Modeling of Extreme Crude Oil Price using the Generalized Pareto Distribution: Brent and West Texas Benchmark Price

  • Ngozi J. Amachukwu Department of Statistics, Nnamdi Azikwe University, Awka, Nigeria
  • Happiness O. Obiora-Ilouno Department of Statistics, Nnamdi Azikwe University, Awka, Nigeria
  • Edwin I. Obisue Department of Statistics, Delta State Polytechnic Oghara, Delta State, Nigeria
Keywords: modeling, extreme, volatility, threshold, generalized Pareto distribution


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.


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How to Cite
Amachukwu, N. J., Obiora-Ilouno, H. O., & Obisue, E. I. (2021). Modeling of Extreme Crude Oil Price using the Generalized Pareto Distribution: Brent and West Texas Benchmark Price. Earthline Journal of Mathematical Sciences, 6(2), 359-374.