AssetMonteCarlo

Create AssetMonteCarlo pricer object for equity instruments using BlackScholes, Merton, Heston, or Bates model

Since R2020b

Description

Create and price a Vanilla, Barrier, Lookback, PartialLookback, Asian, Spread, DoubleBarrier, Cliquet, Touch, DoubleTouch, Binary instrument object with a BlackScholes, Bachelier, Merton, Heston, or Bates model and a AssetMonteCarlo pricing method using this workflow:

1. Use fininstrument to create a Vanilla, Barrier, Lookback, PartialLookback, Asian, Spread, DoubleBarrier, Cliquet, Binary, Touch, or DoubleTouch instrument object.

2. Use finmodel to specify a BlackScholes model for the Vanilla, Barrier, Lookback, PartialLookback, Asian, Spread, DoubleBarrier, Cliquet, Touch, DoubleTouch, or Binary instrument object.

   Use finmodel to specify a Bachelier model for the Vanilla, Spread or Binary instrument object.

   Use finmodel to specify a Merton, Bates, or Heston model for the Vanilla, Barrier, Lookback, PartialLookback, Asian, DoubleBarrier, Touch, DoubleTouch, Cliquet, or Binary instrument object.

3. Use finpricer to specify an AssetMonteCarlo pricer object for the Vanilla, Barrier, Lookback, PartialLookback, Asian, Spread, DoubleBarrier, Cliquet, Touch, DoubleTouch, or Binary instrument object.

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 instruments, models, and pricing methods for Vanilla, Barrier, Lookback, PartialLookback, Asian, Spread, DoubleBarrier, Cliquet, Touch, DoubleTouch, or Binary instruments, see Choose Instruments, Models, and Pricers.

Creation

Syntax

AssetMonteCarloPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj,'SpotPrice',spotprice_value,'SimulationDates',simulation_dates)

AssetMonteCarloPricerObj = finpricer(___,Name,Value)

Description

AssetMonteCarloPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj,'SpotPrice',spotprice_value,'SimulationDates',simulation_dates) creates a AssetMonteCarlo pricer object by specifying PricerType and sets the properties using the required name-value pair arguments Model, DiscountCurve, SpotPrice, and SimulationDates.

AssetMonteCarloPricerObj = finpricer(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, AssetMonteCarloPricerObj = finpricer("assetmontecarlo",'Model',BSModel,'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'SimulationDates',[datetime(2018,1,30); datetime(2019,1,30)],'NumTrials',500,'DividendType','continuous','DividendValue',0.3) creates an AssetMonteCarlo pricer object using a BlackScholes model. You can specify multiple name-value pair arguments.

You can perform quasi-Monte Carlo simulations using the name-value arguments for MonteCarloMethod and BrownianMotionMethod. For more information, see Quasi-Monte Carlo Simulation.

Input Arguments

PricerType — Pricer type

string with value "AssetMonteCarlo" | character vector with value 'AssetMonteCarlo'

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

Data Types: char | string

Name-Value Arguments

Specify required and optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: AssetMonteCarloPricerObj = finpricer("assetmontecarlo",'Model',BSModel,'DiscountCurve',ratecurve_obj,'SpotPrice',1000,'SimulationDates',[datetime(2018,1,30); datetime(2019,1,30)],'NumTrials',500,'DividendType','continuous','DividendValue',0.3)

Required AssetMonteCarlo Name-Value Pair Arguments

Model — Model

BlackScholes object | Merton object | Bates object | Heston object

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

Data Types: object

DiscountCurve — ratecurve object for discounting cash flows

ratecurve object

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

SpotPrice — Current price of underlying asset

nonnegative numeric | positive or negative numeric when using Bachelier model

Current price of the underlying asset, specified as the comma-separated pair consisting of 'SpotPrice' and a scalar nonnegative numeric or scalar positive or negative numeric when using Bachelier model.

Note

If you use a Vanilla, Binary, or Spread instrument with a Bachelier model, the SpotPrice can be a negative numeric value.

Data Types: double

SimulationDates — Simulation dates

[ ] (default) | datetime array | string array | date character vector

Simulation dates, specified as the comma-separated pair consisting of 'SimulationDates' and a scalar or a vector using a datetime array, string array, or date character vectors.

