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OptionEmbeddedFloatBond

OptionEmbeddedFloatBond instrument object

Description

Create and price a OptionEmbeddedFloatBond instrument object using this workflow:

  1. Use fininstrument to create an OptionEmbeddedFloatBond instrument object.

  2. Use finmodel to specify a HullWhite or BlackKarasinski model for the OptionEmbeddedFloatBond instrument.

  3. Use finpricer to specify an IRTree pricing method for the OptionEmbeddedFloatBond 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 OptionEmbeddedFloatBond instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

OptionEmbeddedFloatBondObj = fininstrument(InstrumentType,'Spread',spread_value,'Maturity',maturity_date,'CallSchedule',call_schedule_value) creates a OptionEmbeddedFloatBond object by specifying InstrumentType and the required name-value pair arguments Spread, Maturity, and CallSchedule sets the properties using required name-value pair arguments.

OptionEmbeddedFloatBond supports vanilla bonds with embedded options, stepped coupon bonds with embedded options and amortizing bonds with embedded options.

example

OptionEmbeddedFloatBondObj = fininstrument(InstrumentType,'Spread',spread_value,'Maturity',maturity_date,'PutSchedule',put_schedule_value) creates a OptionEmbeddedFloatBond object by specifying InstrumentType and the required name-value pair arguments Spread, Maturity, and PutSchedule sets the properties using required name-value pair arguments.

example

OptionEmbeddedFloatBondObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, OptionEmbeddedFloatBondObj = fininstrument("OptionEmbeddedFloatBond",'Spread',0.01,'Maturity',datetime(2019,1,30),'Period',4,'Basis',5,'Principal',1000,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',1,'CallSchedule',schedule,'CallExerciseStyle',"american",'ProjectionCurve',ratecurve_obj,'Name',"optionembeddedfloatbond"). You can specify multiple name-value pairs.

Input Arguments

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

Data Types: char | string

OptionEmbeddedFloatBond 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: OptionEmbeddedFloatBondObj = fininstrument("OptionEmbeddedFloatBond",'Spread',0.01,'Maturity',datetime(2019,1,30),'Period',4,'Basis',5,'Principal',1000,'FirstCouponDate',datetime(2016,1,30),'EndMonthRule',1,'CallSchedule',schedule,'CallExerciseStyle',"american",'ProjectionCurve',ratecurve_obj,'Name',"optionembeddedfloatbond")
Required OptionEmbeddedFloatBond Name-Value Pair Arguments

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Number of basis points over the reference rate, specified as the comma-separated pair consisting of 'Spread' and a scalar nonnegative numeric.

Data Types: double

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

Data Types: char | double | string | datetime

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

Data Types: 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 OptionEmbeddedFloatBond instrument supports either CallSchedule and CallExerciseStyle or PutSchedule and PutExerciseStyle, but not both.

Data Types: timetable

Optional OptionEmbeddedFloatBond Name-Value Pair Arguments

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

Data Types: double

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

Data Types: string | char

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

Data Types: string | char

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

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

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

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 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

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

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

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

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

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

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

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Instrument type, returned as a string with the value of "OptionEmbeddedFloatBond".

Data Types: string

Number of basis points over the reference rate, returned as a scalar nonnegative numeric.

Data Types: double

Maturity date, returned as a datetime.

Data Types: datetime

Call schedule, returned as a timetable.

Data Types: cell | datetime

Put schedule, returned as a timetable.

Data Types: cell | datetime

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

Data Types: double

Day count basis, returned as a scalar integer.

Data Types: double

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

Data Types: timetable | double

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

Data Types: logical

Business day conventions, returned as a string

Data Types: string

Holidays used in computing business days, returned as datetimes.

Data Types: datetime

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

Bond issue date, returned as a datetime.

Data Types: datetime

Irregular first coupon date, returned as a datetime.

Data Types: datetime

Irregular last coupon date, returned as a datetime.

Data Types: datetime

Forward starting date of payments, returned as a datetime.

Data Types: datetime

This property is read-only.

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

Data Types: string

This property is read-only.

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

Data Types: string

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

Data Types: string

Object Functions

setCallExercisePolicySet call exercise policy for OptionEmbeddedFixedBond or OptionEmbeddedFloatBond instrument
setPutExercisePolicySet put exercise policy for OptionEmbeddedFixedBond or OptionEmbeddedFloatBond instrument

Examples

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This example shows the workflow to price American, European, and Bermudan exercise styles for three callable OptionEmbeddedFloatBond 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 OptionEmbeddedFloatBond Instrument Objects

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

Maturity = datetime(2024,1,1);

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

CallableBondBermudan = fininstrument("OptionEmbeddedFloatBond",'Maturity',Maturity,...
                              'Spread',0.025,'Reset',Reset, ...
                              'CallSchedule',CallSchedule,'CallExerciseStyle', "bermudan")
CallableBondBermudan = 
  OptionEmbeddedFloatBond with properties:

                      Spread: 0.0250
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 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 float bond (American callable bond)
Strike = 100;
ExerciseDates = datetime(2024,1,1);
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
Reset = 1;

CallableBondAmerican = fininstrument("OptionEmbeddedFloatBond",'Maturity',Maturity,...
                              'Spread',0.025,'Reset', Reset, ...
                              'CallSchedule',CallSchedule,'CallExerciseStyle',"american")
CallableBondAmerican = 
  OptionEmbeddedFloatBond with properties:

                      Spread: 0.0250
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 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 float bond (European callable bond)
Strike = 100;
ExerciseDates = datetime(2024,1,1);
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'}); 
Reset = 1;

CallableBondEuropean = fininstrument("OptionEmbeddedFloatBond",'Maturity',Maturity,...
                              'Spread',0.025,'Reset',Reset, ...
                              'CallSchedule',CallSchedule)                          
CallableBondEuropean = 
  OptionEmbeddedFloatBond with properties:

                      Spread: 0.0250
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 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 = 104.9598
outPR = 
  priceresult with properties:

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

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

    104.96     0      19.597    -7.3926

[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 = 114.5571
outPR = 
  priceresult with properties:

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

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

    114.56    -2.8422e-10    262.58    -50.006

More About

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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.

Introduced in R2020a