Núm. 52 (2020)

VaR and CVaR estimates in BRIC’s Oil Sector: A Normal Inverse Gaussian Distribution Approach

Eduardo Sánchez Ruenes
Tecnológico de Monterrey
José Antonio Núñez Mora
Tecnológico de Monterrey
Martha Beatriz Mota Aragón
Universidad Autónoma Metropolitana
Publicado enero 31, 2020


The Value at Risk (VaR) and the Conditional Value at Risk (CVaR) as measures that estimate risk, have been used in oil sector to measure extreme and unexpected scenarios of oil prices. Additionally, the Normal Inverse Gaussian (NIG) distribution, a special case of the Generalized Hyperbolic (GH) family, has been demonstrated to provide a better fit than Normal distribution to financial data. In this paper, we used NIG distribution to model a distribution of equity price returns in oil companies in Brazil, Russia, India and China (BRIC) economies in periods of unstable oil prices from 2004 to 2017, with the objective of demonstrating an underestimation of the risk measures when a Normal distribution is assumed and a more conservative estimate of those measures when considering a NIG distribution.


  1. Anderson, Theodore Wilbur and Darling, Donald Allan (1954). “A Test of Goodness of Fit”. Journal of the American Statistical Association, 49(268), pp. 765–769. https://doi.org/10.1080/01621459.1954.10501232
  2. Andersson, Fredrik; Mausser, Helmut; Rosen, Dan and Uryasev, Stanislav (2001). “Credit risk optimization with Conditional Value-at-Risk criterion”. Mathematical Programming, 89(2), pp. 273–291. https://doi.org/10.1007/pl00011399
  3. Artzner, Philippe; Delbaen, Freddy; Eber, Jean-Marc and Heath, David (1999). “Coherent Measures of Risk”. Mathematical Finance, 9(3), pp. 203–228. https://doi.org/10.1111/1467-9965.00068
  4. Artzner, Philippe; Delbaen, Freddy; Eber, Jean-Marc and Heath, David (1997). “Thinking coherently”. Risk 10 (11), pp. 68–71
  5. Baffes, John; Kose, Ayhan; Ohnsorge, Franziska and Stocker, Marc (2015). “The Great Plunge in Oil Prices: Causes, Consequences, and Policy Responses”. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2624398
  6. Bali, Turan (2007). “A generalized extreme value approach to financial risk measurement”. Journal of Money, Credit and Banking, 39(7), 1613-1649. https://doi.org/10.1111/jmcb.2007.39.issue-7
  7. Barndorff-Nielsen, Ole Eiler (1997). “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling”. Scandinavian Journal of Statistics, 24(1), pp. 1–13. https://doi.org/10.1111/1467-9469.t01-1-00045
  8. Barndorff-Nielsen, Ole Eiler (1977). “Exponentially Decreasing Distributions for the Logarithm of Particle Size”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 353(1674), pp. 401–419. https://doi.org/10.1098/rspa.1977.0041
  9. Barone-Adesi, Giovanni; Giannopoulos, Kostas and Vosper, Les (2000). “Backtesting the filtered Historical Simulation”. Unpublished manuscript.
  10. Bollerslev, Tim (1986). “Generalized autoregressive conditional heteroscedasticity”. Journal of Econometrics, 31(3), pp. 307–327. https://doi.org/10.1016/0304-4076(86)90063-1
  11. Charpentier, Arthur and Oulidi, Abder (2008). “Estimating allocations for Value-at-Risk portfolio optimization”. Mathematical Methods of Operations Research, 69(3), pp. 395–410. https://doi.org/10.1007/s00186-008-0244-7
  12. Engle, Robert Fry (1982). “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”. Econometrica, 50(4), pp. 987-1007. https://doi.org/10.2307/1912773
  13. Fama, Eugene Francis (1965). “The Behavior of Stock-Market Prices”. The Journal of Business, 38(1), pp. 34-105. https://doi.org/10.1086/294743
  14. Gaivoronski, Alexei and Pflug, Georg (2005). “Value-at-risk in portfolio optimization: properties and computational approach”. The Journal of Risk, 7(2), pp. 1–31. https://doi.org/10.21314/jor.2005.106