To support existing code, AssetMonteCarlo also accepts serial date numbers as inputs, but they are not recommended.

Optional AssetMonteCarlo Name-Value Pair Arguments

NumTrials — Simulation trials

1000 (default) | scalar

Simulation trials, specified as the comma-separated pair consisting of 'NumTrials' and a scalar number of independent sample paths.

Data Types: double

RandomNumbers — Dependent random variates

[ ] (default) | structure

Dependent random variates, specified as the comma-separated pair consisting of 'RandomNumbers' and an NSimulationDates-by-NBrownians-by-NTrials 3D time series array. The 3D time series array has the following fields:

• Z — NSimulationDates-by-NBrownians-by-NTrials 3D time series array of dependent random variates used to generate the Brownian motion vector (that is, Wiener processes) that drive the simulation.

• N — NSimulationDates-by-NBrownians-by-NTrials 3D time series array of dependent random variates used as the number of jumps.

• SizeJ — NSimulationDates-by-NBrownians-by-NTrials 3D time series array of dependent random variates used as the jump sizes.

Note

BlackScholes and Heston models only require Z field.

Data Types: struct

DividendType — Stock dividend type

"continuous" (default) | string with value "cash" or "continuous" | character vector with value 'cash' or 'continuous'

Stock dividend type, specified as the comma-separated pair consisting of 'DividendType' and a character vector or string. DividendType must be either "cash" for actual dollar dividends or "continuous" for a continuous dividend yield.

Data Types: char | string

DividendValue — Dividend yield or dividend schedule for underlying stock

0 (default) | scalar numeric | timetable

Dividend yield for the underlying stock, specified as the comma-separated pair consisting of 'DividendValue' and a scalar numeric for a dividend yield or a timetable for a dividend schedule.

Note

Specify a scalar if DividendType is "continuous" and a timetable if DividendType is "cash".

Data Types: double | timetable

MonteCarloMethod — Monte Carlo method to simulate stochastic processes

"standard" (default) | string with values "standard", "quasi", or "randomized-quasi" | character vector with values 'standard', 'quasi', or 'randomized-quasi'

Monte Carlo method to simulate stochastic processes, specified as the comma-separated pair consisting of 'MonteCarloMethod' and a string or character vector with one of the following values:

• "standard" — Monte Carlo using pseudo random numbers.

• "quasi" — Quasi-Monte Carlo using low-discrepancy sequences.

• "randomized-quasi" — Randomized quasi-Monte Carlo.

For more information on quasi Monte Carlo simulations, see Quasi-Monte Carlo Simulation and for an example using the 'MonteCarloMethod' name-value argument, see Use AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation and Heston Model to Price Asian Instrument.

Data Types: string | char

BrownianMotionMethod — Brownian motion construction method

"standard" (default) | string with value "brownian-bridge" or "principal-components" | character vector with value 'brownian-bridge' or 'principal-components'

Brownian motion construction method, specified as the comma-separated pair consisting of 'BrownianMotionMethod' and a string or character vector with one of the following values:

• "standard" — The Brownian motion path is found by taking the cumulative sum of the Gaussian variates.

• "brownian-bridge" — The last step of the Brownian motion path is calculated first, followed by any order between steps until all steps have been determined.

• "principal-components" — The Brownian motion path is calculated by minimizing the approximation error.

The starting point for a Monte Carlo simulation is the construction of a Brownian motion sample path (or Wiener path). Such paths are built from a set of independent Gaussian variates, using either standard discretization, Brownian-bridge construction, or principal components construction.

Both standard discretization and Brownian-bridge construction share the same variance and therefore the same resulting convergence when used with the MonteCarloMethod using pseudo random numbers. However, the performance differs between the two when the MonteCarloMethod option "quasi" is introduced, with faster convergence seen for "brownian-bridge" construction option and the fastest convergence when using the "principal-components" construction option.

For more information on quasi Monte Carlo simulations, see Quasi-Monte Carlo Simulation and for an example using the 'BrownianMotionMethod' name-value argument, see Use AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation and Heston Model to Price Asian Instrument.

Data Types: string | char

Properties

Model — Model

object

Model, returned as an object.

