Stochastic modeling of crude oil prices

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October, 2015
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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.
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,