Compute price for equity instrument with NumericalIntegration pricer



[Price,PriceResult] = price(inpPricer,inpInstrument) computes the instrument price and related pricing information based on the pricing object inpPricer and the instrument object inpInstrument.


[Price,PriceResult] = price(___,inpSensitivity) adds an optional argument to specify sensitivities.


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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: []

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

    10.732    0.5058    0.012492    -12.969    19.815    27.954

Input Arguments

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Pricer object, specified as a scalar NumericalIntegration pricer object. Use finpricer to create the NumericalIntegration pricer object.

Data Types: object

Instrument object, specified as a scalar Vanilla instrument object. Use fininstrument to create the Vanilla instrument object.

Data Types: object

(Optional) List of sensitivities to compute, specified as a NOUT-by-1 or a 1-by-NOUT cell array of character vectors or string array with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Rho', 'Theta', 'Vegalt', and 'All'.


'Vegalt' is not supported when you price a Vanilla option with a Merton model.

inpSensitivity = {'All'} or inpSensitivity = ["All"] specifies that the output is Delta, Gamma, Vega, Rho, Theta, Vegalt, and Price. This is the same as specifying inpSensitivity to include each sensitivity.

Example: inpSensitivity = {'delta','gamma','vega','rho','theta','vegalt','price'}

Data Types: string | cell

Output Arguments

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Instrument price, returned as a numeric.

Price result, returned as an object. The PriceResult object. The object has the following fields:

  • PriceResult.Results — Table of results that includes sensitivities (if you specify inpSensitivity)

  • PriceResult.PricerData — Structure for pricer data

Introduced in R2020a