Stochastic modeling of crude oil prices
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Date
October, 2015
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Abstract
The prices of crude oil are largely characterized by shocks due to the flow in supply
and demand of soil. In this study, we modeled crude oil prices fluctuations using
stochastic differential equations. Analytical and numerical solutions of the three factors
model proposed by Cortazar and Schwartz (2003) are presented based on
the current price, the future price and volatility of the crude oil. Our simulations
results implementing the model indicated that the simulations achieve better
results when as many paths with smaller time interval are used. We also studied
the price dynamics of WTI crude oil traded at NYMEX from 2004 to 2014. Our
study showed that crude oil prices uctuate over the years with the highest price
recorded in June, 2008 but dropped signifi cantly to $41.12/barrel in December,
2008. We also studied the price dynamics of crude oil futures for the period,
April, 2015 to December, 2023 and observed that despite the continuous fall in
crude oil prices from November, 2014, futures prices increase continuously. Our
simulation results on the value of crude oil options revealed that as the value of
crude oil prices increase, the expected value of the option increases.
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of Master of Philosophy in Applied Mathematics,