price

Compute price for interest-rate instrument with IRMonteCarlo pricer

Since R2021b

Syntax

[Price,PriceResult] = price(inpPricer,inpInstrument)

[Price,PriceResult] = price(___,inpSensitivity)

Description

[Price,PriceResult] = price(inpPricer,inpInstrument) computes the interest-rate instrument price and related pricing information based on the pricing object inpPricer and the instrument object inpInstrument.

[Price,PriceResult] = price(___,inpSensitivity) adds an optional argument to specify sensitivities. Use this syntax with the input argument combination in the previous syntax.

Examples

Price FixedBond Instrument Using HullWhite Model and IRMonteCarlo Pricer

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

Create FixedBond Instrument Object

Use fininstrument to create a FixedBond instrument object.

FixB = fininstrument("FixedBond","Maturity",datetime(2022,9,15),"CouponRate",0.05,'Name',"fixed_bond")

FixB = 
  FixedBond with properties:

                  CouponRate: 0.0500
                      Period: 2
                       Basis: 0
                EndMonthRule: 1
                   Principal: 100
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                   IssueDate: NaT
             FirstCouponDate: NaT
              LastCouponDate: NaT
                   StartDate: NaT
                    Maturity: 15-Sep-2022
                        Name: "fixed_bond"

Create HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",'Alpha',0.32,'Sigma',0.49)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.3200
    Sigma: 0.4900

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',HullWhiteModel,'DiscountCurve',myRC,'SimulationDates',ZeroDates)

outPricer = 
  HWMonteCarlo 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.HullWhite]

Price FixedBond Instrument

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

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

Price = 
115.0303

outPR = 
  priceresult with properties:

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

outPR.Results

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

    115.03    -397.13    1430.4     0  

Price RangeAccrualNote Instrument Using HullWhite Model and IRMonteCarlo Pricer

This example shows the workflow to price a RangeAccrualNote instrument when you use a HullWhite model and an IRMonteCarlo pricing method.

Create RangeAccrualNote Instrument Object

Use fininstrument to create a RangeAccrualNote instrument object.

Maturity = datetime(2026,9,15);
RangeAccrualNoteInstrument = fininstrument("RangeAccrualNote",Maturity=Maturity,ReferenceType="cms",ReferenceTenor=10,CouponRate=0.4,TargetRange=[0,3.25/100],Principal=1000,Name="rangeaccrualnote_instrument")

RangeAccrualNoteInstrument = 
  RangeAccrualNote with properties:

               ReferenceType: "cms"
                      Period: 2
                       Basis: 0
                   Principal: 1000
           CMSReferenceReset: 2
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                EndMonthRule: 1
              ReferenceTenor: 10
                    Maturity: 15-Sep-2026
                  CouponRate: 0.4000
                 TargetRange: [0 0.0325]
                   StartDate: NaT
                        Name: "rangeaccrualnote_instrument"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2024,9,15);
Type = 'zero';
ZeroTimes = [calyears(1:3)]';
ZeroRates = [0.0055 0.0061 0.0073]';
ZeroDates = Settle + ZeroTimes;

myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [3×1 datetime]
                Rates: [3×1 double]
               Settle: 15-Sep-2024
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create a HullWhite Model Object

Use finmodel to create a HullWhite model object.

HullWhiteModel = finmodel("HullWhite",Alpha=0.02,Sigma=0.03)

HullWhiteModel = 
  HullWhite with properties:

    Alpha: 0.0200
    Sigma: 0.0300

Create IRMonteCarlo Pricer Object

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

SimulationDates = Settle:caldays(1):Maturity;
SimulationDates = busdate(SimulationDates,"follow",RangeAccrualNoteInstrument.Holidays);
outPricer = finpricer("IRMonteCarlo",Model=HullWhiteModel,DiscountCurve=myRC,SimulationDates=SimulationDates)

outPricer = 
  HWMonteCarlo with properties:

          NumTrials: 1000
      RandomNumbers: []
      DiscountCurve: [1×1 ratecurve]
    SimulationDates: [16-Sep-2024    17-Sep-2024    18-Sep-2024    19-Sep-2024    20-Sep-2024    23-Sep-2024    24-Sep-2024    25-Sep-2024    26-Sep-2024    27-Sep-2024    30-Sep-2024    01-Oct-2024    02-Oct-2024    03-Oct-2024    …    ] (1×523 datetime)
              Model: [1×1 finmodel.HullWhite]

Price RangeAccrualNote Instrument

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

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

Price = 
1.5111e+03

outPR = 
  priceresult with properties:

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

outPR.Results

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

    1511.1    8244.1    5.9468e+06    -4760.4

Price OptionEmbeddedRangeAccrualNote Instrument Using LinearGaussian2F Model and IRMonteCarlo Pricer

This example shows the workflow to price a OptionEmbeddedangeAccrualNote instrument when you use a LinearGaussian2F model and an IRMonteCarlo pricing method.

Create OptionEmbeddedRangeAccrualNote Instrument Object

Use fininstrument to create a OptionEmbeddedRangeAccrualNote instrument object.

Maturity = datetime(2026,9,15);

Strike = [1000; 1000 ];
ExerciseDates = [datetime(2025,12,1); datetime(2026,12,1)];
CallSchedule =  timetable(ExerciseDates,Strike,'VariableNames',{'Strike Schedule'});

OptionEmbeddedRangeAccrualNoteInstrument = fininstrument("OptionEmbeddedRangeAccrualNote",Maturity=Maturity,ReferenceType="cms",ReferenceTenor=10,CouponRate=0.4, ...
    TargetRange=[0,3.25/100],Principal=1000,CallSchedule=CallSchedule,Name="optionembedded_rangeaccrualnote_instrument")

OptionEmbeddedRangeAccrualNoteInstrument = 
  OptionEmbeddedRangeAccrualNote with properties:

               ReferenceType: "cms"
                      Period: 2
                       Basis: 0
                   Principal: 1000
           CMSReferenceReset: 2
    DaycountAdjustedCashFlow: 0
       BusinessDayConvention: "actual"
                    Holidays: NaT
                EndMonthRule: 1
              ReferenceTenor: 10
                    Maturity: 15-Sep-2026
                  CouponRate: 0.4000
                 TargetRange: [0 0.0325]
                CallSchedule: [1×1 timetable]
                   StartDate: NaT
                        Name: "optionembedded_rangeaccrualnote_instrument"

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2024,9,15);
Type = 'zero';
ZeroTimes = [calyears(1:3)]';
ZeroRates = [0.0055 0.0061 0.0073]';
ZeroDates = Settle + ZeroTimes;

myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 0
                Dates: [3×1 datetime]
                Rates: [3×1 double]
               Settle: 15-Sep-2024
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

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 IRMonteCarlo Pricer Object

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

SimulationDates = Settle:caldays(1):Maturity;
SimulationDates = busdate(SimulationDates,"follow",OptionEmbeddedRangeAccrualNoteInstrument.Holidays);
outPricer = finpricer("IRMonteCarlo",Model=LinearGaussian2FModel,DiscountCurve=myRC,SimulationDates=SimulationDates,NumTrials=1e3)

outPricer = 
  G2PPMonteCarlo with properties:

          NumTrials: 1000
      RandomNumbers: []
      DiscountCurve: [1×1 ratecurve]
    SimulationDates: [16-Sep-2024    17-Sep-2024    18-Sep-2024    19-Sep-2024    20-Sep-2024    23-Sep-2024    24-Sep-2024    25-Sep-2024    26-Sep-2024    27-Sep-2024    30-Sep-2024    01-Oct-2024    02-Oct-2024    03-Oct-2024    …    ] (1×523 datetime)
              Model: [1×1 finmodel.LinearGaussian2F]

Price OptionEmbeddedRangeAccrualNote Instrument

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

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

Price = 
1.3754e+03

outPR = 
  priceresult with properties:

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

outPR.Results

ans=1×4 table
    Price     Delta        Gamma              Vega       
    ______    ______    ___________    __________________

    1375.4    5374.4    -2.8115e+06    -5334.9     5964.5

Input Arguments

inpPricer — Pricer object

IRMonteCarlo object

Pricer object, specified as a previously created IRMonteCarlo pricer object. Create the pricer object using finpricer.

