExerciseStyle — Call option exercise style

"European" (default) | string with value "European", "American", or "Bermudan" | string array with value "European", "American", or "Bermudan" | character vector with value 'European', 'American', or 'Bermudan' | cell array of character vectors with values of 'European', 'American', or 'Bermudan'

Call option exercise style, specified as the comma-separated pair consisting of 'CallExerciseStyle' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Note

The CallSchedule is a timetable of call dates and strikes. If you do not specify a CallExerciseStyle, then based on the CallSchedule specification, a default value of CallExerciseStyle is assigned as follows:

• If there is one exercise date in the CallSchedule, then the CallExerciseStyle is an "European".

• If there are two exercise dates in the CallSchedule, then the CallExerciseStyle is an "American" with a start date and maturity.

• If there are more than two exercise dates in the CallSchedule, then the CallExerciseStyle is an "Bermudan".

If the you define a CallExerciseStyle and this is not consistent with what you have specified in the CallSchedule, you receive an error message.

Data Types: string | cell | char

PutExerciseStyle — Put option exercise style

"European" (default) | string with value "European", "American", or "Bermudan" | string array with value "European", "American", or "Bermudan" | character vector with value 'European', 'American', or 'Bermudan' | cell array of character vectors with values of 'European', 'American', or 'Bermudan'

Put option exercise style, specified as the comma-separated pair consisting of 'PutExerciseStyle' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Note

The PutSchedule is a timetable of call dates and strikes. If you do not specify a PutExerciseStyle, then based on the PutSchedule specification, a default value of PutExerciseStyle is assigned as follows:

• If there is one exercise date in the PutSchedule, then the PutExerciseStyle is an "European".

• If there are two exercise dates in the PutSchedule, then the PutExerciseStyle is an "American" with a start date and maturity.

• If there are more than two exercise dates in the PutSchedule, then the PutExerciseStyle is an "Bermudan".

If the you define a PutExerciseStyle and this is not consistent with what you have specified in the PutSchedule, you receive an error message.

Data Types: string | cell | char

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 — Notional principal amount or principal value schedule

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

Notional 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 OptionEmbeddedFixedBond instruments and use a timetable, the timetable specification applies to all of the OptionEmbeddedFixedBond 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 logicals with values of true or false

Flag indicating whether cash flow adjusts for 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

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

Business day conventions, 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 non-business 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 | cell array of date 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 an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.. For example:

H = holidays(datetime('today'),datetime(2025,12,15));
OptionEmbeddedFixedBondObj = fininstrument("OptionEmbeddedFixedBond",'CouponRate',0.34,'Maturity',datetime(2025,12,15),...
'CallSchedule',schedule,'CallExerciseStyle',"american",'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) | 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 with 30 or fewer days, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar logical 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 | serial date number | date character vector | date string | vector of datetimes | vector of serial date numbers | cell array of date character vectors | date string array

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

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

Data Types: double | char | cell | string | datetime

FirstCouponDate — Irregular first coupon date

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

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

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

Data Types: double | char | cell | string | datetime

LastCouponDate — Irregular last coupon date

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

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

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

Data Types: double | char | cell | string | datetime

StartDate — Forward starting date of payments

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

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, serial date number, date character vector, date string or an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

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

Data Types: char | cell | double | string | datetime

Name — User-defined name for instrument

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

User-defined name for the instrument, 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 — Coupon annual rate

scalar decimal | timetable | vector of decimals

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

Data Types: double | timetable

Maturity — Maturity date

scalar datetime | vector of datetimes

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

Data Types: datetime

CallSchedule — Call schedule

timetable

Call schedule, returned as a timetable.

Data Types: datetime

PutSchedule — Call schedule

timetable

Put schedule, returned as a timetable.

Data Types: datetime

Period — Coupons per year

2 (default) | scalar integer | vector of integers

Coupons 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 — Notional principal amount or principal value schedule

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

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

Data Types: timetable | double

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 adjusted 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 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 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, returned as a scalar logical or an NINST-by-1 vector of logicals.

Data Types: logical

IssueDate — Bond issue date

NaT (default) | scalar 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) | scalar 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) | scalar 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

CallExerciseStyle — Call option exercise style

"European" (default) | string with value "European", "American", or "Bermuda" | string array with values of "European", "American", or "Bermuda"

This property is read-only.

Call option exercise style, returned as a scalar string or an NINST-by-1 string array with values of "European", "American", or "Bermuda".

Data Types: string

PutExerciseStyle — Put option exercise style

"European" (default) | string with value "European", "American", or "Bermuda" | string array with values of "European", "American", or "Bermuda"

This property is read-only.

Put option exercise style, returned as a scalar string or an NINST-by-1 string array with values of "European", "American", or "Bermuda".

