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FFT

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

Description

Create and price a Vanilla instrument object with a Heston, Bates, or Merton model and an FFT 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 an FFT 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

FFTPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj) creates an FFT pricer object by specifying PricerType and sets the properties for the required name-value pair arguments Model and DiscountCurve.

example

FFTPricerObj = finpricer(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, FFTPricerObj = finpricer("FFT",'Model',FFTModel, 'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'DividendValue',0.01,'VolRiskPremium',0.9) creates an FFT 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 "FFT" or a character vector with the value of 'FFT'.

Data Types: char | string

FFT 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: FFTPricerObj = finpricer("FFT",'Model',FFTModel, 'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'DividendValue',0.01,'VolRiskPremium',0.9)
Required FFT Name-Value Pair Arguments

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Model, specified as the comma-separated pair consisting of 'Model' and the name of the 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 the 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 FFT Name-Value Pair Arguments

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

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

Number of grid points in the characteristic function variable and in each column of the log-strike grid, specified as the comma-separated pair consisting of 'NumFFT' and a scalar numeric value.

Data Types: double

Characteristic function variable grid spacing, specified as the comma-separated pair consisting of 'CharacteristicFcnStep' and a scalar numeric value.

Data Types: double

Log-strike grid spacing, specified as the comma-separated pair consisting of 'LogStrikeStep' and a scalar numeric value.

Note

If (LogStrikeStep*CharacteristicFcnStep) is 2*pi/NumFFT, FFT is used. Otherwise, FRFT is used.

Data Types: double

Damping factor for the Carr-Madan formulation, specified as the comma-separated pair consisting of 'DampingFactor' and a scalar numeric value.

Data Types: double

Type of quadrature, specified as the comma-separated pair consisting of 'Quadrature' and a scalar string or character vector.

Data Types: char | string

Properties

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Model, returned as a model 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 nonnegative numeric in decimals.

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

Number of grid points in the characteristic function variable and in each column of the log-strike grid, returned as a scalar numeric value.

Data Types: double

Characteristic function variable grid spacing, returned as a scalar numeric value.

Data Types: double

Log-strike grid spacing, returned as a scalar numeric value.

Data Types: double

Damping factor for the Carr-Madan formulation, returned as a scalar numeric value.

Data Types: double

Type of quadrature, returned as a string.

Data Types: string

Object Functions

priceCompute price for equity instrument with FFT pricer

Examples

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This example shows the workflow to price a Vanilla instrument when you use a Heston model and an FFT pricing method.

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

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

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

Create Heston Model Object

Use finmodel to create a Heston model object.

HestonModel = finmodel("Heston",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9)
HestonModel = 
  Heston with properties:

        V0: 0.0320
    ThetaV: 0.1000
     Kappa: 0.0030
    SigmaV: 0.2000
     RhoSV: 0.9000

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 FFT Pricer Object

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

outPricer = finpricer("fft",'DiscountCurve',myRC,'Model',HestonModel,'SpotPrice',100,'CharacteristicFcnStep', 0.2,'NumFFT',2^13)
outPricer = 
  FFT with properties:

                    Model: [1x1 finmodel.Heston]
            DiscountCurve: [1x1 ratecurve]
                SpotPrice: 100
             DividendType: "continuous"
            DividendValue: 0
                   NumFFT: 8192
    CharacteristicFcnStep: 0.2000
            LogStrikeStep: 0.0038
        CharacteristicFcn: @characteristicFcnHeston
            DampingFactor: 1.5000
               Quadrature: "simpson"
           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 = 14.7545
outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: []

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

    14.754    0.44868    0.021649    -0.20891    120.45    88.192    1.3248

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