Barrier

Barrier instrument object

Description

Create and price a Barrier instrument object using this workflow:

1. Use fininstrument to create a Barrier instrument object.

2. Use finmodel to specify a BlackScholes, Heston, Bates, or Merton model for the Barrier instrument.

3. • When using a BlackScholes model, use finpricer to specify a BlackScholes, AssetTree, or VannaVolga pricing method for the Barrier instrument.

   • When using a BlackScholes, Heston, Bates, or Merton model, use finpricer to specify an AssetMonteCarlo or FiniteDifference pricing method for the Barrier 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 Barrier instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

BarrierOpt = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'BarrierValue',barrier_value)

BarrierOpt = fininstrument(___,Name,Value)

Description

BarrierOpt = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date,'BarrierValue',barrier_value) creates a Barrier object by specifying InstrumentType and sets the properties for the required name-value pair arguments Strike, ExerciseDate, and BarrierValue.

BarrierOpt = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, BarrierOpt = fininstrument("Barrier",'Strike',100,'ExerciseDate',datetime(2019,1,30),'BarrierValue',110,'OptionType',"put",'ExerciseStyle',"European",'BarrierType',"DO",'Name',"barrier_option") creates a Barrier put option with an European exercise. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

string with value "Barrier" | character vector with value 'Barrier' | string with value "Barrier"

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

Data Types: char | string

Barrier 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: BarrierOpt = fininstrument("Barrier",'Strike',100,'ExerciseDate',datetime(2019,1,30),'BarrierValue',110,'OptionType',"put",'ExerciseStyle',"European",'BarrierType',"DO",'Name',"barrier_option")

Required Barrier Name-Value Pair Arguments

'Strike' — Option strike value

nonnegative value

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

Data Types: double

'ExerciseDate' — Option exercise date

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

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.

Note

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

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

'BarrierValue' — Barrier level

numeric

Barrier level, specified as the comma-separated pair consisting of 'BarrierLevel' and a scalar numeric value.

Data Types: double

Optional Barrier 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" or "American" | character vector with value 'European' or 'American'

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

Note

For a Barrier option, the BlackScholes pricer supports only "European" exercise and the FiniteDifference pricer supports an "American" or "European" exercise.

Data Types: string | char

'BarrierType' — Barrier option type

"UO" (default) | string with value: "UI", "UO", "DI", or "DO" | character vector with value: 'UI', 'UO', 'DI', or 'DO'

Barrier option type, specified as the comma-separated pair consisting of 'BarrierType' and a string or character vector with one of the following values:

• "UI" — Up knock-in

  This option becomes effective when the price of the underlying asset passes above the barrier level. If the underlying asset goes above the barrier level during the life of the option, the option holder has the right, but not the obligation, to buy or sell (call or put) the underlying security at the strike price.

• "UO" — Up knock-out

  This option gives the option holder the right, but not the obligation, to buy or sell (call or put) the underlying security at the strike price as long as the underlying asset does not go above the barrier level during the life of the option. This option terminates when the price of the underlying security passes above the barrier level. If the spot price of the underlying asset reaches or exceeds the barrier level with an up-and-out option, the rebate is paid.

• "DI" — Down knock-in

  This option becomes effective when the price of the underlying stock passes below the barrier level. If the underlying security goes below the barrier level during the life of the option, the option holder has the right, but not the obligation, to buy or sell (call or put) the underlying security at the strike price. With a down-and-in option, the rebate is paid if the spot price of the underlying does not reach the barrier level during the life of the option. Note that a Barrier instrument using the FiniteDifference pricer does not support American knock-in barrier options.

• "DO" — Down knock-up

  This option gives the option holder the right, but not the obligation, to buy or sell (call or put) the underlying asset at the strike price as long as the underlying asset does not go below the barrier level during the life of the option. This option terminates when the price of the underlying security passes below the barrier level. If the option is worthless when it expires, the option holder receives a rebate amount.

