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Cap

Cap instrument object

Description

Create and price a Cap instrument object for one or more Cap instruments using this workflow:

  1. Use fininstrument to create a Cap instrument object for one or more Cap instruments.

  2. Use finmodel to specify a HullWhite, BlackKarasinski, Black, Normal, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model for the Cap instrument object.

  3. Choose a pricing method.

    • When using a HullWhite, BlackKarasinski, Black, or Normal model, use finpricer to specify a Normal, Black, HullWhite, or IRTree pricing method for one or more Cap instruments.

    • When using a HullWhite, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model, use finpricer to specify an IRMonteCarlo pricing method for one or more Cap instruments.

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 models and pricing methods for a Cap instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

CapOpt = fininstrument(InstrumentType,'Strike',strike_value,'Maturity',maturity_date) creates a Cap object for one or more Cap instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments Strike and Maturity.

The Cap instrument supports vanilla and amortizing caps.

example

CapOpt = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, CapOpt = fininstrument("Cap",'Strike',0.65,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'ResetOffset',1,'Basis',1,'DaycountAdjustedCashFlow',true,'BusinessDayConvention',"follow",'ProjectionCurve',ratecurve_object,'Name',"cap_option") creates a Cap option with a strike of 0.65. You can specify multiple name-value pair arguments.

Input Arguments

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Instrument type, specified as a string with the value of "Cap", a character vector with the value of 'Cap', an NINST-by-1 string array with values of "Cap", or an NINST-by-1 cell array of character vectors with values of 'Cap'.

Data Types: char | cell | string

Cap 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: CapOpt = fininstrument("Cap",'Strike',0.65,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'ResetOffset',1,'Basis',1,'DaycountAdjustedCashFlow',true,'BusinessDayConvention',"follow",'ProjectionCurve',ratecurve_object,'Name',"cap_option")
Required Cap Name-Value Pair Arguments

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Cap strike price, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative decimal value or an NINST-by-1 nonnegative numeric vector.

Data Types: double

Cap maturity date, specified as the comma-separated pair consisting of 'ExerciseDate' and a scalar datetime, serial date number, date character vector, date string or an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array.

If you use date character vectors or date strings, the format must be recognizable by datetime because the Maturity property is stored as a datetime.

Data Types: double | char | cell | string | datetime

Optional Cap Name-Value Pair Arguments

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Reset frequency payments per year, specified as the comma-separated pair consisting of 'Reset' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Day count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar integer or an NINST-by-1 vector of integers with the following values:

  • 0 — actual/actual

  • 1 — 30/360 (SIA)

  • 2 — actual/360

  • 3 — actual/365

  • 4 — 30/360 (PSA)

  • 5 — 30/360 (ISDA)

  • 6 — 30/360 (European)

  • 7 — actual/365 (Japanese)

  • 8 — actual/actual (ICMA)

  • 9 — actual/360 (ICMA)

  • 10 — actual/365 (ICMA)

  • 11 — 30/360E (ICMA)

  • 12 — actual/365 (ISDA)

  • 13 — BUS/252

For more information, see Basis.

Data Types: double

Principal amount or principal value schedule, specified as the comma-separated pair consisting of 'Principal' and a scalar numeric or an NINST-by-1 numeric vector or a timetable.

Principal accepts a timetable, where the first column is dates and the second column is its associated principal value. The date indicates the last day that the principal value is valid.

Note

If you are creating one or more Cap instruments and use a timetable, the timetable specification applies to all of the Cap instruments. Principal does not accept an NINST-by-1 cell array of timetables as input.

Data Types: double | timetable

Lag in rate setting, specified as the comma-separated pair consisting of 'ResetOffset' and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Flag to adjust cash flows based on the actual period day count, specified as the comma-separated pair consisting of 'DaycountAdjustedCashFlow' and a scalar or an NINST-by-1 vector with values of true or false.

Data Types: logical

Business day conventions, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array for a business day convention. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

  • "actual" — Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.

  • "follow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.

  • "modifiedfollow" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day. However, if the following business day is in a different month, the previous business day is adopted instead.

  • "previous" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.

  • "modifiedprevious" — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However, if the previous business day is in a different month, the following business day is adopted instead.