Data Types: object

DiscountCurve — ratecurve object for discounting cash flows

ratecurve object

This property is read-only.

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

Data Types: object

SpotPrice — Current price of underlying asset

nonnegative numeric | positive or negative numeric when using Bachelier model

Current price of underlying asset, returned as a scalar nonnegative numeric or a scalar positive or negative numeric when using Bachelier model.

Data Types: double

SimulationDates — Simulation dates

datetime

Simulation dates, returned as a datetime array.

Data Types: datetime

NumTrials — Simulation trials

1000 (default) | scalar

Simulation trials, returned as a scalar number of independent sample paths.

Data Types: double

RandomNumbers — Dependent random variates

[ ] (default) | structure

Dependent random variates, returned as an NSimulationDates-by-NBrownians-by-NTrials 3D time series array.

Data Types: struct

EarlyExerciseFunction — Calculation for early exercise premium

@longstaffschwartz_cubic (default) | function handle

Calculation for the early exercise premium, returned as a scalar function handle. The default @longstaffschwartz_cubic uses the Longstaff-Schwartz least squares method.

Data Types: function_handle

DividendType — Dividend type

"continuous" (default) | string with value "cash" or "continuous"

This property is read-only.

Dividend type, returned as a string. DividendType is either "cash" for actual dollar dividends or "continuous" for a continuous dividend yield.

Data Types: string

DividendValue — Dividend yield or dividend schedule for underlying stock

0 (default) | scalar nonnegative numeric | timetable

Dividend yield or dividend schedule for the underlying stock, returned as a scalar numeric for a dividend yield or a timetable for a dividend schedule.

Data Types: double | timetable

MonteCarloMethod — Monte Carlo method to simulate stochastic processes

"standard" (default) | string with values "standard", "quasi", or "randomized-quasi" | character vector with values 'standard', 'quasi', or 'randomized-quasi'

Monte Carlo method to simulate stochastic processes, returned as a string or character vector.

Data Types: string | char

BrownianMotionMethod — Brownian motion construction method

"standard" (default) | string with value "brownian-bridge" or "principal-components" | character vector with value 'brownian-bridge' or 'principal-components'

Brownian motion construction method, returned as a string or character vector.

Data Types: string | char

Object Functions

price

Compute price for equity instrument with AssetMonteCarlo pricer

Examples

Use AssetMonteCarlo Pricer and BlackScholes Model to Price DoubleBarrier Instrument

This example shows the workflow to price a DoubleBarrier instrument when you use a BlackScholes model and an AssetMonteCarlo pricing method.

Create DoubleBarrier Instrument Object

Use fininstrument to create a DoubleBarrier instrument object.

DoubleBarrierOpt = fininstrument("DoubleBarrier",'Strike',100,'ExerciseDate',datetime(2020,8,15),'OptionType',"call",'ExerciseStyle',"american",'BarrierType',"DKO",'BarrierValue',[110 80],'Name',"doublebarrier_option")

DoubleBarrierOpt = 
  DoubleBarrier with properties:

       OptionType: "call"
           Strike: 100
     BarrierValue: [110 80]
    ExerciseStyle: "american"
     ExerciseDate: 15-Aug-2020
      BarrierType: "dko"
           Rebate: [0 0]
             Name: "doublebarrier_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes","Volatility",0.3)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.3000
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2017,9,15);
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-2017
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

ExerciseDate = datetime(2020,08,15);
Settle = datetime(2017,9,15);
outPricer = finpricer("AssetMonteCarlo","DiscountCurve",myRC,"Model",BlackScholesModel,'SpotPrice',100,'simulationDates', Settle+days(1):days(1):ExerciseDate);

Price DoubleBarrier Instrument

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

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

Price = 
6.9667

outPR = 
  priceresult with properties:

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

outPR.Results 

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

    6.9667    0.26875    -0.096337    3.8576    0.39855    9.5406    -1.2907

Use Asset Monte-Carlo Pricer and Heston Model to Price Asian Instrument

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

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',100,'OptionType',"put",'Name',"asian_option")

AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 100
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_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',0.02,'RhoSV',0.9)

HestonModel = 
  Heston with properties:

