FloatBondOption

FloatBondOption instrument object

Description

Create and price a FloatBondOption instrument object for one or more Float Bond Option instruments using this workflow:

1. Use fininstrument to create an FloatBondOption instrument object for one or more Float Bond Option instruments.

2. Use finmodel to specify a HullWhite, BlackKarasinski, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model for the FloatBondOption 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 FloatBondOption instruments.

   • When using a HullWhite, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model, use finpricer to specify an IRMonteCarlo pricing method for one or more FloatBondOption 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 FloatBondOption instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

FloatBondOptionObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'Bond',bond_obj)

FloatBondOptionObj = fininstrument(___,Name,Value)

Description

FloatBondOptionObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'Bond',bond_obj) creates a FloatBond object for one or more Float Bond Option instruments by specifying InstrumentType and sets properties using the required name-value pair arguments Strike, ExerciseDate, and Bond.

FloatBondOptionObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pair arguments in addition to the required arguments in the previous syntax. For example, FloatBondOptionObj = fininstrument("FloatBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"american",'Name',"float_bond_option") creates a FloatBondOption instrument with a strike of 100 and an American exercise. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

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

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

Data Types: char | cell | string

FloatBondOption 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: FloatBondOptionObj = fininstrument("FloatBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"american",'Name',"float_bond_option")

Required FloatBondOption Name-Value Pair Arguments

Strike — Option strike value

nonnegative value | vector of nonnegative values

Option strike value, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative value or an NINST-by-1 vector of nonnegative values.

Data Types: double

ExerciseDate — Option exercise dates

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

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

• For a European option, there is only one ExerciseDate on the option expiry date.

• For a Bermudan option, there is a 1-by-NSTRIKES vector of exercise dates.

• For an American option, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDate.

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: double | cell | char | string | datetime

Bond — Underlying float bond

FloatBond object | vector of FloatBond objects

Underlying float bond, specified as the comma-separated pair consisting of 'Bond' and the name of a FloatBond object or an NINST-by-1 vector of FloatBond objects.

Data Types: object

Optional FloatBondOption Name-Value Pair Arguments

OptionType — Definition of option

"call" (default) | string with value "call" or "put" | string array with values of "call" or "put" | character vector with value 'call' or 'put' | cell array of character vectors with values of 'call' or 'put'

Definition of option, specified as the comma-separated pair consisting of 'OptionType' and a scalar character vector or a string or an NINST-by-1 cell array of character vectors or string array using 'call' or 'put'.

Data Types: char | cell | string

ExerciseStyle — Option type

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

Option type, specified as the comma-separated pair consisting of 'ExerciseStyle' and a scalar character vector or string or an NINST-by-1 cell array of character vectors or string array.

Data Types: string | cell | char

Name — User-defined name for instrument

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

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

Data Types: char | cell | string

Properties

InstrumentType — Instrument type

string with value "FloatBondOption" | string array with values of "FloatBondOption"

Instrument type, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Strike — Option strike value

nonnegative value | nonnegative value

Option strike value, returned as a scalar nonnegative value or an NINST-by-1 vector of nonnegative values.

Data Types: double

ExerciseDate — Option exercise date

datetime | vector of datetimes

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

Data Types: datetime

OptionType — Definition of option

"call" (default) | string with value "call" or "put" | string array with values of "call" or "put"

Definition of option, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

ExerciseStyle — Option type

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

Option type, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Bond — Underlying float bond

FloatBond object | vector of FloatBond objects

Underlying float bond, returned as a scalar FloatBond object or an NINST-by-1 vector of FloatBond objects.

Data Types: object

Name — User-defined name for instrument

" " (default) | string | string array

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

Data Types: string

Object Functions

setExercisePolicy

Set exercise policy for FixedBondOption, FloatBondOption, or Vanilla instrument

Examples

Price a Float Bond Option Instrument Using Hull-White Model and IRTree Pricer

This example shows the workflow to price a FloatBondOption instrument when you use a HullWhite model and an IRTree pricing method.

Create FloatBond Instrument Object

Use fininstrument to create a FloatBond instrument object as the underlying bond.

