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, BlackDermanToy, Black, Normal, BraceGatarekMusiela, SABRBraceGatarekMusiela, CoxIngersollRoss, or LinearGaussian2F model for the Cap instrument object.

3. Choose a pricing method.

   • When using a HullWhite, BlackKarasinski, BlackDermanToy, Black, CoxIngersollRoss, or Normal model, use finpricer for pricing one or more Cap instruments and specify:

     • A Normal pricer when using a Normal model.

     • A Black pricer when using a Black model.

     • A HullWhite pricer when using a HullWhite model.

     • An IRTree pricer when using a BlackKarasinski, CoxIngersollRoss, or BlackDermanToy model.

   • When using a HullWhite, BlackKarasinski, 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

Syntax

CapOpt = fininstrument(InstrumentType,'Strike',strike_value,'Maturity',maturity_date)

CapOpt = fininstrument(___,Name,Value)

Description

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.

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

InstrumentType — Instrument type

string with value "Cap" | string array with values of "Cap" | character vector with value 'Cap' | cell array of character vectors with values of 'Cap'

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

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: 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

Strike — Cap strike price

nonnegative decimal | vector of nonnegative decimals

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

Maturity — Cap maturity date

datetime array | string array | date character vector

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

To support existing code, Cap also accepts serial date numbers as inputs, but they are not recommended.

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

Optional Cap Name-Value Pair Arguments

Reset — Reset frequency payments per year

1 (default) | numeric with value of 0, 1, 2, 3, 4, 6, or 12 | numeric vector with values of 0, 1, 2, 3, 4, 6, or 12

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

Basis — Day count basis

0 (actual/actual) (default) | integer from 0 to 13 | vector of integers from 0 to 13

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 — Principal amount or principal value schedule

100 (default) | scalar numeric | numeric vector | timetable

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

ResetOffset — Lag in rate setting

0 (default) | scalar numeric | numeric vector

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

DaycountAdjustedCashFlow — Flag to adjust cash flows based on actual period day count

false (default) | value of true or false | vector of values of true or false

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

BusinessDayConvention — Business day conventions

"actual" (default) | string | string array | character vector | cell array of character vectors

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 — Holidays used in computing business days

NaT (default) | datetime array | string array | date character vector

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

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

To support existing code, Cap also accepts serial date numbers as inputs, but they are not recommended.

ProjectionCurve — Rate curve used in generating future cash flows

ratecurve.empty (default) | ratecurve object | vector of ratecurve objects

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

Name — User-defined name for instrument

" " (default) | string | string array | character vector | cell array of character vectors

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

Output Arguments

CapOpt — Cap instrument

Cap object

Cap instrument, returned as a Cap object.

Properties

Strike — Option strike price value

nonnegative value | vector of nonnegative values

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

Data Types: double

Maturity — Cap maturity date

datetime | vector of datetimes

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

Data Types: datetime

Reset — Reset frequency payments per year

1 (default) | scalar numeric | numeric vector

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

Data Types: double

Basis — Day count basis

0 (actual/actual) (default) | integer from 0 to 13 | vector of integers from 0 to 13

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

Data Types: double

Principal — Principal amount or principal value schedule

100 (default) | scalar numeric | numeric vector | timetable

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

ResetOffset — Lag in rate setting

0 (default) | scalar numeric | numeric vector

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

Data Types: double

DaycountAdjustedCashFlow — Flag to adjust cash flows based on actual period day count

false (default) | value of true or false | vector of values of true or false

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

BusinessDayConvention — Business day conventions

"actual" (default) | string | string array

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

Data Types: string

Holidays — Holidays used in computing business days

NaT (default) | vector of datetimes

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

Data Types: datetime

ProjectionCurve — Rate curve used in generating future cash flows

ratecurve.empty (default) | ratecurve object | vector of ratecurve objects

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

Name — User-defined name for instrument

" " (default) | string | string array

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

Data Types: string

Examples

Price Vanilla Cap Instrument Using HullWhite Model and HullWhite Pricer

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: [0×0 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: [10×1 datetime]
                Rates: [10×1 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: [1×1 ratecurve]
            Model: [1×1 finmodel.HullWhite]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

Price = price(outPricer,CapOpt)

Price = 
2.9366

Price Multiple Vanilla Cap Instruments Using HullWhite Model and HullWhite Pricer

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 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: [10×1 datetime]
                Rates: [10×1 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: [1×1 ratecurve]
            Model: [1×1 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

Price Vanilla Cap Instrument Using Normal Model and Normal Pricer

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: [10×1 datetime]
                Rates: [10×1 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: [1×1 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: [1×1 ratecurve]
            Shift: 0
            Model: [1×1 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: [1×1 table]
    PricerData: []

