Spread

Spread instrument object

Description

Create and price a Spread instrument object using this workflow:

1. Use fininstrument to create a Spread instrument object.

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

3. Use finpricer to specify a Kirk, BjerksundStensland, or AssetMonteCarlo pricing method for the Spread 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 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 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" | character vector with value 'Spread'

Instrument type, specified as a string with the value of "Spread" or a character vector with a value of 'Spread'.

Data Types: char | string

Spread 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: 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

Option strike price value, specified as the comma-separated pair consisting of 'Strike' and a scalar nonnegative numeric value.

Data Types: double

'ExerciseDate' — Option exercise date

datetime | serial date number | date character vector | date string

Option exercise date, specified as the comma-separated pair consisting of 'ExerciseDate' and a scalar datetime, serial date number, date character vector, or date string.

Note

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

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

Data Types: double | char | string | datetime

Optional Spread Name-Value Pair Arguments

'OptionType' — Option type

"call" (default) | string with value "call" or "put" | character vector with value 'call' or 'put'

Option type, specified as the comma-separated pair consisting of 'OptionType' and a scalar string or character vector.

Data Types: char | string

'ExerciseStyle' — Option exercise style

"European" (default) | string with value "European" | character vector with value 'European'

Option exercise style, specified as the comma-separated pair consisting of 'ExerciseStyle' and a scalar string or character vector.

Data Types: string | char

'Name' — User-defined name for instrument

" " (default) | string | character vector

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

Strike — Option strike price value

nonnegative numeric

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

Data Types: double

ExerciseDate — Option exercise date

datetime

Option exercise date, returned as a datetime.

Data Types: datetime

OptionType — Option type

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

Option type, returned as a string with a value of "call" or "put".

Data Types: string

ExerciseStyle — Option exercise style

"European" (default) | string with value "European"

Option exercise style, returned as a string with a value of "European".

Data Types: string

Name — User-defined name for instrument

" " (default) | string

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

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 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

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.