BondInst = fininstrument("FloatBond",'Maturity',datetime(2030,9,15),'Spread',0.021,'Name',"bond_instrument")

BondInst = 
  FloatBond with properties:

                      Spread: 0.0210
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 2
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
          LatestFloatingRate: NaN
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2030
                        Name: "bond_instrument"

Create FloatBondOption Instrument Objects

Use fininstrument to create three callable FloatBondOption instrument objects with European, American, and Bermudan exercise.

FloatBOptionEuro = fininstrument("FloatBondOption",'ExerciseDate',datetime(2029,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"float_bond_option_european")

FloatBOptionEuro = 
  FloatBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2029
           Strike: 98
             Bond: [1x1 fininstrument.FloatBond]
             Name: "float_bond_option_european"

FloatBOptionAmerican = fininstrument("FloatBondOption",'ExerciseDate',datetime(2029,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"american",'Name',"float_bond_option_american")

FloatBOptionAmerican = 
  FloatBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "american"
     ExerciseDate: 15-Sep-2029
           Strike: 98
             Bond: [1x1 fininstrument.FloatBond]
             Name: "float_bond_option_american"

FloatBOptionBermudan = fininstrument("FloatBondOption",'ExerciseDate',[datetime(2025,9,15) , datetime(2029,09,15)],'Strike',[98,100],'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"bermudan",'Name',"float_bond_option_bermudan")

FloatBOptionBermudan = 
  FloatBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "bermudan"
     ExerciseDate: [15-Sep-2025    15-Sep-2029]
           Strike: [98 100]
             Bond: [1x1 fininstrument.FloatBond]
             Name: "float_bond_option_bermudan"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2024,9,15);
Type = 'zero';
ZeroTimes = [calyears([1:10])]';
ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2024
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create a HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.05)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0100
    Sigma: 0.0500

Create IRTree Pricer Object

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

CFdates = cfdates(Settle, BondInst.Maturity, BondInst.Reset, BondInst.Basis);
HWTreePricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',CFdates')

HWTreePricer = 
  HWBKTree with properties:

             Tree: [1x1 struct]
        TreeDates: [12x1 datetime]
            Model: [1x1 finmodel.HullWhite]
    DiscountCurve: [1x1 ratecurve]

HWTreePricer.Tree

ans = struct with fields:
        tObs: [0 0.4959 1 1.4959 2 2.4959 3 3.4986 4.0027 4.4986 5.0027 ... ]
        dObs: [15-Sep-2024    15-Mar-2025    15-Sep-2025    ...    ]
      CFlowT: {1x12 cell}
       Probs: {1x11 cell}
     Connect: {1x11 cell}
     FwdTree: {1x12 cell}
    RateTree: {1x12 cell}

Price FixedBondOption Instruments

Use price to compute the price and sensitivities for the two FixedBondOption instruments.

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

Price = 3.8040

outPR = 
  priceresult with properties:

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

outPR.Results

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

    3.804    -2.6645e-11    110.75    -20.465

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

Price = 14.1700

outPR = 
  priceresult with properties:

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

outPR.Results

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

    14.17     0      160.87    -38.981

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

Price = 12.0676

outPR = 
  priceresult with properties:

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

outPR.Results

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

    12.068    -2.8422e-10    161.55    -39.402

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

This example shows the workflow to price multiple FloatBondOption instruments when you use a HullWhite model and an IRTree pricing method.

Create FloatBond Instrument Object

Use fininstrument to create a FloatBond instrument object as the underlying bond.

BondInst = fininstrument("FloatBond",'Maturity',datetime(2030,9,15),'Spread',0.021,'Name',"bond_instrument")

BondInst = 
  FloatBond with properties:

                      Spread: 0.0210
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 2
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
          LatestFloatingRate: NaN
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2030
                        Name: "bond_instrument"

Create FloatBondOption Instrument Objects

Use fininstrument to create a FloatBondOption instrument object with European exercise for three Float Bond Option instruments.