Data Types: string

Name — User-defined name for instrument

" " (default) | string | string array

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

Data Types: string

Object Functions

setCallExercisePolicy	Set call exercise policy for OptionEmbeddedFixedBond, OptionEmbeddedFloatBond, or ConvertibleBond instrument
setPutExercisePolicy	Set put exercise policy for OptionEmbeddedFixedBond, OptionEmbeddedFloatBond, or ConvertibleBond instrument

Examples

Price Option Embedded Fixed Bond Instruments Using Hull-White Model and IRTree Pricer

This example shows the workflow to price American, European, and Bermudan exercise styles for three callable OptionEmbeddedFixedBond instruments when you use a HullWhite model and an IRTree pricing method.

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 OptionEmbeddedFixedBond Instrument Objects

Use fininstrument to create three OptionEmbeddedFixedBond instrument objects with the different exercise styles.

Maturity = datetime(2024,1,1);

% Option embedded bond (Bermudan callable bond)
Strike = [100; 100];
ExerciseDates = [datetime(2020,1,1); datetime(2024,1,1)];
Period = 1;
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 

CallableBondBermudan = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...
                              'CouponRate',0.025,'Period',Period, ...
                              'CallSchedule',CallSchedule,'CallExerciseStyle', "bermudan")

CallableBondBermudan = 
  OptionEmbeddedFixedBond with properties:

                  CouponRate: 0.0250
                      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
                   CallDates: [2x1 datetime]
                    PutDates: [0x1 datetime]
                CallSchedule: [2x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "bermudan"
            PutExerciseStyle: [0x0 string]
                        Name: ""

% Option embedded bond (American callable bond)
Strike = 100;
ExerciseDates = datetime(2024,1,1);
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
Period = 1;

CallableBondAmerican = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...
                              'CouponRate',0.025,'Period', Period, ...
                              'CallSchedule',CallSchedule,'CallExerciseStyle',"american")

CallableBondAmerican = 
  OptionEmbeddedFixedBond with properties:

                  CouponRate: 0.0250
                      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
                   CallDates: 01-Jan-2024
                    PutDates: [0x1 datetime]
                CallSchedule: [1x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "american"
            PutExerciseStyle: [0x0 string]
                        Name: ""

% Option embedded bond (European callable bond)
Strike = 100;
ExerciseDates = datetime(2024,1,1);
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
Period = 1;

CallableBondEuropean = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...
                              'CouponRate',0.025,'Period',Period, ...
                              'CallSchedule',CallSchedule)                          

CallableBondEuropean = 
  OptionEmbeddedFixedBond with properties:

                  CouponRate: 0.0250
                      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
                   CallDates: 01-Jan-2024
                    PutDates: [0x1 datetime]
                CallSchedule: [1x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "european"
            PutExerciseStyle: [0x0 string]
                        Name: ""

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

VolCurve = 0.01;
AlphaCurve = 0.1;

HWModel = finmodel("HullWhite",'alpha',AlphaCurve,'sigma',VolCurve);

Create IRTree Pricer Object

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

HWTreePricer = finpricer("IRTree",'Model',HWModel,'DiscountCurve',ZeroCurve,'TreeDates',ZeroDates)

HWTreePricer = 
  HWBKTree with properties:

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

Price OptionEmbeddedFixedBond Instruments

Use price to compute the price and sensitivities for the three OptionEmbeddedFixedBond instruments.

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

Price = 103.2729

outPR = 
  priceresult with properties:

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

outPR.Results

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

    103.27    -148.28    1375.9    -290.33

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

Price = 100

outPR = 
  priceresult with properties:

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

outPR.Results

ans=1×4 table
    Price    Vega    Gamma    Delta
    _____    ____    _____    _____

     100      0        0        0  

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

Price = 107.7023

outPR = 
  priceresult with properties:

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

outPR.Results

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

    107.7     0      4086.4    -602.56

Price Multiple Option Embedded Fixed Bond Instruments Using Hull-White Model and IRTree Pricer

This example shows the workflow to price multiple callable OptionEmbeddedFixedBond instruments with Bermudan exercise styles when you use a HullWhite model and an IRTree pricing method.

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 OptionEmbeddedFixedBond Instrument Objects

Use fininstrument to create an OptionEmbeddedFixedBond instrument object for three Option Embedded Fixed Bond instuments.

