Binary

Binary instrument object

Description

Create and price a Binary instrument object for one or more Binary instruments using this workflow:

1. Use fininstrument to create a Binary instrument object for one or more Binary instruments.

2. Use finmodel to specify a BlackScholes, RoughBergomi, RoughHeston, or Bachelier model for the Binary instrument object.

3. Choose a pricing method.

   • When using a BlackScholes model, use finpricer to specify a BlackScholes or AssetMonteCarlo pricing method for one or more Binary instruments.

   • When using a RoughBergomi or RoughHeston model, use finpricer to specify a RoughVolMonteCarlo pricing method for one or more Binary instruments.

   • When using a Bachelier model, use finpricer to specify an AssetMonteCarlo pricing method for one or more Binary 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 a Binary instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

BinaryOpt = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'PayoffValue',payoff_value)

BinaryOpt = fininstrument(___,Name,Value)

Description

BinaryOpt = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'PayoffValue',payoff_value) creates a Binary instrument object for one or more Binary instruments by specifying InstrumentType and sets properties using the required name-value pair arguments Strike, ExerciseDate, and PayoffValue.

BinaryOpt = fininstrument(___,Name,Value) sets optional properties using additional name-value pair arguments in addition to the required arguments in the previous syntax. For example, BinaryOpt = fininstrument("Binary",'Strike',100,'ExerciseDate',datetime(2019,1,30),'PayoffValue',110,'OptionType',"put",'Name',"binary_option") creates a Binary put option with a PayoffValue of 110. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

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

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

Data Types: char | cell | string

Name-Value Arguments

Specify required and optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: BinaryOpt = fininstrument("Binary",'Strike',100,'ExerciseDate',datetime(2019,1,30),'PayoffValue',110,'OptionType',"put",'Name',"binary_option")

Required Binary Name-Value Pair Arguments

Strike — Option strike price value

nonnegative value | vector of nonnegative values

Option strike price 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 date

datetime array | string array | date character vector

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

To support existing code, Binary also accepts serial date numbers as inputs, but they are not recommended.

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

PayoffValue — Option payoff value

scalar numeric | numeric vector

Option payoff value, specified as the comma-separated pair consisting of 'PayoffValue' and a scalar numeric value or an NINST-by-1 numeric vector.

Data Types: double

Optional Binary Name-Value Pair Arguments

OptionType — Option type

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

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

A call option pays out if the condition is met and the price of the underlying asset is above the specified level at expiration. A put option pays out if the condition is met and the price of the underlying asset is below the specified level at expiration.

Data Types: char | cell | string

ExerciseStyle — Option exercise style

"European" (default) | string with value "European" | string array with a value "European" | character vector with value 'European' | cell array of character vectors with a value 'European'

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

Data Types: string | char | cell

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

Output Arguments

BinaryOpt — Binary instrument

Binary object

Binary instrument, returned as a Binary object.

Properties

Strike — Option strike price value

nonnegative value | nonnegative value | vector of nonnegative values

Option strike price 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 datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

PayoffValue — Option payoff value

scalar numeric | numeric vector

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

Data Types: double

OptionType — Option type

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

Option type, returned as a scalar string or an NINST-by-1 string array with the values of "call" or "put".

Data Types: string

ExerciseStyle — Option exercise style

Read-only: "European" (default) | string with value "European" | string array with values "European"

This property is read-only.

Option exercise style, returned as a scalar string or an NINST-by-1 string array with the value of "European".

Data Types: string

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

Examples

Price Binary Instrument Using BlackScholes Model and AssetMonteCarlo Pricer

This example shows the workflow to price a Binary instrument when you use a BlackScholes model and an AssetMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',.2)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.2000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BlackScholesModel,'SpotPrice',102,'simulationDates',datetime(2022,9,15))

outPricer = 
  GBMMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.BlackScholes]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
113.0166

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×7 table
    Price     Delta    Gamma    Lambda      Rho      Theta     Vega
    ______    _____    _____    ______    _______    ______    ____

    113.02      0        0        0       -451.98    3.9582     0  

Price Binary Instrument Using RoughBergomi Model and RoughVolMonteCarlo Pricer

Since R2024a

This example shows the workflow to price a Binary instrument when you use a RoughBergomi model and a RoughVolMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",ExerciseDate=datetime(2022,9,15),Strike=1000,PayoffValue=130,OptionType="put",Name="binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create RoughBergomi Model Object

Use finmodel to create a RoughBergomi model object.

