Lookback

Lookback instrument

Description

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

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

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

3. Choose a pricing method.

   • When using a BlackScholes model, use finpricer to specify a ConzeViswanathan, AssetTree, or GoldmanSosinGatto pricing method for one or more Lookback instruments.

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

Creation

Syntax

LookbackObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date)

LookbackObj = fininstrument(___,Name,Value)

Description

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

The Lookback instrument supports fixed-strike and floating-strike lookback options. For more information on a Lookback instrument, see More About.

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

Input Arguments

InstrumentType — Instrument type

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

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

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: LookbackObj = fininstrument("Lookback",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"lookback_option")

Required Lookback Name-Value Pair Arguments

Strike — Option strike price value

nonnegative numeric | vector of nonnegative values | NaN

Option strike price value, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative numeric value or an NINST-by-1 vector of nonnegative values for a fixed-strike Lookback option. For a floating-strike Lookback option, specify 'Strike' as a NaN or an NINST-by-1 vector of NaNs.

Note

Use the ConzeViswanathan pricer for a fixed strike Lookback option and use the GoldmanSosinGatto pricer for a floating strike Lookback option.

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.

Note

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

To support existing code, Lookback 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.

Optional Lookback 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 lookback call option gives the holder the right to buy the underlying asset at the highest price observed during the option's term. This allows the holder to benefit from the highest possible purchase price.

A lookback put option provides the holder with the right to sell the underlying asset at the lowest price observed during the option's term. This allows the holder to take advantage of the lowest possible selling price.

Data Types: char | cell | string

ExerciseStyle — Option exercise style

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

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.

Lookback options can be either European-style or American-style, depending on when they can be exercised:

• European Lookback Option — This type of lookback option can only be exercised at the expiration date.

• American Lookback Option — An American-style lookback option allows the holder to exercise the option at any time during the option's term.

Data Types: string | cell | char

AssetMinMax — Maximum or minimum underlying asset price

NaN where SpotPrice of the underlying asset is used (default) | scalar numeric | numeric vector

Maximum or minimum underlying asset price, specified as the comma-separated pair consisting of 'AssetMinMax' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

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

Output Arguments

LookbackObj — Lookback instrument

Lookback object

Lookback instrument, returned as a Lookback object.

Properties

Strike — Option strike price value

nonnegative numeric | vector of nonnegative values

Option strike price value, returned as a scalar nonnegative numeric 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

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

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

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

Data Types: string

AssetMinMax — Maximum or minimum underlying asset price

NaN where SpotPrice of the underlying asset is used (default) | scalar numeric | numeric vector

Maximum or minimum underlying asset price, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Name — User-defined name for instrument

" " (default) | string | string array

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

Data Types: string

Examples

Price Lookback Instrument Using BlackScholes Model and ConzeViswanathan Pricer

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

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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 ConzeViswanathan Pricer Object

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

outPricer = finpricer("analytic","Model",BlackScholesModel,"DiscountCurve",myRC,"SpotPrice",100,"DividendValue",0.25,"DividendType","continuous","PricingMethod","ConzeViswanathan")

outPricer = 
  ConzeViswanathan with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 100
    DividendValue: 0.2500
     DividendType: "continuous"

Price Lookback Instrument

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

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

Price = 
57.8786

outPR = 
  priceresult with properties:

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

outPR.Results

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

    57.879    -0.33404      0      -0.57714    32.587    -5.1863    -350.41

Price Multiple Lookback Instruments Using BlackScholes Model and ConzeViswanathan Pricer

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

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object for three Lookback instruments.

