Spread

Spread instrument object

Since R2020a

Description

Create and price a Spread instrument object for one or more Spread instruments using this workflow:

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

2. Use finmodel to specify a BlackScholes or Bachelier model for the Spread instrument object.

3. Choose a pricing method.

   • When using a BlackScholes model, use finpricer to specify a Kirk, BjerksundStensland, or AssetMonteCarlo pricing method for one or more Spread instruments.

   • When using a Bachelier model, use finpricer to specify an AssetMonteCarlo pricing method for one or more Spread 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 Spread instrument, see Choose Instruments, Models, and Pricers.

Creation

Syntax

SpreadObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date)

SpreadObj = fininstrument(___,Name,Value)

Description

SpreadObj = fininstrument(InstrumentType,'Strike',strike_value,'ExerciseDate',exercise_date) creates a Spread object for one or more Spread instruments by specifying InstrumentType and sets the properties for the required name-value pair arguments Strike and ExerciseDate.

SpreadObj = fininstrument(___,Name,Value) sets optional properties using additional name-value pairs in addition to the required arguments in the previous syntax. For example, SpreadObj = fininstrument("Spread",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"American",'Name',"spread_instrument") creates a Spread put option with an American exercise. You can specify multiple name-value pair arguments.

Input Arguments

InstrumentType — Instrument type

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

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

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: SpreadObj = fininstrument("Spread",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"American",'Name',"spread_instrument")

Required Spread Name-Value Pair Arguments

Strike — Option strike price value

nonnegative numeric | nonnegative numeric vector

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

Data Types: double

ExerciseDate — Option exercise date

datetime array | string array | date character vector

Option exercise date, specified as the comma-separated pair consisting of 'ExerciseDate' and a scalar or an NINST-by-1 vector using a datetime array, string array, or date character vectors.

Note

For a European option, there is only one ExerciseDate on the option expiry date.

To support existing code, Spread 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 ExerciseDate property is stored as a datetime.

Optional Spread Name-Value Pair Arguments

OptionType — Option type

"call" (default) | string with value "call" or "put" | string array with values of "call" or "put" | character vector with value 'call' or 'put' | cell array of character vectors with values of 'call' or 'put'

Option type, specified as the comma-separated pair consisting of 'OptionType' 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

ExerciseStyle — Option exercise style

"European" (default) | string with value "European" | string array with values of "European" | character vector with value 'European' | cell array of character vectors with values of 'European'

Option exercise style, specified as the comma-separated pair consisting of 'ExerciseStyle' and a scalar string or character vector or an NINST-by-1 cell array of character vectors or string array.

Data Types: string | cell | char

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

Strike — Option strike price value

nonnegative numeric | nonnegative numeric vector

Option strike price value, returned as a scalar nonnegative numeric or an NINST-by-1 nonnegative numeric vector.

Data Types: double

ExerciseDate — Option exercise date

datetime | vector of datetimes

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

Data Types: datetime

OptionType — Option type

"call" (default) | string with value "call" or "put" | string array with value "call" or "put"

Option type, returned as a scalar string or an NINST-by-1 string array with values of "call" or "put".

Data Types: string

ExerciseStyle — Option exercise style

"European" (default) | string with value "European" | string array with values of "European"

Option exercise style, returned as a string or an NINST-by-1 string array with values of "European".

Data Types: string

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

Examples

Price Spread Instrument with European Option Using Black-Scholes Model and Bjerksund-Stensland Pricer

This example shows the workflow to price a Spread instrument with a European option when using a BlackScholes model and a BjerksundStensland pricing method.

Create Spread Instrument Object

Use fininstrument to create a Spread instrument object.