RoughBergomiModel = finmodel("RoughBergomi",Alpha=-0.32, Xi=0.1,Eta=0.003,RhoSV=0.9)

RoughBergomiModel = 
  RoughBergomi with properties:

    Alpha: -0.3200
       Xi: 0.1000
      Eta: 0.0030
    RhoSV: 0.9000

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,Basis=12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create RoughVolMonteCarlo Pricer Object

Use finpricer to create a RoughVolMonteCarlo pricer object and use the ratecurve object for the 'DiscountCurve' name-value argument.

outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughBergomiModel,SpotPrice=102,simulationDates=datetime(2022,9,15))

outPricer = 
  RoughBergomiMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.RoughBergomi]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
112.9036

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×7 table
    Price    Delta    Gamma    Lambda      Rho      Theta     Vega
    _____    _____    _____    ______    _______    ______    ____

    112.9      0        0        0       -451.52    3.9542     0  

Price Binary Instrument Using RoughHeston Model and RoughVolMonteCarlo Pricer

Since R2024b

This example shows the workflow to price a Binary instrument when you use a RoughHeston model and a RoughVolMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",ExerciseDate=datetime(2022,9,15),Strike=1000,PayoffValue=130,OptionType="put",Name="binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create RoughHeston Model Object

Use finmodel to create a RoughHeston model object.

RoughBergomiModel = finmodel("RoughHeston",V0=0.4,ThetaV=0.3,Kappa=0.2,SigmaV=0.1,Alpha=-0.02,RhoSV=0.3)

RoughBergomiModel = 
  RoughHeston with properties:

     Alpha: -0.0200
        V0: 0.4000
    ThetaV: 0.3000
     Kappa: 0.2000
    SigmaV: 0.1000
     RhoSV: 0.3000

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,Basis=12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create RoughVolMonteCarlo Pricer Object

Use finpricer to create a RoughVolMonteCarlo pricer object and use the ratecurve object for the 'DiscountCurve' name-value argument.

outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughBergomiModel,SpotPrice=102,simulationDates=datetime(2022,9,15))

outPricer = 
  RoughHestonMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.RoughHeston]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
111.8864

outPR = 
  priceresult with properties:

       Results: [1×8 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×8 table
    Price     Delta    Gamma    Lambda      Rho      Theta     Vega    VegaLT
    ______    _____    _____    ______    _______    ______    ____    ______

    111.89      0        0        0       -447.46    3.9186     0        0   

Price Binary Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

This example shows the workflow to price a Binary instrument when you use a BlackScholes model and an AssetMonteCarlo pricing method with quasi-Monte Carlo simulation.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',.2)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.2000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

Use finpricer to create an AssetMonteCarlo pricer object and use the ratecurve object for the 'DiscountCurve' name-value argument and use the name-value arguments for MonteCarloMethod and BrownianMotionMethod.

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BlackScholesModel,'SpotPrice',102,'simulationDates',datetime(2022,9,15),'NumTrials',1e3, ...
                     'MonteCarloMethod',"quasi",'BrownianMotionMethod',"brownian-bridge")

outPricer = 
  GBMMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.BlackScholes]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "quasi"
    BrownianMotionMethod: "brownian-bridge"

Price Binary Instrument

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

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

Price = 
113.0166

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×7 table
    Price     Delta    Gamma    Lambda      Rho      Theta     Vega
    ______    _____    _____    ______    _______    ______    ____

    113.02      0        0        0       -451.98    3.9582     0  

Price Multiple Binary Instruments Using BlackScholes Model and BlackScholes Pricer

This example shows the workflow to price multiple Binary instruments when you use a BlackScholes model and a BlackScholes pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object with three Binary instruments.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'Strike',[1000 ; 2000 ; 3000],'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt=3×1 Binary array with properties:
    OptionType
    ExerciseDate
    Strike
    PayoffValue
    ExerciseStyle
    Name

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.28)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.2800
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create BlackScholes Pricer Object

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

outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',800,'DividendValue',0.045)

outPricer = 
  BlackScholes with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 800
    DividendValue: 0.0450
     DividendType: "continuous"

Price Binary Instruments

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

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

Price = 3×1

   87.4005
  109.9703
  111.9328

outPR=3×1 priceresult array with properties:
    Results
    PricerData

outPR.Results 

ans=1×7 table
    Price      Delta         Gamma       Lambda      Vega      Theta       Rho  
    _____    _________    ___________    _______    _______    ______    _______