LookbackOpt = fininstrument("Lookback",'Strike',[105 ; 120; 140],'ExerciseDate',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt=3×1 Lookback array with properties:
    OptionType
    Strike
    AssetMinMax
    ExerciseStyle
    ExerciseDate
    Name

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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 ConzeViswanathan Pricer Object

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

outPricer = finpricer("analytic","Model",BlackScholesModel,"DiscountCurve",myRC,"SpotPrice",100,"DividendValue",0.25,"DividendType","continuous","PricingMethod","ConzeViswanathan")

outPricer = 
  ConzeViswanathan with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 100
    DividendValue: 0.2500
     DividendType: "continuous"

Price Lookback Instruments

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

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

Price = 3×1

   57.8786
   71.3008
   88.9673

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

outPR.Results

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

    57.879    -0.33404      0      -0.57714    32.587    -5.1863    -350.41

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

    71.301    -0.32722    2.8422e-06    -0.45894    31.997    -4.5677    -410.15

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

    88.967    -0.32033    1.4211e-06    -0.36005    31.395    -3.7989    -489.96

Price Lookback Instrument Using BlackScholes Model and AssetTree Pricer for LR Binomial Tree

This example shows the workflow to price a LookBack instrument when you use an BlackScholes model and an AssetTree pricing method using a Leisen-Reimer (LR) binomial tree.

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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 AssetTree Pricer Object

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

NumPeriods = 15;
LRPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',150,'PricingMethod',"LeisenReimer",'Maturity',datetime(2022,9,15),'NumPeriods',NumPeriods)

LRPricer = 
  LRTree with properties:

    InversionMethod: PP1
             Strike: 150
               Tree: [1×1 struct]
         NumPeriods: 15
              Model: [1×1 finmodel.BlackScholes]
      DiscountCurve: [1×1 ratecurve]
          SpotPrice: 150
       DividendType: "continuous"
      DividendValue: 0
          TreeDates: [21-Dec-2018 09:36:00    28-Mar-2019 19:12:00    04-Jul-2019 04:48:00    09-Oct-2019 14:24:00    15-Jan-2020 00:00:00    21-Apr-2020 09:36:00    27-Jul-2020 19:12:00    02-Nov-2020 04:48:00    …    ] (1×15 datetime)

LRPricer.Tree

ans = struct with fields:
    Probs: [2×15 double]
    ATree: {1×16 cell}
     dObs: [15-Sep-2018 00:00:00    21-Dec-2018 09:36:00    28-Mar-2019 19:12:00    04-Jul-2019 04:48:00    09-Oct-2019 14:24:00    15-Jan-2020 00:00:00    21-Apr-2020 09:36:00    27-Jul-2020 19:12:00    02-Nov-2020 04:48:00    …    ] (1×16 datetime)
     tObs: [0 0.2667 0.5333 0.8000 1.0667 1.3333 1.6000 1.8667 2.1333 2.4000 2.6667 2.9333 3.2000 3.4667 3.7333 4]

Price Lookback Instrument

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

[Price, outPR] = price(LRPricer,LookbackOpt,["all"])

Price = 
3.9412

outPR = 
  priceresult with properties:

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

outPR.Results

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

    3.9412    -0.13312    -0.011131    67.684    -5.0757    -73.857    -1.0383

Price Lookback Instrument Using BlackScholes Model and AssetTree Pricer for Standard Trinomial Tree

This example shows the workflow to price a LookBack instrument when you use an BlackScholes model and an AssetTree pricing method using a Standard Trinomial (STT) tree.

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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 AssetTree Pricer Object

Use finpricer to create an AssetTree pricer object for a Standard Trinomial (STT) equity tree and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

NumPeriods = 15;
STTPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',150,'PricingMethod',"StandardTrinomial",'Maturity',datetime(2022,9,15),'NumPeriods',NumPeriods)

STTPricer = 
  STTree with properties:

             Tree: [1×1 struct]
       NumPeriods: 15
            Model: [1×1 finmodel.BlackScholes]
    DiscountCurve: [1×1 ratecurve]
        SpotPrice: 150
     DividendType: "continuous"
    DividendValue: 0
        TreeDates: [21-Dec-2018 09:36:00    28-Mar-2019 19:12:00    04-Jul-2019 04:48:00    09-Oct-2019 14:24:00    15-Jan-2020 00:00:00    21-Apr-2020 09:36:00    27-Jul-2020 19:12:00    02-Nov-2020 04:48:00    …    ] (1×15 datetime)