        V0: 0.0320
    ThetaV: 0.1000
     Kappa: 0.0030
    SigmaV: 0.0200
     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 AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",HestonModel,'SpotPrice',80,'simulationDates',Settle+calmonths(1):calmonths(1):datetime(2022,9,15))

outPricer = 
  HestonMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: 80
         SimulationDates: [15-Oct-2018    15-Nov-2018    15-Dec-2018    15-Jan-2019    15-Feb-2019    15-Mar-2019    15-Apr-2019    15-May-2019    15-Jun-2019    15-Jul-2019    15-Aug-2019    15-Sep-2019    15-Oct-2019    ...    ] (1x48 datetime)
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.Heston]
            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 = 
14.7999

outPR = 
  priceresult with properties:

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

outPR.Results 

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

    14.8     -0.71073    0.023453    -3.8418    -173.12    0.61794    27.992    0.15319

Use AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation and Heston Model to Price Asian Instrument

This example shows the workflow to price a fixed-strike Asian instrument when you use a Heston model and an AssetMonteCarlo pricing method with name-value arguments for MonteCarloMethod and BrownianMotionMethod.

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',100,'OptionType',"put",'Name',"asian_option")

AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 100
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_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',0.02,'RhoSV',0.9)

HestonModel = 
  Heston with properties:

        V0: 0.0320
    ThetaV: 0.1000
     Kappa: 0.0030
    SigmaV: 0.0200
     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 AssetMonteCarlo Pricer Object

Use finpricer to create an AssetMonteCarlo pricer object and use the ratecurve object for the DiscountCurve along with the MonteCarloMethod and BrownianMotionMethod name-value arguments.

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",HestonModel,'SpotPrice',80, ...
                     'SimulationDates',Settle+calmonths(1):calmonths(1):datetime(2022,9,15),'NumTrials',1e3, ...
                     'MonteCarloMethod',"quasi",'BrownianMotionMethod',"brownian-bridge")

outPricer = 
  HestonMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: 80
         SimulationDates: [15-Oct-2018    15-Nov-2018    15-Dec-2018    15-Jan-2019    15-Feb-2019    15-Mar-2019    15-Apr-2019    15-May-2019    15-Jun-2019    15-Jul-2019    15-Aug-2019    15-Sep-2019    15-Oct-2019    ...    ] (1x48 datetime)
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.Heston]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "quasi"
    BrownianMotionMethod: "brownian-bridge"

Price Asian Instrument

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

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

Price = 
14.7861

outPR = 
  priceresult with properties:

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

outPR.Results 

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

    14.786    -0.69748    0.013922    -3.7737    -170.46    0.48825    28.393    0.15863

Use AssetMonteCarlo Pricer and Bachelier Model to Price American Option for Vanilla Instrument

This example shows the workflow to price an American option for a Vanilla instrument when you use a Bachelier model and an AssetMonteCarlo pricing method.

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

VanillaOpt = fininstrument("Vanilla",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"call",'ExerciseStyle',"american",'Name',"vanilla_option")

VanillaOpt = 
  Vanilla with properties:

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

Create Bachelier Model Object

Use finmodel to create a Bachelier model object.

BachelierModel = finmodel("Bachelier","Volatility",0.2)

BachelierModel = 
  Bachelier with properties:

     Volatility: 0.2000
    Correlation: 1

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 AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BachelierModel,'SpotPrice',150,'simulationDates',datetime(2022,9,15))

outPricer = 
  BachelierMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: 150
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.Bachelier]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Vanilla Instrument

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

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

Price = 
57.3776

outPR = 
  priceresult with properties:

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

outPR.Results

ans=1×7 table
    Price      Delta       Gamma       Lambda     Rho       Theta        Vega    
    ______    _______    __________    ______    ______    _______    ___________

    57.378    0.99107    -1.579e-14    2.5909    291.94    -2.5576    -2.1316e-10

Use AssetMonteCarlo Pricer and Bachelier Model to Price Binary Instrument With Underlying Negative Value

This example shows the workflow to price a Binary instrument with an underlying negatively valued asset when you use a Bachelier model and an AssetMonteCarlo pricing method.

Create Binary Instrument Object

Use fininstrument to create a Binary instrument object.

