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