Crack Spread Option Pricing
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Transcript of Crack Spread Option Pricing
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3:2:1 Crack Spread Option Pricingby
Monte Carlo Simulations
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Agenda
1. Energy Commodities
2. Crack Spread Options
3. Energy Price Modellingi. Long-Term Mean & Variance Equations (Arma-
Garch)
ii. Geometric Brownian Motion
iii. GBM Mean Reverting
iv. GBM Mean Reverting and Garch Volatility
v. GBM Mean Reverting and Jump Diffusion
4. In sample Root Mean Squared Error
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Agenda
5. Option Pricing Modellingi. Single Commodities
Black Scholes (RMSE, Implied Volatility, Volatility Smile)
Monte Carlo Simulations (RMSE)
ii. 1:1 Crack Spreads
Kirk Formula
1:1 Crack Spreads
iii. 3:2:1 Crack Spreads
Monte Carlo Simulations
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Energy Commodity Prices
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Crack Spread Options
Crack spread options are contracts written on the price differential, orspread, of crude oil futures and refined product futures, i.e., crude oil,heating oil or gasoline futures .
Rafinery Input : Crude OilRafinery Output : Heating Oil and Gasoline
1:1 Crack Spread : Crude Oil – Heating Oil or Crude Oil – Gasoline3:2:1 Crack Spread : (3xCrude Oil - 2xGasoline - 1xHeating Oil) / 3
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3:2:1 Crack Spread Options
fCS = (3fCO - 2fGA - 1fHO) / 3
where
fCS is the crack spread value at maturityfCO is the value of a crude oil future contract at maturityfGA is the value of a gasoline future contract at maturityfHO is the value of a heating oil future contract at maturity
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ARMA-GARCH Modelling
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ARMA-GARCH Modelling Simulation BackTesting
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Geometric Brownian Motion
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Geometric Brownian MotionSimulation BackTesting
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GBM Mean Reverting
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GBM Mean Reverting Simulation BackTesting
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GBM Mean Reverting GARCH (1,1)
GARCH (1,1) Volatility Simulation
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GBM Mean Reverting GARCH (1,1)Simulation BackTesting
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Jump Diffusion
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Jump DiffusionSimulation BackTesting
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InSample Root Mean Squared Error
The best fitted model is GBM-Mean Reverting and GARCH (1,1) Model !
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Empirical Results - Crude Oil OptionsBlack Scholes Method
The overall RMSE figure for ATM options which have below 1 year DTM is 40%.
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Empirical Results - Crude Oil OptionsBS Method – Implied Volatility
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Empirical Results - Crude Oil OptionsMonte Carlo Simulations Method
The overall RMSE figure for ATM options which have below 1 year DTM is 51%.
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Empirical Results – 1:1 Crack Spread Options – Kirk Formula
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Empirical Results – 3:2:1 Crack Spread Options–GBM MeanReverting GARCH(1,1)
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Teşekkürler
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