Kirk

Create Kirk pricer object for Spread instrument using BlackScholes model

Description

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

1. Use fininstrument to create a Spread instrument object.

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

3. Use finpricer to specify a Kirk pricer object for the 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 Spread instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

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

KirkPricerObj = finpricer(___,Name,Value)

Description

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

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

Required Kirk 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.

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

Model — Model

BlackScholes model object

Model object, 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

scalar nonnegative numeric | cell array of nonnegative numerics

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

Data Types: double

Optional Kirk Name-Value Pair Arguments

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 a string or character vector for a continuous dividend yield.

Data Types: char | string

DividendValue — Dividend yield for underlying asset

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

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

Data Types: double

PricingMethod — Analytic pricing method

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

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

KirkPricerObj — Kirk pricer

Kirk object

Kirk pricer, returned as a Kirk object.

Properties

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

Model — Model

BlackScholes model object

Model, returned as a BlackScholes model object.

Data Types: object

SpotPrice — Current price of underlying asset

required input (default) | scalar 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

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

DividendValue — Dividend yield for underlying stock

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

Dividend yield for the underlying stock, returned as a scalar or vector of nonnegative numerics.

Data Types: double

PricingMethod — Analytic pricing method

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

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 Kirk Pricer and BlackScholes Model to Price Spread Instrument

This example shows the workflow to price a Spread instrument when you use a BlackScholes model and a Kirk 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 Kirk Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',[103,105],'DividendValue',[0.025 , 0.028],'PricingMethod',"Kirk")

outPricer = 
  Kirk with properties:

    DiscountCurve: [1×1 ratecurve]
            Model: [1×1 finmodel.BlackScholes]
        SpotPrice: [103 105]
    DividendValue: [0.0250 0.0280]
     DividendType: "continuous"

Price Spread Instrument

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

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

Price = 
17.8614

outPR = 
  priceresult with properties:

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

outPR.Results

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

    17.861    -0.44663     0.58229    0.0093493     0.008195    -2.5756     3.3578    59.518    27.176    -1.7801    -8.1715

More About

Kirk Pricing Method

The Kirk pricing method provides a framework for valuing options based on the dynamics of implied volatility and its relationship with the underlying asset.

Version History

Introduced in R2020a