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Floor

Floor instrument object

Description

Create and price a Floor instrument object for one of more Floor instruments using this workflow:

  1. Use fininstrument to create a Floor instrument object for one of more Floor instruments.

  2. Use finmodel to specify a HullWhite, BlackKarasinski, Black, Normal, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model for the Floor 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 Floor instruments.

    • When using a HullWhite, BraceGatarekMusiela, SABRBraceGatarekMusiela, or LinearGaussian2F model, use finpricer to specify an IRMonteCarlo pricing method for one or more Floor 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 Floor instrument, see Choose Instruments, Models, and Pricers.

Creation

Description

example

FloorOpt = fininstrument(InstrumentType,'Strike',strike_value,'Maturity',maturity_date) creates a Floor object for one of more Floor instruments by specifying InstrumentType and sets the properties for the required name-value pair argumentsStrike and Maturity.

The Floor instrument supports vanilla and amortizing floors.

example

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

Input Arguments

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

Data Types: char | cell | string

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

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

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 Floor 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 Floor instruments and use a timetable, the timetable specification applies to all of the Floor 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 actual period day count, specified as the comma-separated pair consisting of 'DaycountAdjustedCashFlow' and a scalar logical or an NINST-by-1 vector of logicals 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 vector 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));
FloorOpt = fininstrument("floor",'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. This object is 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 numeric or an NINST-by-1 vector of nonnegative values.

Data Types: double

Floor 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 amount 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 actual period day count, returned as a scalar logical or an NINST-by-1 vector of logical values 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 Floor instrument when you use a Black model and a Black pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve for the underlying interest-rate curve for the floor 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 Floor Instrument Object

Use fininstrument to create a Floor instrument object.

FloorOpt = fininstrument("Floor",'Maturity',datetime(2022,9,15),'Strike',0.03,'ProjectionCurve',myRC)
FloorOpt = 
  Floor with properties:

                      Strike: 0.0300
                    Maturity: 15-Sep-2022
                 ResetOffset: 0
                       Reset: 1
                       Basis: 0
                   Principal: 100
             ProjectionCurve: [1x1 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: ""

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 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",'DiscountCurve',myRC,'Model',BlackModel)
outPricer = 
  Black with properties:

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

Price Floor Instrument

Use price to compute the price for the Floor instrument.

[Price, outPR] = price(outPricer,FloorOpt)
Price = 8.0878
outPR = 
  priceresult with properties:

       Results: [1x1 table]
    PricerData: []

This example shows the workflow to price multiple vanilla Floor instruments when you use a Black model and a Black pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve for the underlying interest-rate curve for the floor 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 Floor Instrument Object

Use fininstrument to create a Floor instrument object for three Florr instruments.

FloorOpt = fininstrument("Floor",'Maturity',datetime([2022,9,15 ; 2022,9,15 ; 2022,9,15]),'Strike',[0.03 ; 0.04 ; 0.05],'ProjectionCurve',myRC)
FloorOpt=3×1 object
  3x1 Floor array with properties:

    Strike
    Maturity
    ResetOffset
    Reset
    Basis
    Principal
    ProjectionCurve
    DaycountAdjustedCashFlow
    BusinessDayConvention
    Holidays
    Name

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 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",'DiscountCurve',myRC,'Model',BlackModel)
outPricer = 
  Black with properties:

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

Price Floor Instruments

Use price to compute the prices for the Floor instruments.

[Price, outPR] = price(outPricer,FloorOpt)
Price = 3×1

    8.0878
   12.0033
   15.9263

outPR=3×1 object
  3x1 priceresult array with properties:

    Results
    PricerData

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

Create Floor Instrument Object

Use fininstrument to create a Floor instrument object.

FloorOpt = fininstrument("Floor",'Strike',0.039,'Maturity',datetime(2019,1,30),'Reset',4,'Principal',100,'Basis',12,'Name',"floor_option")
FloorOpt = 
  Floor with properties:

                      Strike: 0.0390
                    Maturity: 30-Jan-2019
                 ResetOffset: 0
                       Reset: 4
                       Basis: 12
                   Principal: 100
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "floor_option"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.032,'Sigma',0.04)
HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0320
    Sigma: 0.0400

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 Floor Instrument

Use price to compute the price for the Floor instrument.

Price = price(outPricer,FloorOpt)
Price = 1.2676

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

Create Floor Instrument Object

Use fininstrument to create an amortizing Floor instrument object.

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

FloorOpt = fininstrument("Floor",'Maturity',datetime(2023,9,1),'Strike',0.015,'Principal',Principal,'Name',"floor_amortizing_option")
FloorOpt = 
  Floor 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: "floor_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 Floor Instrument

Use price to compute the price for the Floor instrument.

Price = price(outPricer,FloorOpt)
Price = 3.0030

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

Create Floor Instrument Object

Use fininstrument to create a Floor instrument object.

FloorOpt = fininstrument("Floor",'Strike',0.03,'Maturity',datetime(2020,1,30),'Reset',4,'Principal',100,'Basis',8,'Name',"floor_option")
FloorOpt = 
  Floor with properties:

                      Strike: 0.0300
                    Maturity: 30-Jan-2020
                 ResetOffset: 0
                       Reset: 4
                       Basis: 8
                   Principal: 100
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "floor_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, FloorOpt.Maturity, FloorOpt.Reset, FloorOpt.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 Floor Instrument

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

[Price, outPR] = price(outPricer,FloorOpt,["all"])
Price = 5.7821
outPR = 
  priceresult with properties:

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

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

    5.7821    31.821    141.45    -110.54

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

Create Floor Instrument Object

Use fininstrument to create a Floor instrument object.

FloorOpt = fininstrument("Floor","Maturity",datetime(2022,9,15),'Strike',0.05,'Reset',1,'Name',"floor_option")
FloorOpt = 
  Floor with properties:

                      Strike: 0.0500
                    Maturity: 15-Sep-2022
                 ResetOffset: 0
                       Reset: 1
                       Basis: 0
                   Principal: 100
             ProjectionCurve: [0x0 ratecurve]
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                        Name: "floor_option"

Create BraceGatarekMusiela Model Object

Use finmodel to create a BraceGatarekMusiela model object.

BGMVolFunc = @(a,t) (a(1)*t + a(2)).*exp(-a(3)*t) + a(4);
BGMVolParams = [.3 -.02 .7 .14];
numRates = 20;
VolFunc(1:numRates-1) = {@(t) BGMVolFunc(BGMVolParams,t)};
Beta = .08;
CorrFunc = @(i,j,Beta) exp(-Beta*abs(i-j));
Correlation = CorrFunc(meshgrid(1:numRates-1)',meshgrid(1:numRates-1),Beta);
BGM = finmodel("BraceGatarekMusiela",'Volatility',VolFunc,'Correlation',Correlation,'Period',1);

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])]';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293]';
ZeroDates = Settle + ZeroTimes;
 
myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [9x1 datetime]
                Rates: [9x1 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',BGM,'DiscountCurve',myRC,'SimulationDates',ZeroDates)
outPricer = 
  BGMMonteCarlo with properties:

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

Price Floor Instrument

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

[Price,outPR] = price(outPricer,FloorOpt,["all"])
Price = 14.7882
outPR = 
  priceresult with properties:

       Results: [1x3 table]
    PricerData: [1x1 struct]

outPR.Results
ans=1×3 table
    Price     Delta     Gamma 
    ______    ______    ______

    14.788    -400.4    1280.7

More About

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Introduced in R2020a