Option	Barrier Type	Payoff If Barrier Crossed	Payoff If Barrier Not Crossed
Call or Put	Down knock-out	Worthless	Standard Call or Put
Call or Put	Down knock-in	Call or Put	Worthless
Call or Put	Up knock-out	Worthless	Standard Call or Put
Call or Put	Up knock-in	Standard Call or Put	Worthless

Data Types: char | string

'Rebate' — Rebate value

0 (default) | numeric

Rebate value, specified as the comma-separated pair consisting of 'Rebate' and a scalar numeric.

• For knock-in options, the Rebate is paid at expiry.

• For knock-out options, the Rebate is paid when BarrierValue is reached.

Data Types: double

'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 value

Option strike value, returned as a scalar nonnegative value.

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 the value "call" or "put".

Data Types: string

ExerciseStyle — Option exercise style

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

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

Data Types: string

BarrierSpec — Barrier option type

"UO" European (default) | string with value: "UI", "UO", "DI", or "DO"

Barrier option type, returned as a string with a value of "UI", "UO", "DI", or "DO".

Data Types: string

BarrierValue — Barrier level

numeric

Barrier level, returned as a scalar numeric value.

Data Types: double

Rebate — Rebate value

0 (default) | numeric

Rebate value, returned as a scalar numeric.

Data Types: double

Name — User-defined name for instrument

" " (default) | string

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

Data Types: string

Examples

Price Barrier Instrument Using Black-Scholes Model and Finite Difference Pricer

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

Create Barrier Instrument Object

Use fininstrument to create an Barrier instrument object.

BarrierOpt = fininstrument("Barrier",'Strike',45,'ExerciseDate',datetime(2019,1,1),'OptionType',"call",'ExerciseStyle',"american",'BarrierType',"DO",'BarrierValue',40,'Name',"barrier_option")

BarrierOpt = 
  Barrier with properties:

       OptionType: "call"
           Strike: 45
      BarrierType: "do"
     BarrierValue: 40
           Rebate: 0
    ExerciseStyle: "american"
     ExerciseDate: 01-Jan-2019
             Name: "barrier_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.30)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
Maturity = datetime(2023,1,1);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2023
                Rates: 0.0350
               Settle: 01-Jan-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create FiniteDifference Pricer Object

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

outPricer = finpricer("FiniteDifference",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',50)

outPricer = 
  FiniteDifference with properties:

     DiscountCurve: [1x1 ratecurve]
             Model: [1x1 finmodel.BlackScholes]
         SpotPrice: 50
    GridProperties: [1x1 struct]
      DividendType: "continuous"
     DividendValue: 0

Price Barrier Instrument

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

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

Price = 8.5014

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results

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

    8.5014    0.85673    0.0057199    5.0388    -1.8461    26.238    6.1837

Price Barrier Instrument Using Black-Scholes Model and Asset Tree Pricer

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

Create Barrier Instrument Object

Use fininstrument to create an Barrier instrument object.

BarrierOpt = fininstrument("Barrier",'Strike',45,'ExerciseDate',datetime(2019,1,1),'OptionType',"call",'ExerciseStyle',"american",'BarrierType',"DO",'BarrierValue',40,'Name',"barrier_option")

BarrierOpt = 
  Barrier with properties:

       OptionType: "call"
           Strike: 45
      BarrierType: "do"
     BarrierValue: 40
           Rebate: 0
    ExerciseStyle: "american"
     ExerciseDate: 01-Jan-2019
             Name: "barrier_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.30)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
Maturity = datetime(2023,1,1);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2023
                Rates: 0.0350
               Settle: 01-Jan-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetTree Pricer Object

Use finpricer to create an AssetTree pricer object with an EQP equity tree and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

NumPeriods = 15;
EQPPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'PricingMethod',"EqualProbability",'Maturity',datetime(2019,1,1),'NumPeriods',NumPeriods)

EQPPricer = 
  EQPTree with properties:

             Tree: [1x1 struct]
       NumPeriods: 15
            Model: [1x1 finmodel.BlackScholes]
    DiscountCurve: [1x1 ratecurve]
        SpotPrice: 1000
     DividendType: "continuous"
    DividendValue: 0
        TreeDates: [1x15 datetime]