FloatBOptionEuro = fininstrument("FloatBondOption",'ExerciseDate',datetime([2030,9,15 ; 2029,09,15 ; 2028,09,15]),'Strike',[98 ; 99 ; 100],'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"float_bond_option_european")

FloatBOptionEuro=3×1 object
  3x1 FloatBondOption array with properties:

    OptionType
    ExerciseStyle
    ExerciseDate
    Strike
    Bond
    Name

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2024,9,15);
Type = 'zero';
ZeroTimes = [calyears([1:10])]';
ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2024
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create a HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.05)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0100
    Sigma: 0.0500

Create IRTree Pricer Object

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

CFdates = cfdates(Settle, BondInst.Maturity, BondInst.Reset, BondInst.Basis);
HWTreePricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',CFdates')

HWTreePricer = 
  HWBKTree with properties:

             Tree: [1x1 struct]
        TreeDates: [12x1 datetime]
            Model: [1x1 finmodel.HullWhite]
    DiscountCurve: [1x1 ratecurve]

HWTreePricer.Tree

ans = struct with fields:
        tObs: [0 0.4959 1 1.4959 2 2.4959 3 3.4986 4.0027 4.4986 5.0027 ... ]
        dObs: [15-Sep-2024    15-Mar-2025    15-Sep-2025    ...    ]
      CFlowT: {1x12 cell}
       Probs: {1x11 cell}
     Connect: {1x11 cell}
     FwdTree: {1x12 cell}
    RateTree: {1x12 cell}

Price FixedBondOption Instruments

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

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

Price = 3×1

    1.8081
    2.8617
    3.9097

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

    Results
    PricerData

outPR.Results

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

    1.8081    4.4409e-12    65.153    -10.854

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

    2.8617    -1.7764e-11    87.167    -15.751

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

    3.9097    -7.1054e-11    108.64    -20.493

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

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

Create FloatBond Instrument Object

Use fininstrument to create a FloatBond instrument object as the underlying bond.

BondInst = fininstrument("FloatBond",'Maturity',datetime(2030,9,15),'Spread',0.021,'Name',"bond_instrument")

BondInst = 
  FloatBond with properties:

                      Spread: 0.0210
             ProjectionCurve: [0x0 ratecurve]
                 ResetOffset: 0
                       Reset: 2
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
          LatestFloatingRate: NaN
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2030
                        Name: "bond_instrument"

Create FloatBondOption Instrument Object

Use fininstrument to create a FloatBondOption instrument object.

FloatBOptionEuro = fininstrument("FloatBondOption",'ExerciseDate',datetime(2020,3,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"float_bond_option_european")

FloatBOptionEuro = 
  FloatBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "european"
     ExerciseDate: 15-Mar-2020
           Strike: 98
             Bond: [1x1 fininstrument.FloatBond]
             Name: "float_bond_option_european"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

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

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.3200
    Sigma: 0.4900

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2019,1,1);
Type = 'zero';
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 01-Jan-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create IRMonteCarlo Pricer Object

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

outPricer = finpricer("IRMonteCarlo",'Model',HullWhiteModel,'DiscountCurve',myRC,'SimulationDates',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 FloatBondOption Instrument

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

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

Price = 18.2369

outPR = 
  priceresult with properties:

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

outPR.Results

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

    18.237    -104.22    788.7    -13.949

More About

Floating-Rate Note Option

A floating-rate note option gives the option holder the right to sell the option back to the issuer (put) or to redeem an option (call) at a specific price and on a specific date.

Financial Instruments Toolbox™ supports three types of put and call options on bonds:

• American option — An option that you exercise any time until its expiration date

• European option — An option that you exercise only on its expiration date

• Bermuda option — A Bermuda option resembles a hybrid of American and European options; you can only exercise it on predetermined dates, usually monthly

For more information, see Bond Options.

Tips

After creating a FloatBondOption instrument object, you can use setExercisePolicy to change the size of the options. For example, consider the following instrument:

FloatBOption = fininstrument("FloatBondOption",'ExerciseDate',datetime(2029,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"European")

To modify the size of the FloatBondOption instrument object by changing the ExerciseStyle from "European" to "American", use setExercisePolicy:

FloatBOption = setExercisePolicy(FloatBOption,[datetime(2021,1,1) datetime(2022,1,1)],100,'American')