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Floor

Floor instrument object

Description

Create and price a Floor instrument object using this workflow:

  1. Use fininstrument to create a Floor instrument object.

  2. Use finmodel to specify a HullWhite, BlackKarasinski, Black, or Normal model for the Floor instrument.

  3. Use finpricer to specify a Normal, Black, HullWhite, or IRTree pricing method for the Floor 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 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 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" or a character vector with the value of 'Floor'.

Data Types: char | 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 value.

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, or date string.

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

Data Types: double | char | 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.

Data Types: double

Day-count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar integer with one of 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 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.

Data Types: double | timetable

Lag in rate setting, specified as the comma-separated pair consisting of 'ResetOffset' and a scalar numeric.

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 with a value 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 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 | string

Holidays used in computing business days, specified as the comma-separated pair consisting of 'Holidays' and dates using 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 ratecurve object. 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 the instrument, specified as the comma-separated pair consisting of 'Name' and a scalar string or character vector.

Data Types: char | string

Properties

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Option strike price value, returned as a scalar nonnegative numeric value.

Data Types: double

Floor maturity date, returned as a datetime.

Data Types: datetime

Reset frequency payments per year, returned as a scalar numeric.

Data Types: double

Day-count basis, returned as a scalar integer.

Data Types: double

Principal amount or principal value schedule, returned as a scalar numeric for principal amount or a timetable for a principal value schedule.

Data Types: double | timetable

Lag in rate setting, returned as a scalar numeric.

Data Types: double

Flag to adjust cash flows based on actual period day count, returned as a logical with a value of true or false.

Data Types: logical

Business day conventions, returned as a string.

Data Types: string

Holidays used in computing business days, returned as datetimes.

Data Types: datetime

Rate curve used in projecting the future cash flows, returned as a ratecurve object.

Data Types: object

User-defined name for the instrument, returned as a string.

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 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

More About

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Introduced in R2020a