STTPricer.Tree

ans = struct with fields:
    ATree: {1×16 cell}
    Probs: {[3×1 double]  [3×3 double]  [3×5 double]  [3×7 double]  [3×9 double]  [3×11 double]  [3×13 double]  [3×15 double]  [3×17 double]  [3×19 double]  [3×21 double]  [3×23 double]  [3×25 double]  [3×27 double]  [3×29 double]}
     dObs: [15-Sep-2018 00:00:00    21-Dec-2018 09:36:00    28-Mar-2019 19:12:00    04-Jul-2019 04:48:00    09-Oct-2019 14:24:00    15-Jan-2020 00:00:00    21-Apr-2020 09:36:00    27-Jul-2020 19:12:00    02-Nov-2020 04:48:00    …    ] (1×16 datetime)
     tObs: [0 0.2667 0.5333 0.8000 1.0667 1.3333 1.6000 1.8667 2.1333 2.4000 2.6667 2.9333 3.2000 3.4667 3.7333 4]

Price Lookback Instrument

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

[Price, outPR] = price(STTPricer,LookbackOpt,["all"])

Price = 
3.3392

outPR = 
  priceresult with properties:

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

outPR.Results

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

    3.3392    -0.15942    -1.0596e-11    63.886    -7.1613    -68.263    -1.0254

Price Lookback Instrument Using BlackScholes Model and AssetMonteCarlo Pricer

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

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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',200,'simulationDates',datetime(2022,9,15))

outPricer = 
  GBMMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 200
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.BlackScholes]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Lookback Instrument

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

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

Price = 
1.8553

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 
    ______    _________    __________    _______    _______    ________    ______

    1.8553    -0.040442    0.00062792    -4.3596    -39.426    -0.71345    42.311

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

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

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)

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',200,'simulationDates',datetime(2022,9,15),'NumTrials',1e3, ...
                     'MonteCarloMethod',"quasi",'BrownianMotionMethod',"brownian-bridge")

outPricer = 
  GBMMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 200
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.BlackScholes]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "quasi"
    BrownianMotionMethod: "brownian-bridge"

Price Lookback Instrument

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

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

Price = 
1.8493

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 
    ______    _________    _________    _______    _______    ________    ______

    1.8493    -0.045633    0.0011617    -4.9352    -43.807    -0.79718    47.192

Price Lookback Instrument Using Bates Model and AssetMonteCarlo Pricer

This example shows the workflow to price a LookBack instrument when you use a Bates model and an AssetMonetCarlo pricing method.

Create Lookback Instrument Object

Use fininstrument to create a Lookback instrument object.

LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")

LookbackOpt = 
  Lookback with properties:

       OptionType: "put"
           Strike: 105
      AssetMinMax: NaN
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
             Name: "lookback_option"

Create Bates Model Object

Use finmodel to create a Bates model object.

BatesModel = finmodel("Bates",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9,'MeanJ',0.11,'JumpVol',.023,'JumpFreq',0.02)

BatesModel = 
  Bates with properties:

          V0: 0.0320
      ThetaV: 0.1000
       Kappa: 0.0030
      SigmaV: 0.2000
       RhoSV: 0.9000
       MeanJ: 0.1100
     JumpVol: 0.0230
    JumpFreq: 0.0200

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",BatesModel,'SpotPrice',100,'simulationDates',datetime(2022,9,15))

outPricer = 
  BatesMonteCarlo with properties:

           DiscountCurve: [1×1 ratecurve]
               SpotPrice: 100
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1×1 finmodel.Bates]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Lookback Instrument

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

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

Price = 
7.2577

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 
    ______    ________    _____    _______    _______    _________    ______    _______

    7.2577    -0.84025      0      -11.577    -29.025    -0.027666    30.748    0.68416

More About

Lookback Option

A lookback option is a path-dependent option based on the maximum or minimum value the underlying asset achieves during the entire life of the option.

A lookback option's value is derived from an underlying asset, such as a stock, index, or currency pair. The option holder has the right to buy (call option) or sell (put option) the underlying asset at the most favorable price observed during the specified period.

Financial Instruments Toolbox™ software supports two types of lookback options: fixed and floating. Fixed lookback options have a specified strike price, while floating lookback options have a strike price determined by the asset path. For more information, see Lookback Option.

Version History

Introduced in R2020a

R2022b: Serial date numbers not recommended

Although Lookback 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.