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DOI:
https://doi.org/10.24275/uam/azc/dcsh/ae/2021v36n93/De-jesusKeywords:
Crude oil, Conditional extreme value theory, VaR modelsAbstract
This paper aims to combine the extreme value theory and CGARCH models to capture the long-term asymmetry effects and long memory in volatility and to improve the estimation of tail risk for Maya crude oil. The results of the backtesting confirm the forecasting ability of the symmetric and asymmetric CGARCH-EVT approaches for the estimation of dynamic VaR even though risk measures based on the GARCH-EVT family approaches provide also a better out of sample performance. The findings have important implications for crude oil market participants as they allow them to improve risk management and design optimal hedging strategies to reduce exposure to price risk of producers and consumers.
JEL Classification: C22; C52; G13; Q40.
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References
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Bali, T. & Theodossiou, P. (2007). A conditional-SGT-VaR approach with alternative GARCH models, Annals Operations Research, vol. 151, no. 1, pp. 241–267. https://doi.org/10.1007/s10479-006-0118-4
Balkema, A. A., and de Haan, L. (1974). Residual lifetime at great age, The Annals of Probability, Vol. 2 (5), pp. 792–804. https://doi.org/ 10.1214/aop/1176996548
Basel Committee. (1996). Supervisory framework for the use of backtesting in conjunction with the internal models approach to market risk capital requirements, Basel Committee on Banking and Supervision, Switzerland.
Beirlant, J., Goegebeur, Y., Teugels, J. and Segers, J. (2004), Statistics of Extremes: Theory and applications, Wiley Series in Probability and Statistics, New York: John Wiley & Sons.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, vol. 31, no. 3, pp. 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
Byström, H.N. (2004). Managing extreme risks in tranquil and volatile markets using conditional extreme value theory, International Review of Financial Analysis, vol. 13, no. 2, pp. 133–152. https://doi.org/10.1016/j.irfa.2004.02.003
Coles, S. (2001). An Introduction to statistical modeling of extreme values. London: Springer-Verlag. https://doi.org/10.1007/978-1-4471-3675-0
Costello, A., Asem, E. and Gardner, E. (2008). Comparison of historically simulated VaR: Evidence from oil prices, Energy Economics, vol. 30, no. 5, pp. 2154-2166. https://doi.org/10.1016/j.eneco.2008.01.011
Chiu, Y.C., Chuang, Y. y Lai, J.Y. (2010). The performance of composite forecast models of value-at-risk in the energy market, Energy Economics, vol. 32, no. 2, pp. 423-431. https://doi.org/10.1016/j.eneco.2009.06.018
De Jesús-Gutiérrez, R., Ortiz, E., García, O. y Morales, V. (2016). Medición del riesgo de la cola en el mercado del petróleo mexicano aplicando la teoría de valores extremos condicional, EconoQuantum, vol. 13, no. 2, pp. 77-98. https://doi.org/10.18381/eq.v13i2.6022
De Jesús-Gutiérrez, R. & Santillán, R.J. (2019). Conditional Extreme Values Theory and Tail-related Risk Measures: Evidence from Latin American Stock Markets, International Journal of Economics and Financial Issues, vol. 9, no. 3, pp. 127-141. https://doi.org/10.32479/ijefi.7596
De Jesús-Gutiérrez, R. y Sosa, M. (2019). Predicción de la volatilidad en los mercados del petróleo mexicano a través de modelos CGARCH asimétricos bajo dos supuestos distribucionales, Cuadernos de Economía, vol. 42, no. 120, pp. 253-267. https://doi.org/10.32826/cude.v42i120.88
Dimitrakopoulos, D.N., Kavussanos, M. & Spyrou, S. (2010). Value at risk for volatile emerging markets equity portfolio, The Quarterly Review of Economics and Finance, vol. 50, no. 4, pp. 515–526. https://doi.org/10.1016/j.qref.2010.06.006
Lee, G.G. y Engle, R. (1999). A Permanent and transitory component model of stock return volatility, in R. Engle and H. White (eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger, Oxford: Oxford University Press, pp. 475-497.
Ewing, B.T., Malik, F. y Anjum, H. (2019). Forecasting value at risk in oil prices in the presence of volatility shifts, Review of Financial Economics, vol. 37, no. 3, pp. 341-351. https://doi.org/10.1002/rfe.1047
Embrechts, P., Klüppelberg, C. y Mikosch, T. (1997), Modelling Extremal Events, Berlin: Springer Verlag.
