TurnbullWakeman

Create TurnbullWakeman pricer object for Asian instrument using BlackScholes model

Description

Create and price a Asian instrument object with a BlackScholes model and a TurnbullWakeman pricing method using this workflow:

1. Use fininstrument to create an Asian instrument object.

2. Use finmodel to specify a BlackScholes model for the Asian instrument object.

3. Use finpricer to specify a TurnbullWakeman pricer object for the Asian 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 an Asian instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

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

TurnbullWakemanPricerObj = finpricer(___,Name,Value)

Description

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

TurnbullWakemanPricerObj = finpricer(___,Name,Value) to set optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, TurnbullWakemanPricerObj = finpricer("Analytic",'DiscountCurve',ratecurve_obj,'Model',BSModel,'SpotPrice',1000,'DividendType',"continuous",'DividendValue',100) creates a TurnbullWakeman 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: TurnbullWakemanPricerObj = finpricer("Analytic",'DiscountCurve',ratecurve_obj,'Model',BSModel,'SpotPrice',1000,'DividendType',"continuous",'DividendValue',100,'PricingMethod','TurnbullWakeman')

Required TurnbullWakeman Name-Value Pair Arguments

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.

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

Model — Model

BlackScholes model object

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

Data Types: object

SpotPrice — Current price of underlying asset

nonnegative numeric

Current price of the underlying asset, specified as the comma-separated pair consisting of 'SpotPrice' and a scalar nonnegative numeric.

Data Types: double

Optional TurnbullWakeman Name-Value Pair Arguments

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 "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

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

Data Types: double | timetable

PricingMethod — Analytic pricing method

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

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

Note

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

Data Types: double

Output Arguments

TurnbullWakemanPricerObj — Turnbull-Wakeman pricer

TurnbullWakeman object

Turnbull-Wakeman pricer, returned as a TurnbullWakeman object.

Properties

DiscountCurve — ratecurve object for discounting cash flows

ratecurve object

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

Data Types: object

Model — Model

BlackScholes model object

Model, returned as a BlackScholes model 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 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 nonnegative numeric for a dividend yield or a timetable for a dividend schedule.

Data Types: double | timetable

PricingMethod — Analytic pricing method

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

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 TurnbullWakeman Pricer and BlackScholes Model to Price Asian Instrument

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

Create Asian Instrument Object

Use fininstrument to create an Asian instrument object.

AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',105,'OptionType',"put",'ExerciseStyle',"european",'Name',"asian_option")

AsianOpt = 
  Asian with properties:

          OptionType: "put"
              Strike: 105
         AverageType: "arithmetic"
        AveragePrice: 0
    AverageStartDate: NaT
       ExerciseStyle: "european"
        ExerciseDate: 15-Sep-2022
                Name: "asian_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',0.35)

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: 0.3500
    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 TurnbullWakeman Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',100,'PricingMethod',"TurnbullWakeman")

outPricer = 
  TurnbullWakeman with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: 100
    DividendValue: 0
     DividendType: "continuous"

Price Asian Instrument

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

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

Price = 
14.3431

outPR = 
  priceresult with properties:

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

outPR.Results 

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

    14.343    -0.37004    0.0085706    -2.5799    44.864    -0.86257    -125.73

More About

Turnbull-Wakeman Pricing Method

The Turnbull-Wakeman pricing method provides an analytical solution for pricing European Asian options under the assumption that the underlying asset follows a geometric Brownian motion.

Version History

Introduced in R2020a