BjerksundStensland

Create BjerksundStensland pricer object for Vanilla or Spread instrument using BlackScholes model

Description

Create and price a Vanilla or Spread instrument object with a BlackScholes model and a BjerksundStensland pricing method using this workflow:

1. Use fininstrument to create a Vanilla or Spread instrument object.

2. Use finmodel to specify a BlackScholes model for the Vanilla or Spread instrument object.

3. Use finpricer to specify a BjerksundStensland pricer object for the Vanilla instrument (American exercise) or Spread 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 or Spread instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

BjerksundStenslandPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj,'SpotPrice',spotprice_value)

BjerksundStenslandPricerObj = finpricer(___,Name,Value)

Description

BjerksundStenslandPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj,'SpotPrice',spotprice_value) creates a BjerksundStensland pricer object by specifying PricerType and sets the properties for the required name-value pair arguments Model, DividendType, and SpotPrice.

BjerksundStenslandPricerObj = finpricer(___,Name,Value) to set optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, BjerksundStenslandPricerObj = finpricer("Analytic",'Model',BSModel,'DiscountCurve',ratecurve_obj,'SpotPrice',[100;105],'DividendValue',[2.5,2.8],'PricingMethod',"BjerksundStensland") creates a BjerksundStensland pricer object.

Input Arguments

PricerType — Pricer type

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

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

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: BjerksundStenslandPricerObj = finpricer("Analytic",'Model',BSModel,'DiscountCurve',ratecurve_obj,'SpotPrice',[100;105],'DividendValue',[2.5,2.8],'PricingMethod',"BjerksundStensland")

Required BjerksundStensland Name-Value Pair Arguments

Model — Model

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 discounting cash flows

ratecurve object

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

scalar nonnegative numeric | vector of nonnegative numerics

Current price of the underlying asset, specified as the comma-separated pair consisting of 'SpotPrice' and a scalar or vector of nonnegative numeric values. Use a vector for SpotPrice when pricing a Spread instrument.

Data Types: double

Optional BjerksundStensland Name-Value Pair Arguments

DividendValue — Dividend yield

[0,0] (default) | scalar nonnegative numeric | vector of nonnegative numerics

Dividend yield, specified as the comma-separated pair consisting of 'DividendValue' and a scalar or vector of nonnegative numeric values. Use a 1-by-2 vector of nonnegative values for DividendValue when pricing a Spread instrument.

Data Types: double

DividendType — Dividend type

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

Dividend type, specified as the comma-separated pair consisting of 'DividendType' and string or character vector.

Data Types: char | string

PricingMethod — Analytic pricing method

default pricer associated with BlackScholes model (default) | string with value "BjerksundStensland" | character vector with value 'BjerksundStensland'

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

Note

The default pricing method for a BlackScholes model is a BlackScholes pricer.

Data Types: string | char

Output Arguments

BjerksundStenslandPricerObj — Bjerksund-Stensland pricer

BjerksundStensland object

Bjerksund-Stensland pricer, returned as a BjerksundStensland object.

Properties

Model — Model

object

Model, returned as a model object.

Data Types: object

DiscountCurve — ratecurve object for discounting cash flows

Read-only: 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 | vector of nonnegative numerics

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

Data Types: double

DividendValue — Dividend yield

scalar nonnegative numeric | vector of nonnegative numerics

Dividend yield, returned as a scalar or vector of nonnegative numeric.

Data Types: double

DividendType — Dividend type

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

This property is read-only.

Dividend type, returned as a string.

Data Types: string

PricingMethod — Analytic pricing method

default pricer associated with BlackScholes model (default) | string with value "BjerksundStensland"

Analytic pricing method, returned as a string.

Data Types: string

Object Functions

price

Compute price for interest-rate, equity, or credit derivative instrument with Analytic pricer

Examples

Use BjerksundStensland Pricer and BlackScholes Model to Price Spread Instrument

This example shows the workflow to price a European exercise Spread instrument when you use a BlackScholes model and a BjerksundStensland pricing method.

Create Spread Instrument Object

Use fininstrument to create a Spread instrument object.

SpreadOpt = fininstrument("Spread",'Strike',5,'ExerciseDate',datetime(2021,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"spread_option")

SpreadOpt = 
  Spread with properties:

       OptionType: "put"
           Strike: 5
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2021
             Name: "spread_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',[0.2,0.1])

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: [0.2000 0.1000]
    Correlation: [2×2 double]

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 BjerksundStensland Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',[100,105],'DividendValue',[0.09,0.17],'PricingMethod',"BjerksundStensland")

outPricer = 
  BjerksundStensland with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: [100 105]
    DividendValue: [0.0900 0.1700]
     DividendType: "continuous"

Price Spread Instrument

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

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

Price = 
7.0596

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: []

outPR.Results

ans=1×7 table
    Price            Delta                    Gamma                   Lambda                Vega          Theta       Rho  
    ______    ____________________    ______________________    __________________    ________________    ______    _______

    7.0596    -0.23249     0.27057    0.0069887    0.0055319    -3.2932     3.8327    41.938    18.303    1.1011    -5.6943

Use BjerksundStensland Pricer and BlackScholes Model to Price an American Exercise Vanilla Instrument

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

Create Vanilla Instrument Object

Use fininstrument to create an American exercise Vanilla instrument object.

VanillaObj = fininstrument("Vanilla",'Strike',120,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"american",'Name',"vanilla_instrument")

VanillaObj = 
  Vanilla with properties:

       OptionType: "put"
    ExerciseStyle: "american"
     ExerciseDate: 30-Jan-2019
           Strike: 120
             Name: "vanilla_instrument"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',.2)

BlackScholesModel = 
  BlackScholes 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 BjerksundStensland Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',120,'DividendValue',0.05,'PricingMethod',"BjerksundStensland")

outPricer = 
  BjerksundStensland with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 120
    DividendValue: 0.0500
     DividendType: "continuous"

Price Vanilla Instrument

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

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

Price = 
6.1080

outPR = 
  priceresult with properties:

       Results: [1×7 table]
    PricerData: []

outPR.Results

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

    6.108    -0.48471    0.026611    -9.5227    28.781    -8.3418    -24.115

More About

Bjerksund-Stensland Pricing Method

The Bjerksund-Stensland pricing method offers a comprehensive approach to option pricing that considers early exercise decisions and dividend impacts.

The Bjerksund-Stensland pricing method is particularly effective for valuing options that can be exercised at any time before expiration, addressing the complexities associated with the early exercise feature of American options.

Version History

Introduced in R2020a