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NumericalIntegration

Create NumericalIntegration pricer object for Vanilla instrument using Heston, Bates, or Merton model

Description

Create and price a Vanilla instrument object with a Heston, Bates, or Merton model and a NumericalIntegration pricing method using this workflow:

  1. Use fininstrument to create a Vanilla instrument object.

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

  3. Use finpricer to specify a NumericalIntegration pricer object 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

NumericalIntegrationPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj,'SpotPrice',spotprice_value) creates a NumericalIntegration pricer object by specifying PricerType and sets the properties for the required name-value pair arguments Model, DiscountCurve, and SpotPrice.

example

NumericalIntegrationPricerObj = finpricer(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, NumericalIntegrationPricerObj = finpricer("NumericalIntegration",'Model',NIModel,'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'DividendValue',100,'VolRiskPremium',0.9) creates a NumericalIntegration pricer object. You can specify multiple name-value pair arguments.

Input Arguments

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

Data Types: char | string

NumericalIntegration 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: NumericalIntegrationPricerObj = finpricer("NumericalIntegration",'Model',NIModel,'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'DividendValue',100,'VolRiskPremium',0.9)
Required NumericalIntegration Name-Value Pair Arguments

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Model, specified as the comma-separated pair consisting of 'Model' and the name of a previously created Merton, Bates, or Heston model object using finmodel.

Data Types: object

This property is read-only.

ratecurve object for discounting cash flows, specified as the comma-separated pair consisting of 'DiscountCurve' and the name of a ratecurve object.

Note

Specify a flat ratecurve object for DiscountCurve. If you use a nonflat ratecurve object, the software uses the rate in the ratecurve object at Maturity and assumes that the value is constant for the life of the equity option.

Data Types: object

Current price of the underlying asset, specified as the comma-separated pair consisting of 'SpotPrice' and a scalar nonnegative numeric.

Data Types: double

Optional NumericalIntegration Name-Value Pair Arguments

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Dividend yield, specified as the comma-separated pair consisting of 'DividendValue' and a scalar numeric.

Data Types: double

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

Data Types: double

Flag indicating Little Heston Trap formulation by Albrecher et al., specified as the comma-separated pair consisting of 'LittleTrap' and a logical:

Note

LittleTrap is supported only for Heston and Bates models.

Data Types: logical

Absolute error tolerance for numerical integration, specified as the comma-separated pair consisting of 'AbsTol' and a scalar numeric value.

Data Types: double

Relative error tolerance for numerical integration, specified as the comma-separated pair consisting of 'RelTol' and a scalar numeric value.

Data Types: double

Numerical integration range used to approximate the continuous integral over [0 Inf], specified as the comma-separated pair consisting of 'IntegrationRange' and a 1-by-2 vector representing [LowerLimit UpperLimit].

Data Types: double

Framework for computing option prices and sensitivities using the numerical integration of models, specified as the comma-separated pair consisting of 'Framework' and a scalar string or character vector with the following values:

  • "heston1993" or 'heston1993' — Method used in Heston (1993)

  • "lewis2001" or 'lewis2001' — Method used in Lewis (2001)

Data Types: char | string

Properties

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Model, returned as a model object.

Data Types: object

ratecurve object for discounting cash flows, returned as a ratecurve object.

Data Types: object

Current price of the underlying asset, returned as a scalar nonnegative numeric.

Data Types: double

Dividend yield, returned as a scalar numeric.

Data Types: double

Volatility risk premium, returned as a scalar numeric value.

Data Types: double

Flag indicating Little Heston Trap formulation by Albrecher et al., returned as a logical.

Data Types: logical

Absolute error tolerance for numerical integration, returned as a scalar numeric value.

Data Types: double

Relative error tolerance for numerical integration, returned as a scalar numeric value.

Data Types: double

Numerical integration range used to approximate the continuous integral over [0 Inf], returned as a 1-by-2 vector representing [LowerLimit UpperLimit].

Data Types: double

Framework for computing option prices and sensitivities using the numerical integration of models, returned as a scalar string.

Data Types: string

Object Functions

priceCompute price for equity instrument with NumericalIntegration pricer

Examples

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

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2020,3,15),'ExerciseStyle',"european",'Strike',105,'Name',"vanilla_option")
VanillaOpt = 
  Vanilla with properties:

       OptionType: "call"
    ExerciseStyle: "european"
     ExerciseDate: 15-Mar-2020
           Strike: 105
             Name: "vanilla_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.

myRC = ratecurve('zero',datetime(2019,9,15),datetime(2020,3,15),0.02)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: 15-Mar-2020
                Rates: 0.0200
               Settle: 15-Sep-2019
         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",'Model',MertonModel,'DiscountCurve',myRC,'SpotPrice',100,'DividendValue',.01,'VolRiskPremium',0.9,'LittleTrap',false,'AbsTol',0.5,'RelTol',0.4,'Framework',"lewis2001")
outPricer = 
  NumericalIntegration with properties:

                Model: [1x1 finmodel.Merton]
        DiscountCurve: [1x1 ratecurve]
            SpotPrice: 100
         DividendType: "continuous"
        DividendValue: 0.0100
               AbsTol: 0.5000
               RelTol: 0.4000
     IntegrationRange: [1.0000e-09 Inf]
    CharacteristicFcn: @characteristicFcnMerton76
            Framework: "lewis2001"
       VolRiskPremium: 0.9000
           LittleTrap: 0

Price Vanilla Instrument

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

[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 10.7325
outPR = 
  priceresult with properties:

       Results: [1x6 table]
    PricerData: []

outPR.Results
ans=1×6 table
    Price     Delta      Gamma       Theta      Rho       Vega 
    ______    ______    ________    _______    ______    ______

    10.732    0.5058    0.012492    -12.969    19.815    27.954

More About

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References

[1] Albrecher, H., P. Mayer, W. Schoutens, and J. Tistaert. “The Little Heston Trap.” Working Paper, Linz and Graz University of Technology, K.U. Leuven, ING Financial Markets, 2006.

Introduced in R2020a