EquityIndexFuture

EquityIndexFuture instrument object

Since R2022a

Description

Create and price an EquityIndexFuture instrument object for one or more Equity Index Future instruments using this workflow:

1. Use fininstrument to create an EquityIndexFuture instrument object for one or more Equity Index Future instruments.

2. Use ratecurve to specify a curve model for the EquityIndexFuture instrument object.

3. Use finpricer to specify a Future pricing method for one or more EquityIndexFuture instruments.

4. Use cashsettle to compute the cash settlement for the EquityIndexFuture instrument and fairdelivery to compute the fair delivery price for the underlying asset for the EquityIndexFuture instrument.

For more detailed 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 an EquityIndexFuture instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

EquityIndexFutureObj = fininstrument(InstrumentType,Maturity=maturity_value,QuotedPrice=quoted_price)

EquityIndexFutureObj = fininstrument(___,Name=Value)

Description

EquityIndexFutureObj = fininstrument(InstrumentType,Maturity=maturity_value,QuotedPrice=quoted_price) creates an EquityIndexFuture object for one or more Equity Index Future instruments by specifying InstrumentType and sets the properties for the required name-value arguments Maturity and QuotedPrice.

The EquityIndexFuture instrument supports stock index futures such as NASDAQ 100 and Dow Jones index futures. For more information, see Equity Index Futures.

EquityIndexFutureObj = fininstrument(___,Name=Value) sets optional properties using additional name-value arguments in addition to the required arguments in the previous syntax. For example, EquityIndexFutureObj = fininstrument("EquityIndexFuture",Maturity=datetime(2022,9,1),QuotedPrice=4800,Size=500,Name="equityindexfuture_instrument") creates an EquityIndexFuture instrument. You can specify multiple name-value arguments.

Input Arguments

InstrumentType — Instrument type

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

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

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.

Example: EquityIndexFutureObj = fininstrument("EquityIndexFuture",Maturity=datetime(2022,9,1),QuotedPrice=4800,Size=500,Name="equityindexfuture_instrument")

Required EquityIndexFuture Name-Value Arguments

Maturity — EquityIndexFuture maturity date

datetime array | string array | date character vector

EquityIndexFuture maturity date, specified as Maturity and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, EquityIndexFuture 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.

QuotedPrice — EquityIndexFuture quoted delivery index price

scalar numeric | numeric vector

EquityIndexFuture quoted delivery index price, specified as QuotedPrice and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Optional EquityIndexFuture Name-Value Arguments

Size — Contract size multiplier

250 (default) | scalar numeric | numeric vector

Contract size multiplier, specified as Size and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

DividendYield — Annualized dividend yield for life of contract

0 (default) | scalar numeric | numeric vector

Annualized dividend yield for the life of the contract, specified as DividendYield and a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

DividendYieldCompounding — Compounding frequency for DividendYield

-1 (continuous compounding) (default) | scalar integer with value of -1, 0, 1, 2, 4, 6, or 12 | vector of integers with values -1, 0, 1, 2, 4, 6, or 12

Compounding frequency for DividendYield, specified as DividendYieldCompounding and a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

DividendYieldBasis — Day count basis for DividendYield

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

Day count basis for DividendYield, specified as DividendYieldBasis and scalar integer or an NINST-by-1 vector of integers using 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

Name — User-defined name for instrument

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

User-defined name for one rf more instruments, specified as 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

EquityIndexFutureObj — Equity Index Future instrument

EquityIndexFuture object

Equity Index Future instrument, returned as an EquityIndexFuture object.

Properties

Maturity — EquityIndexFuture maturity date

scalar datetime | vector of datetimes

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

Data Types: datetime

QuotedPrice — EquityIndexFuture quoted price

scalar numeric | numeric vector

EquityIndexFuture quoted price, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

Size — Contract size multiplier

250 (default) | scalar numeric | numeric vector

Contract size multiplier, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

DividendYield — Annualized dividend yield for life of contract

0 (default) | scalar numeric | numeric vector

Annualized dividend yield for the life of the contract, returned as a scalar numeric or an NINST-by-1 numeric vector.

Data Types: double

DividendYieldCompounding — Compounding frequency for DividendYield

-1 (continuous compounding) (default) | scalar integer with value of -1, 0, 1, 2, 4, 6, or 12 | vector of integers with values -1, 0, 1, 2, 4, 6, or 12

Compounding frequency for DividendYield, returned as a scalar integer or an NINST-by-1 vector of integers.

Data Types: double

DividendYieldBasis — Day count basis for DividendYield

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

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

Data Types: double

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

Object Functions

cashsettle	Compute cash settlement for BondFuture, CommodityFuture, EquityIndexFuture, or FXFuture instrument
fairdelivery	Compute fair delivery price of underlying asset for BondFuture, CommodityFuture, EquityIndexFuture, or FXFuture instrument

Examples

Price EquityIndexFuture Instrument Using ratecurve and Future Pricer

This example shows the workflow to price an EquityIndexFuture instrument when you use a ratecurve object and a Future pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2022,3,1);
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;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=2);

Create EquityIndexFuture Instrument Object

Use fininstrument to create an EquityIndexFuture instrument object.