SpreadOpt = fininstrument("Spread",'Strike',105,'ExerciseDate',datetime(2021,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"spread_option")

SpreadOpt = 
  Spread with properties:

       OptionType: "put"
           Strike: 105
    ExerciseStyle: "european"
     ExerciseDate: 15-Sep-2021
             Name: "spread_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',[0.2,0.1])

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: [0.2000 0.1000]
    Correlation: [2x2 double]

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create BjerksundStensland Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',[103 105],'DividendValue',[0.025 , 0.028],'PricingMethod',"BjerksundStensland")

outPricer = 
  BjerksundStensland with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.BlackScholes]
        SpotPrice: [103 105]
    DividendValue: [0.0250 0.0280]
     DividendType: "continuous"

Price Spread Instrument

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

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

Price = 95.9884

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: []

outPR.Results

ans=1×7 table
    Price           Delta                    Gamma                    Lambda                 Vega          Theta      Rho  
    ______    __________________    _______________________    ____________________    ________________    _____    _______

    95.988    -0.8916    0.90457    0.0021316    0.00048175    -0.95673     0.97064    13.582    1.5785    3.135    -278.49

Price Multiple Spread Instruments with European Option Using Black-Scholes Model and Bjerksund-Stensland Pricer

This example shows the workflow to price multiple Spread instruments with a European option when using a BlackScholes model and a BjerksundStensland pricing method.

Create Spread Instrument Object

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

SpreadOpt = fininstrument("Spread",'Strike',[105 ; 120 ; 150],'ExerciseDate',datetime([2021,9,15 ; 2021,10,15 ; 2021,11,15]),'OptionType',"put",'ExerciseStyle',"european",'Name',"spread_option")

SpreadOpt=3×1 object
  3x1 Spread array with properties:

    OptionType
    Strike
    ExerciseStyle
    ExerciseDate
    Name

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes",'Volatility',[0.2,0.1])

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: [0.2000 0.1000]
    Correlation: [2x2 double]

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create BjerksundStensland Pricer Object

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

outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',[103 160],'DividendValue',[0.025 , 0.028],'PricingMethod',"BjerksundStensland")

outPricer = 
  BjerksundStensland with properties:

    DiscountCurve: [1x1 ratecurve]
            Model: [1x1 finmodel.BlackScholes]
        SpotPrice: [103 160]
    DividendValue: [0.0250 0.0280]
     DividendType: "continuous"

Price Spread Instruments

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

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

Price = 3×1

  146.1732
  159.1989
  185.5513

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

    Results
    PricerData

outPR.Results

ans=1×7 table
    Price            Delta                     Gamma                     Lambda                 Vega           Theta       Rho  
    ______    ____________________    ________________________    ____________________    _________________    ______    _______

    146.17    -0.91985     0.91683    0.00057696    7.9581e-05    -0.64817     0.64604    3.6848    0.60671    4.9043    -282.63

ans=1×7 table
    Price           Delta                     Gamma                     Lambda                 Vega           Theta       Rho  
    _____    ____________________    ________________________    ____________________    _________________    ______    _______

    159.2    -0.92024     0.91557    0.00042064    5.4001e-05    -0.59539     0.59237    2.7723    0.40502    5.3984    -331.26

ans=1×7 table
    Price            Delta                    Gamma                    Lambda                 Vega           Theta       Rho  
    ______    ____________________    ______________________    ____________________    _________________    ______    _______

    185.55    -0.92123     0.91439    0.000216    1.9895e-05    -0.51138     0.50758    1.4478    0.16988    6.3711    -424.75

Price Spread Instrument for a Commodity Using Black-Scholes Model and Analytic Pricers

This example shows the workflow to price a commodity Spread instrument when you use a BlackScholes model and Kirk and BjerksundStensland analytic pricing methods.

Understanding Crack Spread Options

In the petroleum industry, refiners are concerned about the difference between their input costs (crude oil) and output prices (refined products — gasoline, heating oil, diesel fuel, and so on). The differential between these two underlying commodities is referred to as a crack spread. It represents the profit margin between crude oil and the refined products.

A spread option is an option on the spread where the holder has the right, but not the obligation, to enter into a spot or forward spread contract. Crack spread options are often used to protect against declines in the crack spread or to monetize volatility or price expectations on the spread.

