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Asian

Asian instrument object

Description

Create and price an Asian instrument object using this workflow:

  1. Use fininstrument to create an Asian instrument object.

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

  3. When using a BlackScholes model, use finpricer to specify a Levy, KemnaVorst, or TurnbullWakeman pricing method for the Asian instrument.

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

Creation

Description

example

AsianOpt = fininstrument(InstrumentType,'Strike',strike_price,'ExerciseDate',exercise_date) creates an Asian object by specifying InstrumentType and sets the properties for the required name-value pair arguments Strike and ExerciseDate.

The Asian instrument supports arithmetic and geometric average price Asian options. Average price Asian options are also known as fixed-strike Asian options.

example

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

Input Arguments

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

Data Types: string | char

Asian 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: AsianOpt = fininstrument("Asian",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"asian_option")
Required Asian Name-Value Pair Arguments

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

Data Types: double

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 an Asian 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

Optional Asian Name-Value Pair Arguments

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

Data Types: char | string

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

Data Types: string | char

Average types, specified as the comma-separated pair consisting of 'AverageType' and a scalar string or character vector. Use "arithmetic" for an arithmetic average, or "geometric" for a geometric average.

Note

When you use a RollGeskeWhaley pricer, the AverageType must be "geometric".

Data Types: char | string

Average price of the underlying asset, specified as the comma-separated pair consisting of 'AveragePrice' and a scalar numeric.

Data Types: double

Start date of averaging period, specified as the comma-separated pair consisting of 'AverageStartDate' and a scalar datetime, serial date number, date character vector, or date string.

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

Data Types: char | double | datetime | string

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

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Option strike price value, returned as a scalar nonnegative value.

Data Types: double

Option exercise date, returned as a datetime.

Data Types: datetime

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

Data Types: string

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

Data Types: string

Average types, returned as a scalar string with the value "arithmetic" for arithmetic average or "geometric" for geometric average.

Data Types: string

Average price of underlying asset at Settle, returned as a scalar numeric.

Data Types: double

Start date of averaging period, returned as a scalar datetime.

Data Types: datetime

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

Data Types: string

Examples

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This example shows the workflow to price a fixed-strike Asian instrument when you use a BlackScholes model and a TurnbullWakeman pricing method.

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 1000
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_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 TurnbullWakeman Pricer Object

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

outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'PricingMethod',"TurnbullWakeman")
outPricer = 
  TurnbullWakeman with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.BlackScholes]
        SpotPrice: 1000
    DividendValue: 0
     DividendType: "continuous"

Price Asian Instrument

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

[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 56.7068
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: []

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

    56.707    -0.3155    0.0014381    -5.5637    408.85    -2.9341    -832.53

This example shows the workflow to price an Asian instrument for an arithmetic average currency option when you use a BlackScholes model and a Levy pricing method. Assume that the current exchange rate is $0.52 and has a volatility of 12% per annum. The annualized continuously compounded foreign risk-free rate is 8% per annum.

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',0.65,'OptionType',"put",'ExerciseStyle',"european",'Name',"asian_fx_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 0.6500
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_fx_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

Sigma = .12;
BlackScholesModel = finmodel("BlackScholes",'Volatility',Sigma)
BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.1200
    Correlation: 1

Create ratecurve Object

Create a 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 Levy Pricer Object

Use finpricer to create a Levy pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument. When you price currencies using an Asian instrument for an arithmetic average currency option, the DividendType must be 'continuous' and DividendValue is the annualized risk-free interest rate in the foreign country.

ForeignRate = 0.08;
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',.52,'DividendType',"continuous",'DividendValue',ForeignRate,'PricingMethod',"Levy")
outPricer = 
  Levy with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.BlackScholes]
        SpotPrice: 0.5200
    DividendValue: 0.0800
     DividendType: "continuous"

Price Asian FX Instrument

Use price to compute the price and sensitivities for the Asian FX instrument.

[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 0.1516
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: []

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

    0.15161    -0.78532    0.37534    -2.6935    0.015668    -0.0038317    -1.3974

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

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 1000
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_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: [1x1 ratecurve]
          SpotPrice: 200
    SimulationDates: 15-Sep-2022
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.BlackScholes]
       DividendType: "continuous"
      DividendValue: 0

Price Asian Instrument

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

[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 682.3365
outPR = 
  priceresult with properties:

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

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

    682.34    -0.93511    -5.6843e-14    -0.27409    -3129.1    27.433    -1.2121

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

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 1000
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_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',200,'simulationDates',datetime(2022,9,15))
outPricer = 
  MertonMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: 200
    SimulationDates: 15-Sep-2022
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.Merton]
       DividendType: "continuous"
      DividendValue: 0

Price Asian Instrument

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

[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 683.2017
outPR = 
  priceresult with properties:

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

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

    683.2    -0.9047    -1.9895e-13    -0.26484    -3110.3    25.93    20.227

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Introduced in R2020a