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price

Compute price for equity instrument with AssetTree pricer

Since R2021a

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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 in addition to the required arguments in the previous syntax.

example

Examples

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Open Live Script

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: [02-Feb-2018 08:00:00    06-Mar-2018 16:00:00    08-Apr-2018 00:00:00    10-May-2018 08:00:00    11-Jun-2018 16:00:00    14-Jul-2018 00:00:00    15-Aug-2018 08:00:00    16-Sep-2018 16:00:00    ...    ] (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]


outPR.Results
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
Open Live Script

This example shows the workflow to price a Vanilla instrument when you use a BlackScholes model and an AssetTree pricing method for a Standard Trinomial (STT) tree.

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 Standard Trinomial equity tree and use the ratecurve object for the 'DiscountCurve' name-value pair argument.

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

             Tree: [1x1 struct]
       NumPeriods: 15
            Model: [1x1 finmodel.BlackScholes]
    DiscountCurve: [1x1 ratecurve]
        SpotPrice: 30
     DividendType: "continuous"
    DividendValue: 0
        TreeDates: [02-Feb-2018 08:00:00    06-Mar-2018 16:00:00    08-Apr-2018 00:00:00    10-May-2018 08:00:00    11-Jun-2018 16:00:00    14-Jul-2018 00:00:00    15-Aug-2018 08:00:00    16-Sep-2018 16:00:00    ...    ] (1x15 datetime)

Price Vanilla Instrument

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

[Price, outPR] = price(STTPricer,VanillaOpt,"all")
Price = 
2.2826

outPR = 
  priceresult with properties:

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


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

    2.2826    -0.2592    0.030949    12.51    -3.8981    -16.516    -0.73845

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
Asian{'delta','gamma','vega','theta','rho','lambda','price'}
Barrier{'delta','gamma','vega','theta','rho','lambda','price'}
Lookback{'delta','gamma','vega','theta','rho','lambda','price'}
Vanilla{'delta','gamma','vega','theta','rho','lambda','price'}

Note

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.

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 R2021a

See Also

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