  15. Glasserman, Paul; Heidelberger, Philip and Shahabuddin, Perwez (2002). “Portfolio Value-at-Risk with Heavy-Tailed Risk Factors”. Mathematical Finance, 12(3), pp. 239–269. https://doi.org/10.1111/1467-9965.00141
  16. Hendricks, Darryll (1996). “Evaluation of Value-at-Risk Models Using Historical Data”. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1028807
  17. Hong, Jeff; Hu, Zhaolin and Liu, Guangwu (2014). “Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk”. ACM Transactions on Modeling and Computer Simulation, 24(4), pp. 1–37. https://doi.org/10.1145/2661631
  18. Hull, John and White, Alan (1998). “Value at Risk When Daily Changes in Market Variables are not Normally Distributed”. The Journal of Derivatives, 5(3), pp. 9–19. doi:10.3905/jod.1998.407998
  19. Kibzun, Andrey and Kuznetsov, Evgeniy (2003). “Comparison of VaR and CVaR Criteria”. Automation and Remote Control, 64(7), 1154–1164. https://doi.org/10.1023/a:1024794420632
  20. Krokhmal, Pavlo; Palmquist, Jonas and Uryasev, Stanislav (2001). “Portfolio optimization with conditional value-at-risk objective and constraints”. The Journal of Risk, 4(2), pp. 1–36. https://doi.org/10.21314/jor.2002.057
  21. Lauridsen, Sarah (2000). “Estimation of Value at Risk by Extreme Value Method”. Extremes 3(2), pp. 107–144. https://doi.org/10.1023/a:1009979331996
  22. Markowitz, Harry (1952). “Portfolio Selection”. The Journal of Finance, 7(1), pp. 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
  23. Mentel, Grzegorz (2013). “Parametric or Non-Parametric Estimation of Value-At-Risk”. International Journal of Business and Management, 8(11), pp. 103-112. https://doi.org/10.5539/ijbm.v8n11p103
  24. Mota-Aragón, Martha Beatriz and Mata-Mata, Leovardo (2016). “Caracterización Paramétrica de los Rendimientos de los Precios del Petróleo 2010-2015”. Panorama Económico, 11(22), pp. 63-74. https://doi.org/10.29201/pe-ipn.v11i22.24
  25. Núñez, José Antonio; Contreras-Valdez, Mario Iván; Ramírez-García, Alfredo and Sánchez-Ruenes, Eduardo (2018). “Underlying Assets Distribution in Derivatives: The BRIC Case”. Theoretical Economics Letters, 08(03), pp. 502–513. https://doi.org/10.4236/tel.2018.83035
  26. Peña, I. (2002). La Gestión de Riesgos Financieros de Mercado y de Crédito. Madrid: Prentice Hall.
  27. Rockafellar, Ralph Tyrrell and Uryasev, Stanislav (2002). “Conditional value-at-risk for general loss distributions”. Journal of Banking & Finance, 26(7), pp. 1443–1471. https://doi.org/10.1016/s0378-4266(02)00271-6
  28. Sadorsky, Perry (1999). “Oil price shocks and stock market activity”. Energy Economics, 21(5), pp. 449–469. https://doi.org/10.1016/s0140-9883(99)00020-1
  29. Shapiro, Samuel Sanford and Francia, R. S. (1972). “An Approximate Analysis of Variance Test for Normality”. Journal of the American Statistical Association, 67(337), pp. 215–216. https://doi.org/10.1080/01621459.1972.10481232
  30. Shen, Hao; Meng, Xuanjin and Meng, Xiaojin (2017). “How to Manage the Risk in the Precious Metals Market? The Case of Gold”. SSRN Electronic Journal, pp. 1-10. https://doi.org/10.2139/ssrn.3016829
  31. Shen, Hao; Meng, Xuanjin; Guo, Rongjie; Zhao, Yuyan; Ding, Siyi and Meng, Xiaojin (2017). “Heavy-tailed distribution and risk management of gold returns”. International Journal of Academic Research in Economics and Management Sciences, 6(3), pp. 15-24. https://doi.org/10.6007/ijarems/v6-i3/3147
  32. Yamai, Yasuhiro and Yoshiba, Toshinao (2005). “Value-at-risk versus expected shortfall: A practical perspective”. Journal of Banking & Finance, 29(4), pp. 997–1015. https://doi.org/10.1016/j.jbankfin.2004.08.010