Define the Commodity

Assume that current gasoline prices are strong, and you want to model a crack spread option strategy to protect the gasoline margin. A crack spread option strategy is used to maintain profits for the following season. The WTI crude oil futures are at $93.20 per barrel and RBOB gasoline futures contract are at $2.85 per gallon.

Strike = 20;
Rate = 0.05;

Settle = datetime(2020,1,1);
Maturity = datemnth(Settle,3);

% Price and volatility of RBOB gasoline
PriceGallon1 = 2.85;          % Dollars per gallon
Price1 = PriceGallon1 * 42;   % Dollars per barrel
Vol1 = 0.29;

% Price and volatility of WTI crude oil
Price2 = 93.20;         % Dollars per barrel
Vol2 = 0.36;

% Correlation between the prices of the commodities
Corr = 0.42;

Create Spread Instrument Object

Use fininstrument to create a Spread instrument object.

SpreadOpt = fininstrument("Spread", 'ExerciseDate', Maturity, 'Strike', Strike,'ExerciseStyle',"european",'Name',"spread_instrument")

SpreadOpt = 
  Spread with properties:

       OptionType: "call"
           Strike: 20
    ExerciseStyle: "european"
     ExerciseDate: 01-Apr-2020
             Name: "spread_instrument"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

BlackScholesModel = finmodel("BlackScholes", 'Volatility', [Vol1,Vol2], 'Correlation', [1 Corr; Corr 1]);

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

ZeroCurve = ratecurve('zero', Settle, Maturity, Rate, 'Basis', 1);

Create BjerksundStensland Pricer Object

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

BJSPricer = finpricer("Analytic", 'Model', BlackScholesModel, 'SpotPrice', [Price1 , Price2], 'DiscountCurve', ZeroCurve,'PricingMethod', "BjerksundStensland");

Create Kirk Pricer Object

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

KirkPricer = finpricer("Analytic", 'Model', BlackScholesModel,'SpotPrice', [Price1 , Price2], 'DiscountCurve', ZeroCurve,'PricingMethod', "Kirk");

Price Spread Instrument Using BjerksundStensland and Kirk Analytic Pricing Methods

Use price to compute the price and sensitivities for the commodity Spread instrument.

[PriceKirk, outPR_Kirk] = price(KirkPricer, SpreadOpt, "all");
[PriceBJS,  outPR_BJS]  = price(BJSPricer,  SpreadOpt, "all");

[outPR_Kirk.Results; outPR_BJS.Results]

ans=2×7 table
    Price           Delta                  Gamma                 Lambda                Vega           Theta      Rho  
    _____    ___________________    ____________________    _________________    ________________    _______    ______

    11.19    0.67224    -0.60665    0.019081    0.021662    7.1907    -6.4891    11.299    9.8869    -14.539    3.1841
     11.2    0.67371    -0.60816    0.018992    0.021572    7.2003    -6.4997    11.198    9.9878    -14.555    3.1906

Price Spread Instrument with American Option Using Black-Scholes Model and Asset Monte-Carlo Pricer

This example shows the workflow to price a Spread instrument with an American option when using a BlackScholes model and an AssetMonteCarlo pricing method.

Create Spread Instrument Object

Use fininstrument to create a Spread instrument object.

SpreadOpt = fininstrument("Spread",'Strike',100,'ExerciseDate',datetime(2021,9,15),'OptionType',"put",'ExerciseStyle',"American",'Name',"spread_option")

SpreadOpt = 
  Spread with properties:

       OptionType: "put"
           Strike: 100
    ExerciseStyle: "american"
     ExerciseDate: 15-Sep-2021
             Name: "spread_option"

Create BlackScholes Model Object

Use finmodel to create a BlackScholes model object.

