Black

Create Black pricer object for Cap, Floor, or Swaption instrument using Black model

Description

Create and price a Cap, Floor, or Swaption instrument object with a Black model and a Black pricing method using this workflow:

1. Use fininstrument to create a Cap, Floor, or Swaption instrument object.

2. Use finmodel to specify a Black model for the Cap, Floor, or Swaption instrument object.

3. Use finpricer to specify a Black pricer object for the Cap, Floor, or Swaption instrument object.

   Note

   If you do not specify ProjectionCurve when you create a Cap, Floor, or Swaption instrument with the Black pricer, the ProjectionCurve value defaults to the DiscountCurve value.

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 Cap, Floor, or Swaption instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

BlackPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj)

Description

BlackPricerObj = finpricer(PricerType,'Model',model,'DiscountCurve',ratecurve_obj) creates a Black pricer object by specifying PricerType and the required name-value pair arguments for Model and DiscountCurve to set properties using name-value pairs. For example, BlackPricerObj = finpricer("Analytic",'Model',BlackModel,'DiscountCurve',ratecurve_obj) creates a Black 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 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: BlackPricerObj = finpricer("Analytic",'Model',BlackModel,'DiscountCurve',ratecurve_obj)

Model — Model

Black model object

Model, specified as the comma-separated pair consisting of 'Model' and the name of a previously created Black 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.

Data Types: object

Output Arguments

BlackPricerObj — Black pricer

Black object

Black pricer, returned as a Black object.

Properties

Model — Model

Black model object

Model, returned as a Black model object.

Data Types: object

DiscountCurve — ratecurve object for discounting cash flows

ratecurve object

ratecurve object for discounting cash flows, returned as the ratecurve object

Data Types: object

Object Functions

price

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

Examples

Use Black Pricer and Black Model to Price Cap Instrument

This example shows the workflow to price a Cap instrument when you use a Black model and a Black pricing method.

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object.

CapOpt = fininstrument("Cap",'Strike',.02,'Maturity',datetime(2021,12,30),'Reset',4,'Principal',100,'Basis',12,'Name',"cap_option")

CapOpt = 
  Cap with properties:

                      Strike: 0.0200
                    Maturity: 30-Dec-2021
                 ResetOffset: 0
                       Reset: 4
                       Basis: 12
                   Principal: 100
             ProjectionCurve: [0×0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "cap_option"

Create Black Model Object

Use finmodel to create a Black model object.

BlackModel = finmodel("Black",'Volatility',0.09,'Shift',0.002)

BlackModel = 
  Black with properties:

    Volatility: 0.0900
         Shift: 0.0020

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2020,9,14);
Type = 'zero';
ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [10×1 datetime]
                Rates: [10×1 double]
               Settle: 14-Sep-2020
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create Black Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackModel,'DiscountCurve',myRC)

outPricer = 
  Black with properties:

            Model: [1×1 finmodel.Black]
    DiscountCurve: [1×1 ratecurve]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

Price = price(outPricer,CapOpt)

Price = 
4.6412e-29

More About

Black Pricing Method

The Black pricing method is a framework in finance for pricing options on futures and interest-rate derivatives.

The Black pricing method is primarily used for pricing European options, which can only be exercised at expiration. It provides a way to calculate the theoretical price of these options based on the underlying asset's price dynamics.

Version History

Introduced in R2020a