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Compute price for equity instrument with AssetTree pricer



[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.


[Price,PriceResult] = price(___,inpSensitivity) adds an optional argument to specify sensitivities in addition to the required arguments in the previous syntax.


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

Create Vanilla Instrument Object

Use fininstrument to create a Vanilla instrument object.

VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2019,5,1),'Strike',29,'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_option")
VanillaOpt = 
  Vanilla with properties:

       OptionType: "put"
    ExerciseStyle: "european"
     ExerciseDate: 01-May-2019
           Strike: 29
             Name: "vanilla_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.25)
BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.2500
    Correlation: 1

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,1,1);
Maturity = datetime(2020,1,1);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 1
                Dates: 01-Jan-2020
                Rates: 0.0350
               Settle: 01-Jan-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetTree Pricer Object

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

LRPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',30,'PricingMethod',"LeisenReimer",'Maturity',datetime(2019,5,1),'NumPeriods',15)
LRPricer = 
  LRTree with properties:

    InversionMethod: PP1
             Strike: 30
               Tree: [1x1 struct]
         NumPeriods: 15
              Model: [1x1 finmodel.BlackScholes]
      DiscountCurve: [1x1 ratecurve]
          SpotPrice: 30
       DividendType: "continuous"
      DividendValue: 0
          TreeDates: [1x15 datetime]

Price Vanilla Instrument

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

[Price, outPR] = price(LRPricer,VanillaOpt,"all")
Price = 2.2542
outPR = 
  priceresult with properties:

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

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

    2.2542    -0.33628    0.044039    12.724    -4.469    -16.433    -0.76073

Input Arguments

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

Data Types: object

Instrument object, specified as a scalar or 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 a 1-by-NOUT cell array of character vectors or string array with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Theta', 'Rho', 'Lambda', and 'All'.

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

inpInstrumentSupported Sensitivities


Sensitivities are calculated based on yield shifts of 1 basis point, where the ShiftValue = 1/10000. All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide the sensitivities by their respective instrument price.

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

Data Types: string | cell

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 that depends on the instrument that is being priced

    Asian and Lookback have an empty ([]) PricerData field because the pricing functions for these instruments cannot unambiguously assign a price to any node but the root node.

    Vanilla and Barrier have the following shared fields for PriceResult.PricerData.PriceTree:

    • PTree contains the clean prices.

    • ExTree contains the exercise indicator arrays. Each element of the cell array is an array where 1 indicates that an option is exercised and 0 indicates that an option is not exercised.

    • dObs contains the date of each level of the tree.

    • tObs contains the observation times.

    • Probs contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.

Introduced in R2021a