Data Types: object

inpInstrument — Instrument object

Cap object | Floor object | RangeAccrualNote object | Swaption object | Swap object | FixedBond object | OptionEmbeddedFixedBond object | OptionEmbeddedFloatBond object | OptionEmbeddedRangeAccrualNote object | FixedBondOption object | FloatBond object | FloatBondOption object

Instrument object, specified as scalar or a vector of previously created instrument objects. Create the instrument objects using fininstrument. The following instrument objects are supported:

• Cap

• Floor

• RangeAccrualNote

• Swap

• Swaption

• FixedBond

• OptionEmbeddedFixedBond

• OptionEmbeddedRangeAccrualNote

• FixedBondOption

• FloatBond

• FloatBondOption

• OptionEmbeddedFloatBond

Data Types: object

inpSensitivity — List of sensitivities to compute

[ ] (default) | string array with values dependent on pricer object | cell array of character vectors with values dependent on pricer object

(Optional) List of sensitivities to compute, specified as an NOUT-by-1 or 1-by-NOUT cell array of character vectors or string array.

The supported sensitivities depend on the pricing method.

inpInstrument	Supported Sensitivities
Cap	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
Floor	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
Swap	{'delta','gamma','vega','price'}
Swaption	{'delta','gamma','vega','price'}
FixedBond	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
OptionEmbeddedFixedBond	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
FixedBondOption	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
FloatBond	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
FloatBondOption	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
OptionEmbeddedFloatBond	{'delta','gamma','vega','price'} ('vega' not supported when using SABRBraceGatarekMusiela model with the IRMonteCarlo pricer.)
RangeAccrualNote	{'delta','gamma','vega','price'} ('vega' not supported when using HullWhite or LinearGaussian2F models with the IRMonteCarlo pricer.)
OptionEmbeddedRangeAccrualNote	{'delta','gamma','vega','price'} ('vega' not supported when using HullWhite or LinearGaussian2F models with the IRMonteCarlo pricer.)

inpSensitivity = 'All' or inpSensitivity = "All" specifies that all sensitivities for the pricing method are returned. This is the same as specifying inpSensitivity to include each sensitivity.

Example: inpSensitivity = ["delta","gamma","vega","price"]

Data Types: cell | string

Output Arguments

Price — Instrument price

numeric

Instrument price, returned as a numeric.

PriceResult — Price result

PriceResult object

Price result, returned as a PriceResult object. The object has the following fields:

• PriceResult.Results — Table of results that includes sensitivities (if you specify inpSensitivity)

• PriceResult.PricerData — Structure for pricer data

More About

Delta

A delta sensitivity measures the rate at which the price of an option is expected to change relative to a $1 change in the price of the underlying asset.

Delta is not a static measure; it changes as the price of the underlying asset changes (a concept known as gamma sensitivity), and as time passes. Options that are near the money or have longer until expiration are more sensitive to changes in delta.

Gamma

A gamma sensitivity measures the rate of change of an option's delta in response to a change in the price of the underlying asset.

In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. This is important because this helps you understand the convexity of an option's value in relation to the underlying asset's price.

Vega

A vega sensitivity measures the sensitivity of an option's price to changes in the volatility of the underlying asset.

Vega represents the amount by which the price of an option would be expected to change for a 1% change in the implied volatility of the underlying asset. Vega is expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls.

Version History

Introduced in R2021b

R2026a: Support for Pricing RangeAccrualNote and OptionEmbeddedRangeAccrualNote Instruments

You can use price for pricing RangeAccrualNote and OptionEmbeddedRangeAccrualNote instruments using a HullWhite or LinearGaussian2F model and a IRMonteCarlo pricing method.