Maturity = datetime([2025,1,1 ; 2026,1,1 ; 2027,1,1]);

% Option embedded bond (Bermudan callable bond)
Strike = [100 ; 200 ; 300]; 
ExerciseDates = datetime([2022,1,1 ; 2023,1,1 ; 2024,1,1]); 
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
Period = 1;

CallableBondBermudan = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...
                              'CouponRate',0.025,'Period', Period, ...
                              'CallSchedule',CallSchedule,'CallExerciseStyle',"Bermudan")  

CallableBondBermudan=3×1 object
  3x1 OptionEmbeddedFixedBond array with properties:

    CouponRate
    Period
    Basis
    EndMonthRule
    Principal
    DaycountAdjustedCashFlow
    BusinessDayConvention
    Holidays
    IssueDate
    FirstCouponDate
    LastCouponDate
    StartDate
    Maturity
    CallDates
    PutDates
    CallSchedule
    PutSchedule
    CallExerciseStyle
    PutExerciseStyle
    Name

When you create multiple OptionEmbeddedFixedBond instruments and use a timetable for CallSchedule, the timetable specification applies to all of the OptionEmbeddedFixedBond instruments. The CallSchedule input argument does not accept an NINST-by-1 cell array of timetables as input.

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

VolCurve = 0.01;
AlphaCurve = 0.1;

HWModel = finmodel("HullWhite",'alpha',AlphaCurve,'sigma',VolCurve);

Create IRTree Pricer Object

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

HWTreePricer = finpricer("IRTree",'Model',HWModel,'DiscountCurve',ZeroCurve,'TreeDates',ZeroDates)

HWTreePricer = 
  HWBKTree with properties:

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

Price OptionEmbeddedFixedBond Instruments

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

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

Price = 3×1

  104.5001
  102.0649
   97.6664

outPR=3×1 object
  3x1 priceresult array with properties:

    Results
    PricerData

outPR.Results

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

    104.5    -166.73    4134.2    -584.34

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

    102.06    -201.07    4850.3    -621.72

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

    97.666    -84.933    6857.7    -743.76

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

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

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 OptionEmbeddedFixedBondOption Instrument Object

Use fininstrument to create an OptionEmbeddedFixedBondOption instrument object.

% Option embedded bond (European callable bond)
Maturity = datetime(2022,9,15);
Strike = 100;
ExerciseDates = datetime(2024,1,1);
CallSchedule = timetable(datetime(2020,3,15), 50);
Period = 1;

CallableBondEuropean = fininstrument("OptionEmbeddedFixedBond",'Maturity',Maturity,...
                              'CouponRate',0.025,'Period',Period, ...
                              'CallSchedule',CallSchedule)      

CallableBondEuropean = 
  OptionEmbeddedFixedBond with properties:

                  CouponRate: 0.0250
                      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-2022
                   CallDates: 15-Mar-2020
                    PutDates: [0x1 datetime]
                CallSchedule: [1x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "european"
            PutExerciseStyle: [0x0 string]
                        Name: ""

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 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',datetime(2019,3,15)+calmonths(0:6:48)')

outPricer = 
  HWMonteCarlo with properties:

          NumTrials: 1000
      RandomNumbers: []
      DiscountCurve: [1x1 ratecurve]
    SimulationDates: [15-Mar-2019    15-Sep-2019    15-Mar-2020    ...    ]
              Model: [1x1 finmodel.HullWhite]

Price OptionEmbeddedFixedBondOption Instrument

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

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

Price = 58.1882

outPR = 
  priceresult with properties:

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

outPR.Results

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

    58.188    -125.43    356.04    18.24

Price OptionEmbeddedFixedBond Instrument and Obtain Exercise Probabilities Using Black-Karasinski Model and IRTree Pricer

This example shows the workflow to price a callable OptionEmbeddedFixedBond instrument and obtain the exercise probabilities when you use a BlackKarasinski model and an IRTree pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018, 1, 1);
ZeroTimes = calyears(1:4)';
ZeroRates = [0.035; 0.042147; 0.047345; 0.052707];
ZeroDates = Settle + ZeroTimes;
Compounding = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding)

ZeroCurve = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: 1
                Basis: 0
                Dates: [4x1 datetime]
                Rates: [4x1 double]
               Settle: 01-Jan-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create OptionEmbeddedFixedBond Instrument Object

Use fininstrument to create an OptionEmbeddedFixedBond instrument object with an American exercise style.

CouponRate = 0.0425;
Strike = [95; 98];
ExerciseDates = [datetime(2021,1,1); datetime(2022,1,1)];
Maturity = datetime(2022,1,1);
Period = 1;
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
CallableBond = fininstrument("OptionEmbeddedFixedBond", 'Maturity',Maturity,...
                              'CouponRate',CouponRate,'Period', Period, ...
                              'CallSchedule',CallSchedule,...
                              'CallExerciseStyle', "American",...
                              'Name',"MyCallableBond")                

CallableBond = 
  OptionEmbeddedFixedBond with properties:

                  CouponRate: 0.0425
                      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-2022
                   CallDates: [2x1 datetime]
                    PutDates: [0x1 datetime]
                CallSchedule: [2x1 timetable]
                 PutSchedule: [0x0 timetable]
           CallExerciseStyle: "american"
            PutExerciseStyle: [0x0 string]
                        Name: "MyCallableBond"

Create BlackKarasinski Model Object

Use finmodel to create a BlackKarasinski model object.

