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


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

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

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

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

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 pricing methods for a Cap, Floor, or Swaption instrument when using a Black model, see Choose Instruments, Models, and Pricers.




BlackModelObj = finmodel(ModelType,'Volatility',volatility_value) creates a Black model object by specifying ModelType and sets the properties for the required name-value pair argument Volatility. For more information on a Black model, see More About and Algorithms.


BlackModelObj = finmodel(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, BlackModelObj = finmodel("Black",'Volatility',0.032,'Shift',0.002) creates a Black model object. You can specify multiple name-value pair arguments.

Input Arguments

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

Data Types: char | string

Black Name-Value Pair Arguments

Specify required and optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: BlackModelObj = finmodel("Black",'Volatility',0.032,'Shift',0.002)
Required Black Name-Value Pair Arguments

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Volatility value for the underlying asset, specified as the comma-separated pair consisting of 'Volatility' and a scalar nonnegative numeric.

Data Types: double

Optional Black Name-Value Pair Argument

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Shift in decimals for the shifted Black model, specified as the comma-separated pair consisting of 'Shift' and a scalar rate shift in positive decimals. Set this parameter to a positive rate shift in decimals to add a positive shift to the forward rate and strike, which effectively sets a negative lower bound for the forward rate. For example, a Shift value of 0.01 is equal to a 1% shift.

Data Types: double


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Volatility value, returned as a scalar nonnegative numeric.

Data Types: double

Shift in decimals for the shifted Black model, returned as a scalar rate shift in a positive decimal.

Data Types: double


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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',.001,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"cap_option")
CapOpt = 
  Cap with properties:

                      Strike: 1.0000e-03
                    Maturity: 30-Jan-2019
                 ResetOffset: 0
                       Reset: 4
                       Basis: 8
                   Principal: 100
             ProjectionCurve: [0x0 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',0.032,'Shift',0.002)
BlackModel = 
  Black with properties:

    Volatility: 0.0320
         Shift: 0.0020

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
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: [10x1 datetime]
                Rates: [10x1 double]
               Settle: 15-Sep-2018
         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: [1x1 finmodel.Black]
    DiscountCurve: [1x1 ratecurve]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

Price = price(outPricer,CapOpt)
Price = 0.1575

More About

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Introduced in R2020a