Bates

Create Bates model object for Vanilla instrument

Description

Create and price a Vanilla instrument object with a Bates model using this workflow:

  1. Use fininstrument to create a Vanilla instrument object.

  2. Use finmodel to specify a Bates model object for the Vanilla instrument.

  3. Use finpricer to specify a FiniteDifference, NumericalIntegration, or FFT pricing method for the Vanilla 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 pricing methods for a Vanilla instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

BatesObj = finmodel(ModelType,'V0',V0_value,'ThetaV',thetav_value,'Kappa',kappa_value,'SigmaV',sigmav_value,'RhoSV',rhosv_value, 'MeanJ',meanj_value, 'JumpVol',jumpvol_value,'JumpFreq',jumpfreq_value) creates an Bates object by specifying ModelType and the required name-value pair arguments V0, ThetaV, Kappa, SigmaV, RhoSV, MeanJ, JumpVol, and JumpFreq. The required name-value pair arguments set properties. For example, BatesObj = 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) creates a Bates model object.

Input Arguments

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

Data Types: char | string

Bates 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: Bates = 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)

Initial variance of the underlying asset, specified as the comma-separated pair consisting of 'V0' and a scalar numeric value.

Data Types: double

Long-term variance of the underlying asset, specified as the comma-separated pair consisting of 'ThetaV' and a scalar numeric value.

Data Types: double

Mean revision speed for the underlying asset, specified as the comma-separated pair consisting of 'Kappa' and a scalar numeric value.

Data Types: double

Volatility of the variance of the underlying asset, specified as the comma-separated pair consisting of 'SigmaV' and a scalar numeric value.

Data Types: double

Correlation between the Weiner processes for the underlying asset and its variance, specified as the comma-separated pair consisting of 'RhoSV' and a scalar numeric value.

Data Types: double

Mean of the random percentage jump size (J), specified as the comma-separated pair consisting of 'MeanJ' and a scalar decimal value where log(1+J) is normally distributed with mean (log(1+MeanJ)-0.5*JumpVol^2) and the standard deviation JumpVol.

Data Types: double

Standard deviation of log(1+J), where J is the random percentage jump size, specified as the comma-separated pair consisting of 'JumpVol' and a scalar decimal value.

Data Types: double

Annual frequency of the Poisson jump process, specified as the comma-separated pair consisting of 'JumpFreq' and a scalar numeric value.

Data Types: double

Properties

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Initial variance of the underlying asset, returned as a scalar numeric value.

Data Types: double

Long-term variance of the underlying asset, returned as a scalar numeric value.

Data Types: double

Mean revision speed for the underlying asset, returned as a scalar numeric value.

Data Types: double

Volatility of the variance of the underlying asset, returned as a scalar numeric value.

Data Types: double

Correlation between the Weiner processes for the underlying asset and its variance, returned as a scalar numeric value.

Data Types: double

Mean of the random percentage jump size (J), returned as a scalar decimal value.

Data Types: double

Standard deviation of log(1+J), where J is the random percentage jump size, returned as a scalar decimal value.

Data Types: double

Annual frequency of the Poisson jump process, returned as a scalar numeric value.

Data Types: double

Examples

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This example shows the workflow to price a Vanilla instrument when you use a Bates model and a NumericalIntegration pricing method.

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

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

       OptionType: "put"
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2022
           Strike: 105
             Name: "vanilla_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 NumericalIntegration Pricer Object

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

outPricer = finpricer("numericalintegration",'DiscountCurve',myRC,'Model',BatesModel,'SpotPrice',100)
outPricer = 
  NumericalIntegration with properties:

                Model: [1x1 finmodel.Bates]
        DiscountCurve: [1x1 ratecurve]
            SpotPrice: 100
         DividendType: "continuous"
        DividendValue: 0
               AbsTol: 1.0000e-10
               RelTol: 1.0000e-10
     IntegrationRange: [1.0000e-09 Inf]
    CharacteristicFcn: @characteristicFcnBates
            Framework: "heston1993"
       VolRiskPremium: 0
           LittleTrap: 1

Price Vanilla Instrument

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

[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 6.4007
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: []

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

    6.4007    -0.53541    0.02006    1.106    -239.77    94.257    1.3059

Introduced in R2020a