OptionEmbeddedFixedBond

OptionEmbeddedFixedBond instrument object

Description

Create and price a OptionEmbeddedFixedBond instrument object using this workflow:

1. Use fininstrument to create an OptionEmbeddedFixedBond instrument object.

2. use finmodel to specify a HullWhite or BlackKarasinski model for the OptionEmbeddedFixedBond instrument.

3. Use finpricer to specify an IRTree pricing method for the OptionEmbeddedFixedBond instrument.

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 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 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" | character vector with value 'OptionEmbeddedFixedBond'

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

Data Types: char | 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 | timetable

Coupon rate for OptionEmbeddedFixedBond, specified as the comma-separated pair consisting of 'CouponRate' as 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' — Maturity date for OptionEmbeddedFixedBond

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

Maturity date for OptionEmbeddedFixedBond, 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

'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.

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.

Data Types: timetable

Optional OptionEmbeddedFixedBond Name-Value Pair Arguments

'Period' — Frequency of payments per year

2 (default) | integer

Frequency of payments per year, specified as the comma-separated pair consisting of 'Period' and a scalar integer. 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" | character vector with value 'European', 'American', or 'Bermudan'

Call option exercise style, specified as the comma-separated pair consisting of 'CallExerciseStyle' and a scalar string or character vector.

Data Types: string | char

'PutExerciseStyle' — Put option exercise style

"European" (default) | string with value "European", "American", or "Bermudan" | character vector with value 'European', 'American', or 'Bermudan'

Put option exercise style, specified as the comma-separated pair consisting of 'PutExerciseStyle' and a scalar string or character vector.

Data Types: string | char

'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' — Notional principal amount or principal value schedule

100 (default) | scalar numeric | timetable

Notional 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 adjusts for 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

"actual" (default) | string | character vector

Business day conventions, 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 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 | 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 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) | 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 — Coupon annual rate

scalar decimal | timetable

Coupon annual rate, returned as a scalar decimal or timetable.

Data Types: double | timetable

Maturity — Maturity date

datetime

Maturity date, returned as a datetime.

Data Types: datetime

CallSchedule — Call schedule

timetable

Call schedule, returned as a timetable.

Data Types: cell | datetime

PutSchedule — Call schedule

timetable

Put schedule, returned as a timetable.

Data Types: cell | datetime

Period — Coupons per year

2 (default) | integer

Coupons 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 — Notional principal amount or principal value schedule

100 (default) | scalar numeric | timetable

Notional principal amount or principal value schedule, returned as a scalar numeric or timetable.

Data Types: timetable | double

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

false (default) | value of true or false

Flag indicating whether cash flow adjusted 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 with 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

CallExerciseStyle — Call option exercise style

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

This property is read-only.

Call option exercise style, returned as a string with a value of "European", "American", or "Bermuda".

Data Types: string

PutExerciseStyle — Put option exercise style

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

This property is read-only.

Put option exercise style, returned as a string with a value of "European", "American", or "Bermuda".

Data Types: string

Name — User-defined name for instrument

" " (default) | string

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

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 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.