Data Types: char | cell | string

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using an NINST-by-1 vector of datetimes, serial date numbers, cell array of date character vectors, or date string array. For example:

H = holidays(datetime('today'),datetime(2025,12,15));
CapOpt = fininstrument("Cap",'Strike',100,'Maturity',datetime(2025,12,15),'Holidays',H)

Data Types: double | cell | datetime | string

Rate curve used in projecting the future cash flows, specified as the comma-separated pair consisting of 'ProjectionCurve' and a scalar ratecurve object or an NINST-by-1 vector of ratecurve objects. These objects must be created using ratecurve. Use this optional input if the forward curve is different from the discount curve.

Data Types: object

User-defined name for one of more instruments, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: char | cell | string

Properties

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Option strike price value, returned as a scalar nonnegative value or an NINST-by-1 vector of nonnegative values.

Data Types: double

Cap maturity date, returned as a scalar datetime or an NINST-by-1 vector of datetimes.

Data Types: datetime

Reset frequency payments per year, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Day count basis, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

Principal amount or principal value schedule, returned as a scalar numeric or an NINST-by-1 numeric vector for principal amounts or a timetable for a principal value schedule.

Data Types: double | timetable

Lag in rate setting, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Flag to adjust cash flows based on the actual period day count, returned as a scalar logical or an NINST-by-1 vector with values of true or false.

Data Types: logical

Business day conventions, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Holidays used in computing business days, returned as an NINST-by-1 vector of datetimes.

Data Types: datetime

Rate curve used in projecting the future cash flows, returned as a scalar ratecurve object or an NINST-by-1 vector of ratecurve objects.

Data Types: object

User-defined name for the instrument, returned as a scalar string or an NINST-by-1 string array.

Data Types: string

Examples

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This example shows the workflow to price a vanilla Cap instrument when using a HullWhite model and a HullWhite pricing method.

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object.

CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"cap_option")
CapOpt = 
  Cap with properties:

                      Strike: 0.0200
                    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 HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.62,'Sigma',0.99)
HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.6200
    Sigma: 0.9900

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 HullWhite Pricer Object

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

outPricer = finpricer("analytic",'Model',HullWhiteModel,'DiscountCurve',myRC)
outPricer = 
  HullWhite with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.HullWhite]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

Price = price(outPricer,CapOpt)
Price = 2.9366

This example shows the workflow to price multiple vanilla Cap instruments when using a HullWhite model and a HullWhite pricing method.

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object for three Cap instruments.

CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime([2019,1,30 ; 2019,2,30 ; 2019,3,30]),'Reset',4,'Principal',[100 ; 200 ; 300],'Basis',8,'Name',"cap_option")
CapOpt=3×1 object
  3x1 Cap array with properties:

    Strike
    Maturity
    ResetOffset
    Reset
    Basis
    Principal
    ProjectionCurve
    DaycountAdjustedCashFlow
    BusinessDayConvention
    Holidays
    Name

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.62,'Sigma',0.99)
HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.6200
    Sigma: 0.9900

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 HullWhite Pricer Object

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

outPricer = finpricer("analytic",'Model',HullWhiteModel,'DiscountCurve',myRC)
outPricer = 
  HullWhite with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.HullWhite]

Price Cap Instruments

Use price to compute the prices for the Cap instruments.

Price = price(outPricer,CapOpt)
Price = 3×1

    2.9366
    7.4694
   17.7915

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

Create ratecurve Object

Create a ratecurve object using ratecurve for the underlying interest-rate curve for the cap instrument.

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 Cap Instrument Object

Use fininstrument to create a Cap instrument object.

CapOpt = fininstrument("Cap",'Maturity',datetime(2022,9,15),'Strike',0.04,'ProjectionCurve',myRC)
CapOpt = 
  Cap with properties:

                      Strike: 0.0400
                    Maturity: 15-Sep-2022
                 ResetOffset: 0
                       Reset: 1
                       Basis: 0
                   Principal: 100
             ProjectionCurve: [1x1 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: ""

Create Normal Model Object

Use finmodel to create a Normal model object.

NormalModel = finmodel("Normal",'Volatility',0.01)
NormalModel = 
  Normal with properties:

    Volatility: 0.0100

Create Normal Pricer Object

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

outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',NormalModel)
outPricer = 
  Normal with properties:

    DiscountCurve: [1x1 ratecurve]
            Shift: 0
            Model: [1x1 finmodel.Normal]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

[Price, outPR] = price(outPricer, CapOpt)
Price = 0.0701
outPR = 
  priceresult with properties:

       Results: [1x1 table]
    PricerData: []

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

Create Cap Instrument Object

Use fininstrument to create an amortizing Cap instrument object.

