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Bachelier

Create Bachelier model object for Vanilla, Spread, or Binary instrument

Description

Create and price a Vanilla, Spread, or Binary instrument object with a Bachelier model using this workflow:

  1. Use fininstrument to create a Vanilla, Spread, or Binary instrument object.

  2. Use finmodel to specify a Bachelier model object for the Vanilla, Spread, or Binary instrument object.

  3. Use finpricer to specify an AssetMonteCarlo pricing method for the Vanilla, Spread, or Binary instrument object.

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 pricing methods for a Vanilla, Spread, or Binary instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

BachelierModelObj = finmodel(ModelType,'Volatility',volatility_value) creates a Bachelier model object by specifying ModelType and the required name-value pair argument Volatility to set properties using name-value pair arguments. For example, BachelierModelObj = finmodel("Bachelier",'Volatility',0.063) creates a Bachelier model object.

example

BachelierModelObj = finmodel(ModelType,Name,Value) sets optional properties using an additional name-value pair argument in addition to the required arguments in the previous syntax. For example, BachelierModelObj = finmodel("Bachelier",'Volatility',0.063,'Correlation',Corr) creates a Bachelier model object with a specified Correlation value.

Input Arguments

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Model type, specified as a string with the value "Bachelier" or a character vector with the value 'Bachelier'.

Data Types: char | string

Bachelier Name-Value Pair Arguments

Specify required 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: BachelierModelObj = finmodel("Bachelier",'Volatility',0.063,'Correlation',Corr)

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

Data Types: double

Correlation for the underlying assets, specified as the comma-separated pair consisting of 'Correlation' and a positive semidefinite matrix. For more information on creating a positive semidefinite matrix, see nearcorr.

Data Types: double

Properties

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Volatility value, returned as a scalar nonnegative numeric.

Data Types: double

Correlation for the underlying assets, returned as a matrix.

Data Types: double

Examples

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

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

VanillaOpt = fininstrument("Vanilla",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"call",'ExerciseStyle',"american",'Name',"vanilla_option")
VanillaOpt = 
  Vanilla with properties:

       OptionType: "call"
    ExerciseStyle: "american"
     ExerciseDate: 15-Sep-2022
           Strike: 105
             Name: "vanilla_option"

Create Bachelier Model Object

Use finmodel to create a Bachelier model object.

BachelierModel = finmodel("Bachelier","Volatility",0.2)
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',150,'simulationDates',datetime(2022,9,15))
outPricer = 
  BachelierMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: 150
    SimulationDates: 15-Sep-2022
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.Bachelier]
       DividendType: "continuous"
      DividendValue: 0

Price Vanilla Instrument

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

[Price, outPR] = price(outPricer,VanillaOpt,"all")
Price = 57.3776
outPR = 
  priceresult with properties:

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

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

    57.378    0.99107    -1.579e-14    2.5909    291.94    -2.5576    -2.1316e-10

Introduced in R2021a