Modeling of Extreme Crude Oil Price using the Generalized Pareto Distribution: Brent and West Texas Benchmark Price
Abstract
Background and objective: Crude oil is an essential commodity in many countries of the world. This work studies the risk involved in the extreme crude oil price, using the daily crude oil price of the Brent and the West Texas benchmark from year 1990 to 2019.
Materials and methods: The Peak Over Threshold (POT) approach of the Generalized Pareto Distribution (GPD) was used to model the extreme crude oil price while the value at risk and the expected shortfall was used to quantify the risk involved in extreme price of crude oil. The GPD, using the Q-Q plot was found to be a good model for the extreme values of the crude oil price.
Results: The Value at Risk (VaR) and the Expected Shortfall (ES) calculated at 90%, 95% and 99% with the Maximum Likelihood estimators of GPD parameters and the threshold values were found to decrease with increase in quantile for both benchmark. This shows that risk involved in extreme crude oil price will be borne only by the investors and public.
Conclusion: It was also found that the VaR and ES of the Brent are higher than that of West Texas. This implies that it is safer to invest in West Texas crude oil.
References
S. Coles, An Introduction to Statistical Modeling of Extreme Values, London: Springer-Verlag, 2001. https://doi.org/10.1007/978-1-4471-3675-0
A.C. Davison and R.L. Smith, Models for exceedances over high thresholds, J. R. Stat. Soc. B 52(3) (1990), 393-442. https://doi.org/10.1111/j.2517-6161.1990.tb01796.x
S. Huang, H. An, S. Wen and F. An, Revisiting driving factors of oil price shocks across time scales, Energy 139 (2017), 617-629. https://doi.org/10.1016/j.energy.2017.07.158
R.J. Karobia, Modeling extreme claims using generalized Pareto distributions family in an insurance company, Thesis paper, Presented to the School of Mathematics, University of Nairobi, 2015.
G. Lalude, Importance of oil to the global community, Global Journal of Human-Social Science 15(1) Version 1.0 (2015). Retrieved from https://socialscienceresearch.org/index.php/GJHSS/article/view/1524
A.J. McNeil, R. Frey and P. Embrechts, Quantitative Risk Management, New Jersey: Princeton University Press, 2005.
A. Murat and E. Tokat, Forecasting oil price movements with crack spread futures, Energy Economics 31 (2009), 85-90. https://doi.org/10.1016/j.eneco.2008.07.008
R.S. Pindyck, The long-run forecasting of energy prices, The Energy Journal 20 (1999), 1-27. https://doi.org/10.5547/ISSN0195-6574-EJ-Vol20-No2-1
F. Ren and D.E. Giles, Extreme value analysis of daily Canadian crude oil prices, Applied Financial Economics 20(12) (2010), 941-954. https://doi.org/10.1080/09603101003724323
T.M. Rybezynski, The Economics of Oil Crisis, London: Macmillan Press, 1996.
L. Xu and Q. Zhang, Modeling agricultural catastrophic risk, Agriculture and Agricultural Science Procedia 1 (2010), 251-257. https://doi.org/10.1016/j.aaspro.2010.09.031
X. Zhao, Extreme value modeling with application in finance and neonatal research, PhD thesis, The University of Canterbury, 2010. Retrieved from http://ir.canterbury.ac.nz/bitstream/10092/4024/1/thesisfulltext.pdf
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