CADates = [datetime(2020,9,1) ; datetime(2023,9,1)];
CAPrincipal = [100; 85];
Principal = timetable(CADates,CAPrincipal);

CapOpt = fininstrument("Cap",'Maturity',datetime(2023,9,1),'Strike',0.015,'Principal',Principal,'Name',"cap_amortizing_option")
CapOpt = 
  Cap with properties:

                      Strike: 0.0150
                    Maturity: 01-Sep-2023
                 ResetOffset: 0
                       Reset: 1
                       Basis: 0
                   Principal: [2x1 timetable]
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "cap_amortizing_option"

Create Black Model Object

Use finmodel to create a Black model object.

BlackModel = finmodel("Black",'Volatility',0.2)
BlackModel = 
  Black with properties:

    Volatility: 0.2000
         Shift: 0

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2018,9,1);
Type = 'zero';
ZeroTimes = [calyears([1 2 3 4 5 7 10])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168]';
ZeroDates = Settle + ZeroTimes;
            
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates);

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 = 0.3897

This example shows the workflow to price a vanilla Cap instrument when using a HullWhite model and an IRTree pricing method.

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object.

CapOpt = fininstrument("Cap",'Strike',0.02,'Maturity',datetime(2020,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"cap_option")
CapOpt = 
  Cap with properties:

                      Strike: 0.0200
                    Maturity: 30-Jan-2020
                 ResetOffset: 0
                       Reset: 4
                       Basis: 8
                   Principal: 100
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "cap_option"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.10)
HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0100
    Sigma: 0.1000

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 IRTree Pricer Object

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

CFdates = cfdates(Settle, CapOpt.Maturity, CapOpt.Reset, CapOpt.Basis);
outPricer = finpricer("IRTree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',CFdates')
outPricer = 
  HWBKTree with properties:

             Tree: [1x1 struct]
        TreeDates: [6x1 datetime]
            Model: [1x1 finmodel.HullWhite]
    DiscountCurve: [1x1 ratecurve]

Price Cap Instrument

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

[Price, outPR] = price(outPricer,CapOpt,["all"])
Price = 2.7733
outPR = 
  priceresult with properties:

       Results: [1x4 table]
    PricerData: [1x1 struct]

outPR.Results
ans=1×4 table
    Price      Vega      Gamma     Delta 
    ______    ______    _______    ______

    2.7733    31.655    -49.227    28.932

This example shows the workflow to price a Cap instrument when using a LinearGaussian2F model and an IRMonteCarlo pricing method.

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object.

CapOpt = fininstrument("Cap","Maturity",datetime(2022,9,15),'Strike',0.01,'Reset',2,'Name',"cap_option")
CapOpt = 
  Cap with properties:

                      Strike: 0.0100
                    Maturity: 15-Sep-2022
                 ResetOffset: 0
                       Reset: 2
                       Basis: 0
                   Principal: 100
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "cap_option"

Create LinearGaussian2F Model Object

Use finmodel to create a LinearGaussian2F model object.

LinearGaussian2FModel = finmodel("LinearGaussian2F",'Alpha1',0.07,'Sigma1',0.01,'Alpha2',0.5,'Sigma2',0.006,'Correlation',-0.7)
LinearGaussian2FModel = 
  LinearGaussian2F with properties:

         Alpha1: 0.0700
         Sigma1: 0.0100
         Alpha2: 0.5000
         Sigma2: 0.0060
    Correlation: -0.7000

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2019,1,1);
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: 01-Jan-2019
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create IRMonteCarlo Pricer Object

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

outPricer = finpricer("IRMonteCarlo",'Model',LinearGaussian2FModel,'DiscountCurve',myRC,'SimulationDates',ZeroDates)
outPricer = 
  G2PPMonteCarlo with properties:

          NumTrials: 1000
      RandomNumbers: []
      DiscountCurve: [1x1 ratecurve]
    SimulationDates: [01-Jul-2019    01-Jan-2020    01-Jan-2021    ...    ]
              Model: [1x1 finmodel.LinearGaussian2F]

Price Cap Instrument

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

[Price,outPR] = price(outPricer,CapOpt,["all"])
Price = 1.2389
outPR = 
  priceresult with properties:

       Results: [1x4 table]
    PricerData: [1x1 struct]

outPR.Results
ans=1×4 table
    Price     Delta     Gamma          Vega       
    ______    ______    _____    _________________

    1.2389    132.71    11038    131.63    -163.71

More About

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Introduced in R2020a