FRA

FRA instrument object

Description

Create and price a FRA (forward rate agreement) instrument object for one or more FRA instruments using this workflow:

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

2. Use ratecurve to specify an interest-rate model for the FRA instrument object.

3. Use finpricer to specify a Discount pricing method for one or more FRA 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 FRA instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

FRAObj = fininstrument(InstrumentType,'StartDate',start_date,'Maturity',maturity_date,'Rate',rate_value)

FRAObj = fininstrument(___,Name,Value)

Description

FRAObj = fininstrument(InstrumentType,'StartDate',start_date,'Maturity',maturity_date,'Rate',rate_value) creates a FRA object for one or more FRA instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments StartDate, Maturity, and Rate. For more information on a FRA instrument, see More About.

FRAObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, FRAObj = fininstrument("FRA",'StartDate',datetime(2016,1,30),'Maturity',datetime(2019,1,30),'Rate',0.025,'Principal',100,'Basis',1,'BusinessDayConvention',"follow",'Name',"FRA_instrument") creates a FRA instrument with a principal of 100 and a maturity of January 30, 2019. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

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

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

Data Types: char | cell | string

FRA 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: FRAObj = fininstrument("FRA",'StartDate',datetime(2016,1,30),'Maturity',datetime(2019,1,30),'Rate',0.025,'Principal',100,'Basis',1,'BusinessDayConvention',"follow",'Name',"FRA_instrument")

Required FRA Name-Value Pair Arguments

StartDate — FRA start date

datetime | serial date number | date character vector | date string | vector of datetimes | vector of serial date numbers | cell array of date character vectors | date string array

FRA start date, specified as the comma-separated pair consisting of 'StartDate' 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 StartDate property is stored as a datetime.

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

Maturity — FRA maturity date

datetime | serial date number | date character vector | date string | vector of datetimes | vector of serial date numbers | cell array of date character vectors | date string array

FRA maturity date, specified as the comma-separated pair consisting of 'Maturity' 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: char | cell | double | string | datetime

Rate — FRA coupon rate

scalar decimal | vector of decimals

FRA coupon rate, specified as the comma-separated pair consisting of 'Rate' and a scalar decimal or an NINST-by-1 vector of decimals.

Data Types: double

Optional FRA Name-Value Pair Arguments

Basis — Day count basis

0 (actual/actual) (default) | scalar 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 scalar value or an NINST-by-1 vector of integers from the following:

• 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

100 (default) | scalar numeric | numeric vector

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

Data Types: double

BusinessDayConvention — Business day convention

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

Business day convention, 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. 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) | datetimes | cell array of character vectors | date string array | serial date numbers

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));
FRAObj = fininstrument("FRA",'StartDate',datetime(2016,1,30),'Maturity',datetime(2025,12,15),'Rate',0.025,'Holidays',H)

Data Types: double | cell | datetime | string

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

Properties

StartDate — FRA start date

scalar datetime | vector of datetimes

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

Data Types: datetime

Maturity — FRA maturity date

scalar datetime | vector of datetimes

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

Data Types: datetime

Rate — FRA coupon rate

scalar decimal | vector of decimals

FRA coupon rate, returned as a scalar decimal or an NINST-by-1 vector of decimals.

Data Types: double

Basis — Day count basis

[0 0] (actual/actual) (default) | scalar 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

100 (default) | scalar numeric | numeric vector

Principal amount, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

BusinessDayConvention — Business day convention

"actual" (default) | scalar string | string array

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

Data Types: string

Holidays — Holidays used in computing business days

NaT (default) | datetimes

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

Data Types: datetime

Name — User-defined name for instrument

" " (default) | scalar string | string array

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

Data Types: string

Object Functions

cashflows

Compute cash flow for FixedBond, FloatBond, Swap, FRA, STIRFuture, OISFuture, OvernightIndexedSwap, or Deposit instrument

Examples

Price FRA Instrument Using ratecurve and Discount Pricer

This example shows the workflow to price a FRA (forward rate agreement) instrument when you use a ratecurve and a Discount pricing method.

Create FRA Instrument Object

Use fininstrument to create a FRA instrument object.

FRAObj = fininstrument("FRA",'StartDate',datetime(2020,9,15),'Maturity',datetime(2022,9,15),'Rate',0.0175)

FRAObj = 
  FRA with properties:

                     Rate: 0.0175
                    Basis: 2
                StartDate: 15-Sep-2020
                 Maturity: 15-Sep-2022
                Principal: 100
    BusinessDayConvention: "actual"
                 Holidays: NaT
                     Name: ""

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 Discount Pricer Object

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

outPricer = finpricer("Discount",'DiscountCurve',myRC)

outPricer = 
  Discount with properties:

    DiscountCurve: [1x1 ratecurve]

Price FRA Instrument

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

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

Price = 3.4176

outPR = 
  priceresult with properties:

       Results: [1x2 table]
    PricerData: []

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    3.4176    0.001368

Price Multiple FRA Instruments Using ratecurve and Discount Pricer

This example shows the workflow to price multiple FRA (forward rate agreement) instruments when you use a ratecurve and a Discount pricing method.

Create FRA Instrument Object

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

FRAObj = fininstrument("FRA",'StartDate',datetime([2020,9,15 ; 2020,10,15 ; 2020,11,15]),'Maturity',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'Rate',0.0175)

FRAObj=3×1 object
  3x1 FRA array with properties:

    Rate
    Basis
    StartDate
    Maturity
    Principal
    BusinessDayConvention
    Holidays
    Name

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 Discount Pricer Object

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

outPricer = finpricer("Discount",'DiscountCurve',myRC)

outPricer = 
  Discount with properties:

    DiscountCurve: [1x1 ratecurve]

Price FRA Instruments

Use price to compute the prices and sensitivities for the FRA instruments.

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

Price = 3×1

    3.4176
    3.4121
    3.4063

outPR=1×3 object
  1x3 priceresult array with properties:

    Results
    PricerData

outPR.Results

ans=1×2 table
    Price       DV01  
    ______    ________

    3.4176    0.001368

ans=1×2 table
    Price       DV01   
    ______    _________

    3.4121    0.0013938

ans=1×2 table
    Price       DV01   
    ______    _________

    3.4063    0.0014204

More About

FRA Instrument

A FRA (forward rate agreement) instrument is an over-the-counter contract between parties that determines the rate of interest to be paid on an agreed upon date in the future.

The FRA determines the rates to be used along with the termination date and notional value. FRAs are cash-settled with the payment based on the net difference between the interest rate of the contract and the floating rate in the market, called the reference rate. The notional amount is not exchanged, but is rather a cash amount based on the rate differentials and the notional value of the contract.