Corr = 0.42;
BlackScholesModel = finmodel("BlackScholes","Volatility",[0.3,0.1],"Correlation", [1 Corr;Corr 1])

BlackScholesModel = 
  BlackScholes with properties:

     Volatility: [0.3000 0.1000]
    Correlation: [2x2 double]

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo","DiscountCurve",myRC,"Model",BlackScholesModel,'SpotPrice',[100,95],'simulationDates',datetime(2021,9,15),'dividendType',["continuous","continuous"],'dividendvalue',[0,0.01])

outPricer = 
  GBMMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: [100 95]
    SimulationDates: 15-Sep-2021
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.BlackScholes]
       DividendType: ["continuous"    "continuous"]
      DividendValue: [0 0.0100]

Price Spread Instrument

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

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

Price = 95

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results

ans=1×7 table
    Price     Delta           Gamma               Lambda          Rho    Theta     Vega 
    _____    ________    _______________    __________________    ___    _____    ______

     95      -1     1    0    3.1492e-14    -1.0526          1     0       0      0    0

Price Spread Instrument with American Option Using Bachelier Model and Asset Monte-Carlo Pricer

This example shows the workflow to price a Spread instrument with an American option when using a Bachelier model and an AssetMonteCarlo pricing method.

Create Spread Instrument Object

Use fininstrument to create a Spread instrument object.

SpreadOpt = fininstrument("Spread",'Strike',100,'ExerciseDate',datetime(2021,9,15),'OptionType',"put",'ExerciseStyle',"American",'Name',"spread_option")

SpreadOpt = 
  Spread with properties:

       OptionType: "put"
           Strike: 100
    ExerciseStyle: "american"
     ExerciseDate: 15-Sep-2021
             Name: "spread_option"

Create Bachelier Model Object

Use finmodel to create a Bachelier model object.

Corr = 0.42;
BachelierModel = finmodel("BlackScholes","Volatility",[0.3,0.1],"Correlation", [1 Corr;Corr 1])

BachelierModel = 
  BlackScholes with properties:

     Volatility: [0.3000 0.1000]
    Correlation: [2x2 double]

Create ratecurve Object

Create a flat ratecurve object using ratecurve.

Settle = datetime(2018,9,15);
Maturity = datetime(2023,9,15);
Rate = 0.035;
myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)

myRC = 
  ratecurve with properties:

                 Type: "zero"
          Compounding: -1
                Basis: 12
                Dates: 15-Sep-2023
                Rates: 0.0350
               Settle: 15-Sep-2018
         InterpMethod: "linear"
    ShortExtrapMethod: "next"
     LongExtrapMethod: "previous"

Create AssetMonteCarlo Pricer Object

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

outPricer = finpricer("AssetMonteCarlo","DiscountCurve",myRC,"Model",BachelierModel,'SpotPrice',[100,95],'simulationDates',datetime(2021,9,15),'dividendType',["continuous","continuous"],'dividendvalue',[0,0.01])

outPricer = 
  GBMMonteCarlo with properties:

      DiscountCurve: [1x1 ratecurve]
          SpotPrice: [100 95]
    SimulationDates: 15-Sep-2021
          NumTrials: 1000
      RandomNumbers: []
              Model: [1x1 finmodel.BlackScholes]
       DividendType: ["continuous"    "continuous"]
      DividendValue: [0 0.0100]

Price Spread Instrument

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

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

Price = 95

outPR = 
  priceresult with properties:

       Results: [1x7 table]
    PricerData: [1x1 struct]

outPR.Results

ans=1×7 table
    Price     Delta           Gamma               Lambda          Rho    Theta     Vega 
    _____    ________    _______________    __________________    ___    _____    ______

     95      -1     1    0    3.1492e-14    -1.0526          1     0       0      0    0

More About

Spread Option

A spread option is written on the difference of two underlying assets.

For example, a European call on the difference of two assets X1 and X2 has the following pay off at maturity:

$$\max (X1-X2-K,0)$$

K is the strike price.

For more information, see Spread Option.

Version History

Introduced in R2020a

R2022b: Serial date numbers not recommended

Although Spread 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.