Price Amortizing Cap Instrument Using Black Model and Black Pricer

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: [2×1 timetable]
             ProjectionCurve: [0×0 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: [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 = 
0.3897

Price Vanilla Cap Instrument Using HullWhite Model and IRTree Pricer

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: [0×0 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: [10×1 datetime]
                Rates: [10×1 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: [1×1 struct]
        TreeDates: [6×1 datetime]
            Model: [1×1 finmodel.HullWhite]
    DiscountCurve: [1×1 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: [1×4 table]
    PricerData: [1×1 struct]

outPR.Results

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

    2.7733    28.932    -49.227    31.655

Price Cap Instrument Using LinearGaussian2F Model and IRMonteCarlo Pricer

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: [0×0 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: [10×1 datetime]
                Rates: [10×1 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: [1×1 ratecurve]
    SimulationDates: [01-Jul-2019    01-Jan-2020    01-Jan-2021    01-Jan-2022    01-Jan-2023    01-Jan-2024    01-Jan-2026    01-Jan-2029    01-Jan-2039    01-Jan-2049]
              Model: [1×1 finmodel.LinearGaussian2F]

Price Cap Instrument

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

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

Price = 
1.2156

outPR = 
  priceresult with properties:

       Results: [1×4 table]
    PricerData: [1×1 struct]

outPR.Results

ans=1×4 table
    Price     Delta     Gamma          Vega      
    ______    ______    _____    ________________

    1.2156    131.37    11048    126.5    -157.38

Price Cap Instrument Using CoxIngersollRoss Model and IRTree Pricer

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

Create Cap Instrument Object

Use fininstrument to create a Cap instrument object.

Maturity = datetime(2027,1,1); 
StrikeCap = 0.055;
Reset = 1;
Cap = fininstrument("Cap",Strike=StrikeCap,Maturity=Maturity,Reset=Reset,Name="Cap_inst")

Cap = 
  Cap with properties:

                      Strike: 0.0550
                    Maturity: 01-Jan-2027
                 ResetOffset: 0
                       Reset: 1
                       Basis: 0
                   Principal: 100
             ProjectionCurve: [0×0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "Cap_inst"

Create CoxIngersollRoss Model Object

Use finmodel to create a CoxIngersollRoss model object.

alpha = 0.03; 
theta = 0.02; 
sigma = 0.1; 
CIRModel = finmodel("CoxIngersollRoss",Sigma=sigma,Alpha=alpha,Theta=theta)

CIRModel = 
  CoxIngersollRoss with properties:

    Sigma: 0.1000
    Alpha: 0.0300
    Theta: 0.0200

Create ratecurve Object

Create a ratecurve object using ratecurve.

Times= [calyears([1 2 3 4 ])]';
Settle = datetime(2023,1,1);
ZRates = [0.035; 0.042147; 0.047345; 0.052707]';
ZDates = Settle + Times;
Compounding = -1; 
Basis = 1;
ZeroCurve = ratecurve("zero",Settle,ZDates,ZRates,Compounding = Compounding, Basis = Basis);

Create IRTree Pricer Object

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

CIRPricer = finpricer("irtree",Model=CIRModel,DiscountCurve=ZeroCurve,Maturity=ZDates(end),NumPeriods=length(ZDates))

CIRPricer = 
  CIRTree with properties:

             Tree: [1×1 struct]
        TreeDates: [4×1 datetime]
            Model: [1×1 finmodel.CoxIngersollRoss]
    DiscountCurve: [1×1 ratecurve]

Price Cap Instrument

Use price to compute the price for the Cap instrument.

[Price,outPR] = price(CIRPricer,Cap,"all")

Price = 
3.3361

outPR = 
  priceresult with properties:

       Results: [1×4 table]
    PricerData: [1×1 struct]

outPR.Results

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

    3.3361    142.25    -2632.5    26.325

More About

Cap

A cap is a contract that includes a guarantee that sets the maximum interest rate the holder pays, based on an otherwise floating interest rate.

A cap is a contract between two parties, where the buyer pays a premium to the seller in exchange for the right to receive payments if a specified interest rate exceeds a predetermined level (the cap rate) during a specified period. The cap rate is the maximum interest rate level above which the buyer of the cap instrument will receive payments. If the reference interest rate (for example, LIBOR) exceeds the cap rate, the buyer is entitled to receive a payment from the seller.

The payoff for a cap is: $$\max (CurrentRate-CapRate,0)$$

For more information, see Cap.

Version History

Introduced in R2020a

R2023b: Support for Pricing Cap Instruments Using CoxIngersollRoss Model and IRTree Pricer

You can price Cap instruments using a CoxIngersollRoss model object and an IRTree pricing method.

R2022b: Serial date numbers not recommended

Although Cap supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.