EQPPricer.Tree

ans = struct with fields:
    Probs: [2x15 double]
    ATree: {1x16 cell}
     dObs: [1x16 datetime]
     tObs: [1x16 double]

Price Barrier Instrument

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

[Price, outPR] = price(EQPPricer,BarrierOpt,["all"])

Price = 956.5478

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results

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

    956.55      1      9.3133e-18    -6.8212e-09    1.0454    43.45    -1.5208

outPR.PricerData.PriceTree

ans = struct with fields:
     PTree: {1x16 cell}
    ExTree: {1x16 cell}
      tObs: [1x16 double]
      dObs: [1x16 datetime]
     Probs: [2x15 double]

Price Barrier Instrument Using Black-Scholes Model and Asset Monte-Carlo Pricer

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

Create Barrier Instrument Object

Use fininstrument to create an Barrier instrument object.

BarrierOpt = fininstrument("Barrier",'Strike',45,'ExerciseDate',datetime(2019,1,1),'OptionType',"call",'ExerciseStyle',"american",'BarrierType',"DO",'BarrierValue',40,'Name',"barrier_option")

BarrierOpt = 
  Barrier with properties:

       OptionType: "call"
           Strike: 45
      BarrierType: "do"
     BarrierValue: 40
           Rebate: 0
    ExerciseStyle: "american"
     ExerciseDate: 01-Jan-2019
             Name: "barrier_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.30)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
Maturity = datetime(2023,1,1);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2023
                Rates: 0.0350
               Settle: 01-Jan-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',200,'simulationDates',datetime(2019,1,1))

outPricer = 
  GBMMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: 200
    SimulationDates: 01-Jan-2019
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.BlackScholes]
       DividendType: "continuous"
      DividendValue: 0

Price Barrier Instrument

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

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

Price = 156.6270

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results

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

    156.63    1.0004    -7.6028e-12    1.2774    43.45      0      0.67904

Price Barrier Instrument Using Heston Model and Asset Monte-Carlo Pricer

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

Create Barrier Instrument Object

Use fininstrument to create an Barrier instrument object.

BarrierOpt = fininstrument("Barrier",'Strike',45,'ExerciseDate',datetime(2019,1,1),'OptionType',"call",'ExerciseStyle',"american",'BarrierType',"DO",'BarrierValue',40,'Name',"barrier_option")

BarrierOpt = 
  Barrier with properties:

       OptionType: "call"
           Strike: 45
      BarrierType: "do"
     BarrierValue: 40
           Rebate: 0
    ExerciseStyle: "american"
     ExerciseDate: 01-Jan-2019
             Name: "barrier_option"

Create Heston Model Object

Use finmodel to create a Heston model object.

HestonModel = finmodel("Heston",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9)

HestonModel = 
  Heston with properties:

        V0: 0.0320
    ThetaV: 0.1000
     Kappa: 0.0030
    SigmaV: 0.2000
     RhoSV: 0.9000

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
Maturity = datetime(2023,1,1);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2023
                Rates: 0.0350
               Settle: 01-Jan-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",HestonModel,'SpotPrice',200,'simulationDates',datetime(2019,1,1))

outPricer = 
  HestonMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: 200
    SimulationDates: 01-Jan-2019
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.Heston]
       DividendType: "continuous"
      DividendValue: 0

Price Barrier Instrument

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

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

Price = 156.9962

outPR = 
  priceresult with properties:

       Results: [1x8 table]
    PricerData: [1x1 struct]

outPR.Results

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

     157     1.0022    -1.08e-12    1.2768    43.45      0      2.7882    0.0013677

More About

Barrier Option

A barrier option has not only a strike price but also a barrier level and sometimes a rebate.

The payoff for this type of option depends on whether the underlying asset crosses the predetermined trigger value (barrier level), indicated by BarrierValue, during the life of the option. If the option cannot be exercised because the barrier level either has or has not been reached, a fixed rebate amount is paid. For more information, see Barrier Option.