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price

Compute price for equity instrument with RoughVolMonteCarlo pricer

Since R2024a

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Syntax

[Price,PriceResult] = price(inpPricer,inpInstrument)
[Price,PriceResult] = price(___,inpSensitivity)

Description

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

example

[Price,PriceResult] = price(___,inpSensitivity) adds an optional argument to specify sensitivities. Use this syntax with the input argument combination in the previous syntax.

example

Examples

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Open Live Script

This example shows the workflow to price a fixed-strike Asian instrument when you use a RoughBergomi model and an RoughVolMonteCarlo pricing method.

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object. 

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2019,1,30),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 1000
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 30-Jan-2019
                Name: "asian_option"

Create RoughBergomi Model Object

Use finmodel to create a RoughBergomi model object. 

RoughBergomiModel = finmodel("RoughBergomi",Alpha=-0.32, Xi=0.1,Eta=0.003,RhoSV=0.9)
RoughBergomiModel = 
  RoughBergomi with properties:

    Alpha: -0.3200
       Xi: 0.1000
      Eta: 0.0030
    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 RoughVolMonteCarlo Pricer Object

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

outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughBergomiModel,SpotPrice=900,simulationDates=datetime(2019,1,30))
outPricer = 
  RoughBergomiMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: 900
         SimulationDates: 30-Jan-2019
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.RoughBergomi]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Asian Instrument

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

[Price, outPR] = price(outPricer,AsianOpt,"all")
Price = 
103.0639

outPR = 
  priceresult with properties:

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


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

    103.06    -0.77793    0.0024128    -6.7932    -166.05    -1.4838    88.272

Since R2024b

Open Live Script

This example shows the workflow to price a fixed-strike Asian instrument when you use a RoughHeston model and a RoughVolMonteCarlo pricing method.

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object. 

AsianOpt = fininstrument("Asian",ExerciseDate=datetime(2019,1,30),Strike=1000,OptionType="put",Name="asian_option")
AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 1000
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 30-Jan-2019
                Name: "asian_option"

Create RoughHeston Model Object

Use finmodel to create a RoughHeston model object. 

RoughHestonModel = finmodel("RoughHeston",V0=0.4,ThetaV=0.3,Kappa=0.2,SigmaV=0.1,Alpha=-0.02,RhoSV=0.3)
RoughHestonModel = 
  RoughHeston with properties:

     Alpha: -0.0200
        V0: 0.4000
    ThetaV: 0.3000
     Kappa: 0.2000
    SigmaV: 0.1000
     RhoSV: 0.3000

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 RoughVolMonteCarlo Pricer Object

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

outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughHestonModel,SpotPrice=900,simulationDates=datetime(2019,1,30))
outPricer = 
  RoughHestonMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: 900
         SimulationDates: 30-Jan-2019
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.RoughHeston]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Asian Instrument

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

[Price, outPR] = price(outPricer,AsianOpt,"all")
Price = 
131.2194

outPR = 
  priceresult with properties:

       Results: [1x8 table]
    PricerData: [1x1 struct]


outPR.Results 
ans=1×8 table
    Price      Delta       Gamma     Lambda      Rho       Theta      Vega     VegaLT
    ______    ________    _______    _______    ______    _______    ______    ______

    131.22    -0.67246    0.00155    -4.6122    -152.4    -74.841    105.65      0

Input Arguments

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Pricer object, specified as a previously created RoughVolMonteCarlo pricer object. Create the pricer object using finpricer.

Data Types: object

Instrument object, specified as a scalar or a vector of previously created instrument objects. Create the instrument objects using fininstrument. The following instrument objects are supported:

Data Types: object

(Optional) List of sensitivities to compute, specified as an NOUT-by-1 or 1-by-NOUT cell array of character vectors or string array.

The supported sensitivities depend on the pricing method.

inpInstrument ObjectSupported Sensitivities
Vanilla{'delta','gamma','vega', 'theta','rho','price','lambda'}
Asian{'delta','gamma','vega','theta','rho','price','lambda'}
Cliquet{'delta','gamma','vega','theta','rho','price','lambda}'
Binary{'delta','gamma','vega','theta','rho','price','lambda'}

inpSensitivity = {'All'} or inpSensitivity = ["All"] specifies that all sensitivities for the pricing method are returned. This is the same as specifying inpSensitivity to include each sensitivity.

Example: inpSensitivity = ["delta","gamma","vega","lambda","rho","theta","price"]

Data Types: cell | string

Output Arguments

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Instrument price, returned as a numeric.

Price result, returned as a 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

More About

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Delta

A delta sensitivity measures the rate at which the price of an option is expected to change relative to a $1 change in the price of the underlying asset.

Delta is not a static measure; it changes as the price of the underlying asset changes (a concept known as gamma sensitivity), and as time passes. Options that are near the money or have longer until expiration are more sensitive to changes in delta.

Gamma

A gamma sensitivity measures the rate of change of an option's delta in response to a change in the price of the underlying asset.

In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. This is important because this helps you understand the convexity of an option's value in relation to the underlying asset's price.

Vega

A vega sensitivity measures the sensitivity of an option's price to changes in the volatility of the underlying asset.

Vega represents the amount by which the price of an option would be expected to change for a 1% change in the implied volatility of the underlying asset. Vega is expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls.

Theta

A theta sensitivity measures the rate at which the price of an option decreases as time passes, all else being equal.

Theta is essentially a quantification of time decay, which is a key concept in options pricing. Theta provides an estimate of the dollar amount that an option's price would decrease each day, assuming no movement in the price of the underlying asset and no change in volatility.

Rho

A rho sensitivity measures the rate at which the price of an option is expected to change in response to a change in the risk-free interest rate.

Rho is expressed as the amount of money an option's price would gain or lose for a one percentage point (1%) change in the risk-free interest rate.

Lambda

A lambda sensitivity measures the percentage change in an option's price for a 1% change in the price of the underlying asset.

Lambda is a measure of leverage, indicating how much more sensitive an option is to price movements in the underlying asset compared to owning the asset outright.

Version History

Introduced in R2024a

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