BinaryOpt = fininstrument("Binary",'ExerciseDate',datetime(2022,9,15),'Strike',15,'PayoffValue',13,'OptionType',"put",'Name',"binary_option")

BinaryOpt = 
  Binary with properties:

       OptionType: "put"
     ExerciseDate: 15-Sep-2022
           Strike: 15
      PayoffValue: 13
    ExerciseStyle: "european"
             Name: "binary_option"

Create Bachelier Model Object

Use finmodel to create a Bachelier model object.

BachelierModel = finmodel("Bachelier","Volatility",0.2)

BachelierModel = 
  Bachelier with properties:

     Volatility: 0.2000
    Correlation: 1

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 AssetMonteCarlo Pricer Object

Use finpricer to create an AssetMonteCarlo pricer object and use the ratecurve object for the 'DiscountCurve' name-value pair argument. Note that when using a Bachelier model with a Vanilla, Binary, or Spread instrument, the SpotPrice can be a positive or negative numeric value.

outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BachelierModel,'SpotPrice',-6,'simulationDates',datetime(2022,9,15))

outPricer = 
  BachelierMonteCarlo with properties:

           DiscountCurve: [1x1 ratecurve]
               SpotPrice: -6
         SimulationDates: 15-Sep-2022
               NumTrials: 1000
           RandomNumbers: []
                   Model: [1x1 finmodel.Bachelier]
            DividendType: "continuous"
           DividendValue: 0
        MonteCarloMethod: "standard"
    BrownianMotionMethod: "standard"

Price Binary Instrument

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

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

Price = 
11.3017

outPR = 
  priceresult with properties:

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

outPR.Results

ans=1×7 table
    Price     Delta    Gamma    Lambda      Rho       Theta     Vega
    ______    _____    _____    ______    _______    _______    ____

    11.302      0        0        0       -45.198    0.39582     0  

More About

Quasi-Monte Carlo Simulation

Quasi-Monte Carlo simulation is a Monte Carlo simulation that uses quasi-random sequences instead of pseudo random numbers.

The quasi-random sequences, also called low-discrepancy sequences, are deterministic, uniformly distributed sequences that are specifically designed to place sample points as uniformly as possible. In many cases, this distributed sequences improves the performance of Monte Carlo simulations with faster computational times and sometimes higher accuracy.

The standard Monte Carlo simulation using pseudo random numbers has a convergence rate of only O(N^-1/2), while the quasi-Monte Carlo rate of convergence can be much faster with an error of O(N^-1) in the best cases. For example, for a standard Monte Carlo simulation, it is necessary to increase 100 times the number of simulations NTrials to reduce the error by a factor of 10, whereas a quasi-Monte Carlo simulation requires less, or much less, than 100 times to achieve the same goal.

Quasi-Monte Carlo simulation produces a purely deterministic result. Therefore, when computing the variance and constructing a confidence band for the estimates, randomized quasi-Monte Carlo simulation is useful because of faster computational times and sometimes higher accuracy. You can also use randomized quasi-Monte Carlo to introduce randomization into the low-discrepancy sequences.

The starting point for a Monte Carlo simulation is the construction of a Brownian motion sample path (or Wiener path). Such paths are built from a set of independent Gaussian variates, using either standard discretization, or Brownian-bridge construction, or principal components construction.

For examples of using the MonteCarloMethod and BrownianMotionMethod name-value arguments to perform Quasi-Monte Carlo simulation with the AssetMonteCarlo pricer, see the following:

• Use AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation and Heston Model to Price Asian Instrument

• Price Barrier Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price American Option for Vanilla Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price Lookback Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price PartialLookback Instrument Using Heston Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price Spread Instrument with American Option Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price DoubleBarrier Instrument Using Heston Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price Absolute Return for Cliquet Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price Binary Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price Touch Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

• Price DoubleTouch Instrument Using BlackScholes Model and AssetMonteCarlo Pricer with Quasi-Monte Carlo Simulation

Version History

Introduced in R2020b

R2023b: Perform Quasi-Monte Carlo simulation

Perform Quasi-Monte Carlo simulation using the name-value argument MonteCarloMethod.

R2023b: Perform Brownian bridge and principal components construction

Perform Brownian bridge and principal components construction using the name-value argument BrownianMotionMethod.

R2022b: Serial date numbers not recommended

Although AssetMonteCarlo supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.