VolCurve = 0.01;
AlphaCurve = 0.1;
BKModel = finmodel("BlackKarasinski",'alpha',AlphaCurve,'sigma',VolCurve)

BKModel = 
  BlackKarasinski with properties:

    Alpha: 0.1000
    Sigma: 0.0100

Create IRTree Pricer Object

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

BKTreePricer = finpricer("IRTree",'Model',BKModel,'DiscountCurve',ZeroCurve,'TreeDates',ZeroDates)

BKTreePricer = 
  HWBKTree with properties:

             Tree: [1x1 struct]
        TreeDates: [4x1 datetime]
            Model: [1x1 finmodel.BlackKarasinski]
    DiscountCurve: [1x1 ratecurve]

Price OptionEmbeddedFixedBond Instrument

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

[Price,  PriceResults]= price(BKTreePricer, CallableBond)

Price = 92.5235

PriceResults = 
  priceresult with properties:

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

Examine the output PriceResults.PricerData.PriceTree.ExTree, which contains the exercise indicator arrays. In the cell array, a 1 indicates an exercised option and a 0 indicates an unexercised option.

PriceResults.PricerData.PriceTree.ExTree{5} 

ans = 1x7 logical array

   1   1   1   1   1   1   1

No options are exercised.

PriceResults.PricerData.PriceTree.ExTree{4} 

ans = 1x7 logical array

   0   0   0   0   0   0   0

The instrument is exercised at all nodes.

PriceResults.PricerData.PriceTree.ExTree{3} 

ans = 1x5 logical array

   0   0   0   0   0

No options are exercised.

PriceResults.PricerData.PriceTree.ExTree{2} 

ans = 1x3 logical array

   0   0   0

No options are exercised.

View the probability of reaching each node from the root node using PriceResults.PricerData.PriceTree.ProbTree.

PriceResults.PricerData.PriceTree.ProbTree{2}

ans = 1×3

    0.1667    0.6667    0.1667

PriceResults.PricerData.PriceTree.ProbTree{3}

ans = 1×5

    0.0203    0.2206    0.5183    0.2206    0.0203

PriceResults.PricerData.PriceTree.ProbTree{4}

ans = 1×7

    0.0018    0.0395    0.2370    0.4433    0.2370    0.0395    0.0018

PriceResults.PricerData.PriceTree.ProbTree{5}

ans = 1×7

    0.0018    0.0395    0.2370    0.4433    0.2370    0.0395    0.0018

View the exercise probabilities using PriceResults.PricerData.PriceTree.ExProbTree. PriceResults.PricerData.PriceTree.ExProbTree contains the exercise probabilities. Each element in the cell array is an array containing 0's where there is no exercise, or the probability of reaching that node where exercise happens.

PriceResults.PricerData.PriceTree.ExProbTree{5}

ans = 1×7

    0.0018    0.0395    0.2370    0.4433    0.2370    0.0395    0.0018

PriceResults.PricerData.PriceTree.ExProbTree{4}

ans = 1×7

     0     0     0     0     0     0     0

PriceResults.PricerData.PriceTree.ExProbTree{3}

ans = 1×5

     0     0     0     0     0

PriceResults.PricerData.PriceTree.ExProbTree{2}

ans = 1×3

     0     0     0

View the exercise probabilities at each tree level using PriceResults.PricerData.PriceTree.ExProbsByTreeLevel. PriceResults.PricerData.PriceTree.ExProbsByTreeLevel is an array in which each row holds the exercise probability for a given option at each tree observation time.

PriceResults.PricerData.PriceTree.ExProbsByTreeLevel

ans = 1×5

         0         0         0         0    1.0000

More About

Vanilla Bond with Embedded Option

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. A vanilla bond with an embedded option is where an option contract has an underlying asset of a vanilla bond.

Stepped Coupon Bond with Callable and Puttable Features

A step-up bond and step-down bond is a debt security 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. Stepped coupon bonds can have options features (call and puts).

Amortizing Callable and Puttable Bond

An amortizing callable bond or amortizing puttable bond work under a scheduled Principal.

An amortizing callable bond gives the issuer the right to call back the bond, but instead of paying the Principal amount at maturity, it repays part of the principal along with the coupon payments. An amortizing puttable bond, repays part of the principal along with the coupon payments and gives the bondholder the right to sell the bond back to the issuer.

Tips

After creating an OptionEmbeddedFixedBond object, you can modify the CallSchedule and CallExerciseStyle using setCallExercisePolicy. Or, you can modify the PutSchedule and PutExerciseStyle values using setPutExercisePolicy.