EquityIndexFut = fininstrument("EquityIndexFuture",Maturity=datetime(2022,9,1),QuotedPrice=4800,DividendYield=.03,Name="equityindexfuture_instrument")

EquityIndexFut = 
  EquityIndexFuture with properties:

                    Maturity: 01-Sep-2022
                 QuotedPrice: 4800
                        Size: 250
               DividendYield: 0.0300
    DividendYieldCompounding: -1
          DividendYieldBasis: 0
                        Name: "equityindexfuture_instrument"

Create Future Pricer Object

Use finpricer to create a Future pricer object and use the ratecurve object with the DiscountCurve name-value argument.

outPricer = finpricer("Future",DiscountCurve=ZeroCurve,SpotPrice=4460)

outPricer = 
  Future with properties:

    DiscountCurve: [1×1 ratecurve]
        SpotPrice: 4460

Price EquityIndexFuture Instrument

Use price to compute the price and price result for the EquityIndexFuture instrument.

[Price,outPR] = price(outPricer,EquityIndexFut)

Price = 
-9.8598e+04

outPR = 
  priceresult with properties:

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

outPR.Results

ans=1×4 table
    Price     FairDeliveryPrice    FairFuturePrice    AccruedInterest
    ______    _________________    _______________    _______________

    -98598       1.1011e+06            4404.6                0       

Price Multiple EquityIndexFuture Instruments Using ratecurve and Future Pricer

This example shows the workflow to price multiple EquityIndexFuture instruments when you use a ratecurve object and a Future pricing method.

Create ratecurve Object

Create a ratecurve object using ratecurve.

Settle = datetime(2022,3,1);
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;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=2);

Create EquityIndexFuture Instrument Object

Use fininstrument to create an EquityIndexFuture instrument object for three Equity Index Future instruments.

EquityIndexFut = fininstrument("EquityIndexFuture",Maturity=datetime([2022,9,1 ; 2022,10,1 ; 2022,11,1]),QuotedPrice=[4800 ; 5000 ; 5200],DividendYield=.03,Name="equityindexfuture_instrument")

EquityIndexFut=3×1 EquityIndexFuture array with properties:
    Maturity
    QuotedPrice
    Size
    DividendYield
    DividendYieldCompounding
    DividendYieldBasis
    Name

Create Future Pricer Object

Use finpricer to create a Future pricer object and use the ratecurve object with the DiscountCurve name-value argument.

outPricer = finpricer("Future",DiscountCurve=ZeroCurve,SpotPrice=4460)

outPricer = 
  Future with properties:

    DiscountCurve: [1×1 ratecurve]
        SpotPrice: 4460

Price EquityIndexFuture Instruments

Use price to compute the prices and price results for the EquityIndexFuture instruments.

[Price,outPR] = price(outPricer,EquityIndexFut)

Price = 3×1
105 ×

   -0.9860
   -1.5060
   -2.0262

outPR=1×3 priceresult array with properties:
    Results
    PricerData

outPR.Results

ans=1×4 table
    Price     FairDeliveryPrice    FairFuturePrice    AccruedInterest
    ______    _________________    _______________    _______________

    -98598       1.1011e+06            4404.6                0       

ans=1×4 table
      Price       FairDeliveryPrice    FairFuturePrice    AccruedInterest
    __________    _________________    _______________    _______________

    -1.506e+05       1.0989e+06            4395.7                0       

ans=1×4 table
       Price       FairDeliveryPrice    FairFuturePrice    AccruedInterest
    ___________    _________________    _______________    _______________

    -2.0262e+05       1.0967e+06            4386.6                0       

More About

Equity Index Futures

An equity index future is a "futures contract" on an equity index.

Equity index futures are cash settled contracts with the majority having quarterly expiration dates scheduled for the months of March, June, September, and December. In the equity index futures market, the underlying asset is an equity index (for example, S&P 500) multiplied by a size multiplier that is standardized to each specific type of equity index future (for example, $250 for S&P 500 Future, and $50 for E-Mini S&P 500 Future). If the equity index has dividends, computing the fair future price requires the dividend yield for the life of the contract in addition to the interest rate.

$$\begin{array}{l}{F}_0=S_0\exp (r-q)T\\ FairDeliveryPrice=F_0\times Size\end{array}$$

• F₀ — Fair future price of equity index

• S₀ — Spot price of equity index

• r — Continuously compounded zero rate

• q — Continuously compounded annualized dividend yield

• T — Time to maturity of contract

• Size — Size multiplier for equity index futures (for example, $250 for S&P 500 Future)

There are two workflows.

• The first workflow is to compute the discounted present value of the futures contract using cashsettle assuming it is held until maturity like a forward contract.

  $$f=(F_0-K)\exp (-rT)Size=(F_0-K)\times DiscountFactor\times Size$$

  • F₀ — Fair future price

  • K — Contractual price

  • r — Continuously compounded zero rate

  • T — Time to maturity of contract

• Since futures contracts are settled on every trading day, the second workflow is to use fairdelivery to compute the current fair delivery price of the futures contract to support marking to market.

  $$MarkToMarket=(ChangeinFuturePrice\text{)}\times \text{(}ContractSize\text{)}$$

Version History

Introduced in R2022a

R2022b: Serial date numbers not recommended

Although EquityIndexFuture 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.