Study of Random Walk Models for Crude Oil Prices
STUDY OF RANDOM WALK MODELS FOR CRUDE OIL PRICES Suhag Patel, Zeel Parikh DAIICT, Gandhinagar [email protected] [email protected] Supervisor Prof. Mukesh Tiwari Prof. Alka Parikh Abstract – In this report we attempt to model the crude oil prices for a period of 15 years ranging from 1990 – 2015. Based on the nature of the fluctuations observed, we attempt to model the variation in crude oil prices as Brownian motion or Random walk. Our studies suggest that depending on the economic conditions different variants of the random walk model is applicable for small intervals of the data. However, no single model is able to provide reasonable fit to the entire data range. We show that most of the data range can be modelled via one of the following three methods, viz. purely geometric random walk, random walk with drift and the reversal to a fixed mean through the Ornstein-Uhlenbeck process. Keywords – Oil Price Modelling, Data analysis, Random walk, Mean Reversion. I. INTRODUCTION Crude oil is one of the major sources of energy. Oil has powered the world in the form of transportation fuels for more than a century, and the demand is expected to grow over the long term. India is the fifth biggest importer of the crude oil [1]. India produces 897,300 barrels of crude oil per day [2] which is only one fifth of its total usage. Speculations in the futures market, wars, natural calamities, production, inflation and several other economic factors are responsible for the dynamic nature of the crude oil [3].
In this project, we aim at modelling the crude oil prices in a manner such that their volatility is also taken into consideration so as to get realistic results for their prediction. We aim to study how far the random walk based models would be successful in such studies. We would also like to point out that such models have been successful to model a variety of problems in the financial market [4], [5]. For the present study, we look at the variation in oil prices over a range of 15 years as shown in Fig.1. The reason that we choose this data range is because, first of all, it gives us large enough dataset to analyse the problem, secondly it captures a wide spectrum in the variations and finally, we believe that such a study would eventually allow us to provide some estimation of the near future prices. The rest of the report is laid out as follows. In Section II, we provide a brief overview of the different random walk models that have been used as tools to study the oil prices in this report. Results of our analysis are shown in Section III wherein we present a comparison between the generated data and the relevant data set. The methods used to estimate the parameters are also presented. Conclusions are presented at the end. [pic 1] Fig. 1 Time series plot of crude oil prices for the period Jan, 1990 – March, 2015 [6].