AssetTree

Create AssetTree pricer object for Vanilla, Barrier, Asian, or Lookback instrument

Since R2021a

Description

Create and price a Vanilla, Barrier, Asian, or Lookback instrument object with a BlackScholes model and an AssetTree pricing method using this workflow:

1. Use fininstrument to create a Vanilla, Lookback, Barrier, or Asian instrument object.

2. Use finmodel to specify a BlackScholes model for the Vanilla, Barrier, Asian, or Lookback instrument object.

3. Use finpricer to specify an AssetTree pricer object for a Cox-Ross-Rubinstein (CRR), equal-probability (EQP), Leisen-Reimer (LR), or Standard Trinomial (ST) lattice tree model for the Vanilla, Barrier, Asian, or Lookback 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 a Vanilla, Barrier, Asian, or Lookback instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

AssetTreePricerObj = finpricer(PricerType,'Model',model_type,'DiscountCurve',ratecurve_obj,'SpotPrice',spot_price)

AssetTreePricerObj = finpricer(___,Name,Value)

Description

AssetTreePricerObj = finpricer(PricerType,'Model',model_type,'DiscountCurve',ratecurve_obj,'SpotPrice',spot_price) creates an AssetTree pricer object by specifying PricerType and the required name-value pair arguments for Model, DiscountCurve, and SpotPrice.

AssetTreePricerObj = finpricer(___,Name,Value) sets optional properties using additional name-value pair arguments in addition to the required arguments in the previous syntax. For example, AssetTreePricerObj = finpricer("AssetTree",'Model',BlackScholes,'DiscountCurve',ratecure_obj,'SpotPrice',1000) creates an AssetTree pricer object.

Input Arguments

PricerType — Pricer type

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

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

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: AssetTreePricerObj = finpricer("AssetTree",'Model',BlackScholes,'DiscountCurve',ratecure_obj,'SpotPrice',1000)

Model — Model

BlackScholes object

Model, specified as the comma-separated pair consisting of 'Model' and the name of the previously created BlackScholes model object using finmodel.

Data Types: object

DiscountCurve — ratecurve object for creating AssetTree object and discounting cash flows

Read-only: ratecurve object

This property is read-only.

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

Data Types: object

SpotPrice — Underlying spot price

scalar numeric

Underlying spot price, specified as the comma-separated pair consisting of 'SpotPrice' and a scalar numeric.

Data Types: double

Optional AssetTree Name-Value Pair Arguments

PricingMethod — Asset pricing method

"CoxRossRubinstein" (default) | string with value "CoxRossRubinstein", "EqualProbability", "LeisenReimer", or "StandardTrinomial" | character vector with value 'CoxRossRubinstein', 'EqualProbability', 'LeisenReimer', or "StandardTrinomial"

Asset pricing method, specified as the comma-separated pair consisting of 'PricingMethod' and a string or character vector.

Data Types: char | string

Maturity — Maturity date

datetime scalar | string scalar | date character vector

Maturity date, specified as the comma-separated pair consisting of 'Maturity' and a scalar datetime, string, or date character vector.

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

If you use a date character vector or string, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

NumPeriods — Number of levels or time steps of the tree

10 (default) | numeric

Number of levels or time steps of the tree, specified as the comma-separated pair consisting of 'NumPeriods' and a scalar.

Data Types: double

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 string or character vector. DividendType must be "cash" for actual dollar dividends or "continuous" for a continuous dividend yield.

Data Types: char | string

DividendValue — Dividend amount or dividend schedule for underlying stock

0 (default) | scalar numeric | timetable

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

Note

DividendValue must be a scalar for a "continuous" DividendType or a timetable for "cash" DividendType.

Data Types: double | timetable

Strike — Option strike used with Leisen-Reimer pricing method

SpotPrice (default) | nonnegative numeric

Option strike used with the Leisen-Reimer pricing method, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative numeric.

Data Types: double

InversionMethod — Inversion method for Leisen-Reimer pricing method

'PP1' (default) | string with value "PP1" or "PP2" | character vector with value 'PP1' or 'PP2'

Inversion method for the Leisen-Reimer pricing method, specified as the comma-separated pair consisting of 'InversionMethod' and a string or character vector.

• 'PP1' — Peizer-Pratt method 1 inversion

• 'PP2' — Peizer-Pratt method 2 inversion

Data Types: string | char

Output Arguments

AssetTreePricerObj — AssetTree pricer

AssetTree object

AssetTree pricer, returned as an AssetTree object.

Properties

InversionMethod — Inversion method for Leisen-Reimer pricing method

'PP1' (default) | string with value "PP1" or "PP2"

Inversion method for the Leisen-Reimer pricing method, returned as a string.

Data Types: string

Strike — Option strike used with Leisen-Reimer pricing method

SpotPrice (default) | nonnegative numeric

Option strike used with the Leisen-Reimer pricing method, returned as a nonnegative numeric.

Data Types: double

Tree — CRR, EQP, LR binomial tree or STT trinomial tree

structure

CRR, EQP, LR binomial tree or STT trinomial tree, returned as a structure with the following properties:

• Probs contains a 2-by-NumLevels numeric array with the up and down probabilities that apply to each level of the tree except for the last one. All nodes in a given level share the same up and down probabilities. The columns of the Probs array are ordered from the root node. The first row of the array corresponds to the probability of an up move, while the second row corresponds to a down move.

• ATree contains the price tree for the underlying asset.

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

• tObs contains the time factor of each level of the tree.

Data Types: struct

NumPeriods — Number of levels or time steps of the tree

numeric

Number of levels or time steps of the tree, returned as a numeric.

Data Types: datetime

Model — Model type

object

Model type, returned as an object.

Data Types: object

DiscountCurve — ratecurve object for creating AssetTree object and discounting cash flows

Read-only: ratecurve object

This property is read-only.

ratecurve object for creating the AssetTree object and discounting cash flows, returned as a ratecurve object.

Data Types: object

SpotPrice — Current price of underlying asset

nonnegative numeric

Current price of the underlying asset, returned as a scalar nonnegative numeric.

Data Types: double

DividendType — Stock dividend type

Read-only: "continuous" (default) | string with value "cash" or "continuous"

This property is read-only.

Stock 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 amount or dividend schedule for underlying stock

0 (default) | scalar nonnegative numeric | timetable

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

Data Types: double | timetable

TreeDates — Tree dates

datetime

Tree dates, returned as a scalar datetime or datetime array.

Data Types: datetime

Object Functions

price

Compute price for equity instrument with AssetTree pricer

Examples

Use AssetTree Pricer and BlackScholes Model to Price Vanilla Instrument

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: [1×1 struct]
         NumPeriods: 15
              Model: [1×1 finmodel.BlackScholes]
      DiscountCurve: [1×1 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    …    ] (1×15 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: [1×7 table]
    PricerData: [1×1 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

Use AssetTree Pricer and BlackScholes Model to Price Vanilla Instrument

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: [1×1 struct]
       NumPeriods: 15
            Model: [1×1 finmodel.BlackScholes]
    DiscountCurve: [1×1 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    …    ] (1×15 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: [1×7 table]
    PricerData: [1×1 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

References

[1] Hull, John, and Alan White. “The General Hull–White Model and Supercalibration.” Financial Analysts Journal, 57, no. 6, (November 2001): 34–43.

Version History

Introduced in R2021a

R2022b: Serial date numbers not recommended

Although AssetTree 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.

R2022a: Support for Standard Trinomial Tree model

The name-value argument option for PricingMethod supports a "StandardTrinomial" lattice tree model.