    87.4     -0.075973    -3.1264e-05    -0.6954    -23.084    3.2599    -592.61

ans=1×7 table
    Price       Delta         Gamma        Lambda      Vega      Theta       Rho  
    ______    _________    ___________    ________    _______    ______    _______

    109.97    -0.014137    -4.4054e-05    -0.10284    -32.196    4.8405    -495.01

ans=1×7 table
    Price       Delta         Gamma        Lambda       Vega      Theta       Rho  
    ______    __________    __________    _________    _______    ______    _______

    111.93    -0.0027668    -1.279e-05    -0.019775    -9.4868    4.2144    -475.57

Price Binary Instrument Using Merton Model and AssetMonteCarlo Pricer

This example shows the workflow to price a Binary instrument when you use a Merton model and an AssetMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create Merton Model Object

Use finmodel to create a Merton model object.

MertonModel = finmodel("Merton",'Volatility',0.45,'MeanJ',0.02,'JumpVol',0.07,'JumpFreq',0.09)

MertonModel = 
  Merton with properties:

    Volatility: 0.4500
         MeanJ: 0.0200
       JumpVol: 0.0700
      JumpFreq: 0.0900

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",MertonModel,'SpotPrice',102,'simulationDates',datetime(2022,9,15))

outPricer = 
  MertonMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.Merton]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
112.4515

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×7 table
    Price     Delta    Gamma    Lambda      Rho      Theta     Vega
    ______    _____    _____    ______    _______    ______    ____

    112.45      0        0        0       -449.72    3.9384     0  

Price Binary Instrument Using Bachelier Model and AssetMonteCarlo Pricer

This example shows the workflow to price a Binary instrument when you use a Bachelier model and an AssetMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create Bachelier Model Object

Use finmodel to create a Bachelier model object.

BachelierModel = finmodel("Bachelier",'Volatility',.2)

BachelierModel = 
  Bachelier with properties:

     Volatility: 0.2000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BachelierModel,'SpotPrice',102,'simulationDates',datetime(2022,9,15))

outPricer = 
  BachelierMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 102
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.Bachelier]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
113.0166

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: [1×1 struct]

outPR.Results 

ans=1×7 table
    Price     Delta    Gamma    Lambda      Rho      Theta     Vega
    ______    _____    _____    ______    _______    ______    ____

    113.02      0        0        0       -451.98    3.9582     0  

Price Binary Instrument Using BlackScholes Model and BlackScholes Pricer

This example shows the workflow to price a Binary instrument when you use a BlackScholes model and a BlackScholes pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'PayoffValue',130,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 1000
      PayoffValue: 130
    ExerciseStyle: "european"
             Name: "binary_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.28)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.2800
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create BlackScholes Pricer Object

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

outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',800,'DividendValue',0.045)

outPricer = 
  BlackScholes with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 800
    DividendValue: 0.0450
     DividendType: "continuous"

Price Binary Instrument

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

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

Price = 
87.4005

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: []

outPR.Results 

ans=1×7 table
    Price      Delta         Gamma       Lambda      Vega      Theta       Rho  
    _____    _________    ___________    _______    _______    ______    _______

    87.4     -0.075973    -3.1264e-05    -0.6954    -23.084    3.2599    -592.61

More About

Binary Option

A binary option is where the buyer receives a payout or loses their investment, depending on whether the option expires in the money.

A binary option is typically based on an underlying asset, such as stocks, currencies, commodities, or market indices. The option's value is derived from the price movement of the underlying asset.

Binary options depend on the outcome of a "yes or no" proposition, hence the name "binary." Binary options have an expiry date and/or time. At the time of expiry, the price of the underlying asset must be on the correct side of the strike price (based on the trade taken) for the trader to make a profit.

A binary option automatically exercises, meaning the gain or loss on the trade is automatically credited or debited to the trader's account when the option expires.

Version History

Introduced in R2020b

R2024b: Support for RoughHeston model and RoughVolMonteCarlo pricer

The Binary instrument object supports pricing with a RoughHeston model and a RoughVolMonteCarlo pricing method.

R2024a: Support for RoughBergomi model and RoughVolMonteCarlo pricer

The Binary instrument object supports pricing with a RoughBergomi model and a RoughVolMonteCarlo pricing method.

R2022b: Serial date numbers not recommended

Although Binary supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.