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

Syntax

AsianOpt = fininstrument(InstrumentType,'Strike',strike_price,'ExerciseDate',exercise_date)

AsianOpt = fininstrument(___,Name,Value)

Description

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.

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

InstrumentType — Instrument type

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

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

'Strike' — Option strike price value

nonnegative value

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

Data Types: double

'ExerciseDate' — Option exercise dates

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 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

'OptionType' — Option type

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

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

Data Types: char | string

'ExerciseStyle' — Option exercise style

"European" (default) | string with value "European" | character vector with value 'European'

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

Data Types: string | char

'AverageType' — Average type

"arithmetic" (default) | string with value "arithmetic" or "geometric" | character vector with value 'arithmetic' or 'geometric'

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

'AveragePrice' — Average price of underlying asset

0 (default) | scalar numeric

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

Data Types: double

'AverageStartDate' — Start date of averaging period

NaT (default) | datetime | serial date number | date character vector | date string

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

'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 price value

nonnegative value

Option strike price 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"

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

Data Types: string

AverageType — Average type

"arithmetic" (default) | string with value "arithmetic" or "geometric"

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

Data Types: string

AveragePrice — Average price of underlying asset at Settle

0 (default) | scalar numeric

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

Data Types: double

AverageStartDate — Start date of averaging period

NaT (default) | datetime

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

Data Types: datetime

Name — User-defined name for instrument

" " (default) | string

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

Data Types: string

Examples

Price Asian Instrument Using a Black-Scholes Model and Turnbull-Wakeman Pricer

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

Price Asian Instrument for Foreign Exchange Using Black-Scholes Model and Levy Pricer

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

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

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

Price Asian Instrument Using a Merton Model and Asset Monte-Carlo Pricer

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

More About

Asian Option

An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option.

Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.