yourcompany

Murat Gençer

3:2:1 Crack Spread Option Pricingby

Monte Carlo Simulations

yourcompany

Murat Gençer2

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

yourcompany

Murat Gençer3

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

yourcompany

Murat Gençer4

Energy Commodity Prices

yourcompany

Murat Gençer5

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

yourcompany

Murat Gençer6

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

yourcompany

Murat Gençer7

ARMA-GARCH Modelling

yourcompany

Murat Gençer8

ARMA-GARCH Modelling Simulation BackTesting

yourcompany

Murat Gençer9

Geometric Brownian Motion

yourcompany

Murat Gençer10

Geometric Brownian MotionSimulation BackTesting

yourcompany

Murat Gençer11

GBM Mean Reverting

yourcompany

Murat Gençer12

GBM Mean Reverting Simulation BackTesting

yourcompany

Murat Gençer13

GBM Mean Reverting GARCH (1,1)

GARCH (1,1) Volatility Simulation

yourcompany

Murat Gençer14

GBM Mean Reverting GARCH (1,1)Simulation BackTesting

yourcompany

Murat Gençer15

Jump Diffusion

yourcompany

Murat Gençer16

Jump DiffusionSimulation BackTesting

yourcompany

Murat Gençer17

InSample Root Mean Squared Error

The best fitted model is GBM-Mean Reverting and GARCH (1,1) Model !

yourcompany

Murat Gençer18

Empirical Results - Crude Oil OptionsBlack Scholes Method

The overall RMSE figure for ATM options which have below 1 year DTM is 40%.

yourcompany

Murat Gençer19

Empirical Results - Crude Oil OptionsBS Method – Implied Volatility

yourcompany

Murat Gençer20

Empirical Results - Crude Oil OptionsMonte Carlo Simulations Method

The overall RMSE figure for ATM options which have below 1 year DTM is 51%.

yourcompany

Murat Gençer21

Empirical Results – 1:1 Crack Spread Options – Kirk Formula

yourcompany

Murat Gençer22

Empirical Results – 3:2:1 Crack Spread Options–GBM MeanReverting GARCH(1,1)

yourcompany

Murat Gençer23

Teşekkürler

Murat Gençer