FixedBondOption

FixedBondOption instrument object

Description

Create and price a FixedBondOption instrument object using this workflow:

1. Use fininstrument to create a FixedBondOption instrument object.

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

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

Creation

Syntax

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

FixedBondOptionObj = fininstrument(___,Name,Value)

Description

FixedBondOptionObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'Bond',bond_obj) creates a FixedBondOption object by specifying InstrumentType and sets the properties for the required name-value pair arguments Strike, ExerciseDate, and Bond.

The FixedBondOption instrument supports a European or American option. For more information, see More About.

FixedBondOptionObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, FixedBondOptionObj = fininstrument("FixedBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"American",'Name',"fixed_bond_option") creates a FixedBondOption 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 "FixedBondOption" | character vector with value 'FixedBondOption'

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

Data Types: char | string

FixedBondOption 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: FixedBondOptionObj = fininstrument("FixedBondOption",'Strike',100,'ExerciseDate',datetime(2019,1,30),'Bond',bond_obj,'OptionType','put','ExerciseStyle',"American",'Name',"fixed_bond_option")

Required FixedBondOption Name-Value Pair Arguments

'Strike' — Option strike value

nonnegative numeric

Option strike value, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative numeric.

Data Types: double

'ExerciseDate' — Option exercise date

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

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

• 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 Settle of the ratecurve and the single listed ExerciseDate.

If you use a date character vector or date string, the format must be recognizable by datetime because the ExerciseDate property is stored as a datetime.

Data Types: double | char | string | datetime

'Bond' — Underlying FixedBond instrument

FixedBond object

Underlying FixedBond instrument, specified as the comma-separated pair consisting of 'BondInstrument' and a FixedBond object.

Data Types: object

Optional FixedBondOption Name-Value Pair Arguments

'OptionType' — Option type

"call" (default) | string with value "call" or "put" | character vector with value 'call' or 'put'

Option type, specified as the comma-separated pair consisting of 'OptionType' and a scalar string or character vector.

Data Types: char | string

'ExerciseStyle' — Option exercise style

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

Option exercise style, specified as the comma-separated pair consisting of 'ExerciseStyle' and a scalar string or character vector with a value of "European", "American", or "Bermudan".

Data Types: string | char

'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

Strike — Option strike value

nonnegative numeric

Option strike value, returned as a scalar nonnegative numeric.

Data Types: double

ExerciseDate — Option exercise date

datetime

Option exercise date, returned as a datetime.

Data Types: datetime

OptionType — Option type

"call" (default) | string with value "call" or "put"

Option type, returned as a string with a value of "call" or "put".

Data Types: string

ExerciseStyle — Option exercise style

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

Option exercise style, returned as a string with a value of "European" or "American".

Data Types: string

Bond — Underlying FixedBond instrument

FixedBond object

Underlying FixedBond instrument, returned as a FixedBond object.

Data Types: object

Name — User-defined name for instrument

" " (default) | string

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

Data Types: string

Object Functions

setExercisePolicy

Set exercise policy for FixedBondOption, FloatBondOption, or Vanilla instrument

Examples

Price a FixedBondOption Instrument Using Hull-White Model and Hull-White Tree Pricer

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

Create FixedBond Instrument Object

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

BondInst = fininstrument("FixedBond",'Maturity',datetime(2029,9,15),'CouponRate',.021,'Period',1,'Name',"bond_instrument")

BondInst = 
  FixedBond with properties:

                  CouponRate: 0.0210
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2029
                        Name: "bond_instrument"

Create FixedBondOption Instrument Objects

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

FixedBOptionEuro = fininstrument("FixedBondOption",'ExerciseDate',datetime(2025,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")

FixedBOptionEuro = 
  FixedBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2025
           Strike: 98
             Bond: [1x1 fininstrument.FixedBond]
             Name: "fixed_bond_option_european"

FixedBOptionAmerican = fininstrument("FixedBondOption",'ExerciseDate',datetime(2025,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"american",'Name',"fixed_bond_option_american")

FixedBOptionAmerican = 
  FixedBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "american"
     ExerciseDate: 15-Sep-2025
           Strike: 98
             Bond: [1x1 fininstrument.FixedBond]
             Name: "fixed_bond_option_american"

FixedBOptionBermudan = fininstrument("FixedBondOption",'ExerciseDate',[datetime(2025,9,15) ; datetime(2025,11,15)],'Strike',[98,1000],'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"bermudan",'Name',"fixed_bond_option_bermudan")

FixedBOptionBermudan = 
  FixedBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "bermudan"
     ExerciseDate: [15-Sep-2025    15-Nov-2025]
           Strike: [98 1000]
             Bond: [1x1 fininstrument.FixedBond]
             Name: "fixed_bond_option_bermudan"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2019,9,15);
Type = 'zero';
ZeroTimes = [calyears([1:10])]';
ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create 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.

HWTreePricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',ZeroDates)

HWTreePricer = 
  HWBKTree with properties:

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

HWTreePricer.Tree

ans = struct with fields:
     FinObj: 'HWFwdTree'
       tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
       dObs: [1x10 datetime]
     CFlowT: {1x10 cell}
      Probs: {1x9 cell}
    Connect: {1x9 cell}
    FwdTree: {1x10 cell}

Price FixedBondOption Instruments

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

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

Price = 10.7571

outPR = 
  priceresult with properties:

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

outPR.Results

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

    10.757    308.87    2207.3    -178.78

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

Price = 19.2984

outPR = 
  priceresult with properties:

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

outPR.Results

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

    19.298    437.32    4977.1    -459.06

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

Price = 11.1241

outPR = 
  priceresult with properties:

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

outPR.Results

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

    11.124    322.94    2243.7    -182.44

Price a FixedBondOption Instrument on a Stepped FixedBond Using Hull-White Model and Hull-White Tree Pricer

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

Create Stepped FixedBond Instrument Object

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

Maturity = datetime(2027,1,1);
Period = 1;
CDates = datetime([2022,1,1 ; 2027,1,1]);
CRates = [.022; .027];
CouponRate = timetable(CDates,CRates);

SBond = fininstrument("FixedBond",'Maturity',Maturity,'CouponRate',CouponRate,'Period',Period,'Name',"stepped_bond_instrument") 

SBond = 
  FixedBond with properties:

                  CouponRate: [2x1 timetable]
                      Period: 1
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 01-Jan-2027
                        Name: "stepped_bond_instrument"

Create FixedBondOption Instrument Object

Use fininstrument to create a FixedBondOption instrument object with European exercise.

FixedBOption = fininstrument("FixedBondOption",'ExerciseDate',datetime(2026,1,1),'Strike',90,'Bond',SBond,'OptionType',"call",'ExerciseStyle',"european",'Name',"fixed_bond_option_european")

FixedBOption = 
  FixedBondOption with properties:

       OptionType: "call"
    ExerciseStyle: "european"
     ExerciseDate: 01-Jan-2026
           Strike: 90
             Bond: [1x1 fininstrument.FixedBond]
             Name: "fixed_bond_option_european"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
ZeroTimes = calyears(1:10)';
ZeroRates = [0.0055 0.0063 0.0071 0.0083 0.0099 0.0131 0.0178 0.0262 0.0343 0.0387]';
ZeroDates = Settle + ZeroTimes;
Compounding = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates, "Compounding",Compounding);

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

VolCurve = 0.15;
AlphaCurve = 0.03;

HWModel = finmodel("HullWhite",'Alpha',AlphaCurve,'Sigma',VolCurve)

HWModel = 
  HullWhite with properties:

    Alpha: 0.0300
    Sigma: 0.1500

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]

HWTreePricer.Tree

ans = struct with fields:
     FinObj: 'HWFwdTree'
       tObs: [0 1 2 3.0027 4.0027 5.0027 6.0027 7.0055 8.0055 9.0055]
       dObs: [1x10 datetime]
     CFlowT: {1x10 cell}
      Probs: {1x9 cell}
    Connect: {1x9 cell}
    FwdTree: {1x10 cell}

Price FixedBondOption Instrument

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

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

Price = 12.2717

outPR = 
  priceresult with properties:

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

outPR.Results

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

    12.272    100.91    1438.4    -130.1

More About

Bond Option

A bond option gives the holder the right to sell a bond back to the issuer (put) or to redeem a bond from its current owner (call) at a specific price and on a specific date.

The FixedBondOption instrument supports two 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.

For more information, see Bond Options.

Tips

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

FixedBOption = fininstrument("FixedBondOption",'ExerciseDate',datetime(2022,9,15),'Strike',98,'Bond',BondInst,'OptionType',"call",'ExerciseStyle',"European")

To modify the FixedBondOption instrument's size by changing the ExerciseStyle from "European" to "American", use setExercisePolicy:

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