Fan, Y., Zhang, Y.J., Tsai, H.T. & Wei, Y.M. (2008). Estimating value at risk of crude oil price and its spillover effect using the GED-GARCH approach, Energy Economics, vol. 30, no. 6, pp. 3156-3171. https://doi.org/10.1016/j.eneco.2008.04.002
Furió, D. & Climent, F.J. (2014). Extreme value theory versus traditional GARCH approaches applied to financial data: A comparative evaluation, Quantitative Finance, vol. 13, no., pp. 45-63. https://doi.org/10.1080/14697688.2012.696679
Ghorbel, A. y Trabelsi, A. (2014). Energy portfolio risk management using time-varying extreme value copula methods, Economic Modelling, vol. 38, February, pp. 470-485. https://doi.org/10.1016/j.econmod.2013.12.023
Karmakar, M. (2013). Estimation of tail-related risk measures in the Indian stock market: An extreme value approach, Review of Financial Economics, vol. 22, no. 3, pp. 79-85. https://doi.org/10.1016/j.rfe.2013.05.001
Karmakar, M. & Shukla, G.K. (2015). Managing extreme risk in some major stock markets: An extreme value approach, International Review of Economics and Finance, vol. 35, pp. 1-25. https://doi.org/10.1016/j.iref.2014.09.001
Krehbiel, T. & Adkins, L.C. (2005). Price risk in the NYMEX energy complex: An extreme value approach. The Journal of Futures Markets, vol. 25, no. 4, pp. 309-337. https://doi.org/10.1002/fut.20150
Kupiec, P.H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, vol. 3, no. 2, pp. 73-84. https://doi.org/10.3905/jod.1995.407942
Liew, V. (2004). Which lag length selection criteria should we employ? Economics Bulletin, vol. 3, no. 33, pp. 1–9. http://www.economicsbulletin.com/2004/volume3/EB−04C20021A.pdf
Li, Y.X., Lian, J.G. y Hang, H. (2016). Forecast and backtesting of VaR models in crude oil market, Research & Reviews: Journal of Statistics and Mathematical Sciences, vol. 2, no. 1, pp. 131–140. https://www.rroij.com/open-access/forecast-and-backtesting-of-var-models-in-crude-oil-market-.php?aid=75292
Marimoutou, V., Raggad, B. & Trabelsi, A. (2009). Extreme value theory and value at risk: application to oil market. Energy Economics, vol. 31, no. 4, pp. 519-530. https://doi.org/10.1016/j.eneco.2009.02.005
Maheu, J.M. (2005). Can GARCH models capture long-range dependence? Studies in Nonlinear Dynamics & Econometrics, vol. 9, no. 4, pp. 1-41. https://doi.org/10.2202/1558-3708.1269
McNeil, A.J. & Frey, R. (2000). Estimation of tail-related risk measures for heteroscedasticity financial time series: An extreme value approach, Journal of Empirical Finance, vol. 7, no. 3-4, pp. 271–300. https://doi.org/10.1016/S0927-5398(00)00012-8
Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3 (1), 119–131. https://doi.org/10.1214/aos/1176343003
Ren, F. & Giles, D.E. (2010). Extreme value analysis of daily Canadian crude oil prices, Applied Financial Economics, vol. 20, no. 12, pp. 941-954. https://doi.org/10.1080/09603101003724323
Serrano, R. y Núñez, J.A. (2020). Valor en riesgo en el sector petrolero: un análisis de la eficiencia en la medición del riesgo de la distribución α-estable versus las distribuciones t-Student generalizada asimétrica y normal, Contaduría y Administración, Vol. 65 (2), 1-19. http://dx.doi.org/10.22201/fca.24488410e.2019.2021
Sowgagur, V. & Narsoo, J. (2017). Forecasting value at risk using GARCH and extreme value theory approaches for daily returns, International Journal of Statistics and Applications, vol. 7, no. 2, pp. 137-151. 10.5923/j.statistics.20170702.10
Weru, S.K., Waititu, A. & Ngunyi, A. (2019). Modelling energy market volatility using GARCH models and estimating value at risk, Journal of Statistics and Actuarial Research, vol. 2, no. 1, pp. 1-32. https://www.iprjb.org/journals/index.php/JSAR/article/view/902
Zikovic, S. (2011). Measuring risk of crude oil at extreme quantiles, Journal of Economics and Business, vol. 29, no. 1, pp. 9-31. https://hrcak.srce.hr/69459
Youssef, M., Belkacem, L. & Mokni, K. (2015). Value-at-risk estimation of energy commodities: A long-memory GARCH-EVT approach, Energy Economics. vol. 51, September, pp. 99-110. https://doi.org/10.1016/j.eneco.2015.06.010
Bali, T. & Theodossiou, P. (2007). A conditional-SGT-VaR approach with alternative GARCH models, Annals Operations Research, vol. 151, no. 1, pp. 241–267. https://doi.org/10.1007/s10479-006-0118-4
Balkema, A. A., and de Haan, L. (1974). Residual lifetime at great age, The Annals of Probability, Vol. 2 (5), pp. 792–804. https://doi.org/ 10.1214/aop/1176996548
Basel Committee. (1996). Supervisory framework for the use of backtesting in conjunction with the internal models approach to market risk capital requirements, Basel Committee on Banking and Supervision, Switzerland.
Beirlant, J., Goegebeur, Y., Teugels, J. and Segers, J. (2004), Statistics of Extremes: Theory and applications, Wiley Series in Probability and Statistics, New York: John Wiley & Sons.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, vol. 31, no. 3, pp. 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
Byström, H.N. (2004). Managing extreme risks in tranquil and volatile markets using conditional extreme value theory, International Review of Financial Analysis, vol. 13, no. 2, pp. 133–152. https://doi.org/10.1016/j.irfa.2004.02.003
Coles, S. (2001). An Introduction to statistical modeling of extreme values. London: Springer-Verlag. https://doi.org/10.1007/978-1-4471-3675-0
Costello, A., Asem, E. and Gardner, E. (2008). Comparison of historically simulated VaR: Evidence from oil prices, Energy Economics, vol. 30, no. 5, pp. 2154-2166. https://doi.org/10.1016/j.eneco.2008.01.011
Chiu, Y.C., Chuang, Y. y Lai, J.Y. (2010). The performance of composite forecast models of value-at-risk in the energy market, Energy Economics, vol. 32, no. 2, pp. 423-431. https://doi.org/10.1016/j.eneco.2009.06.018
De Jesús-Gutiérrez, R., Ortiz, E., García, O. y Morales, V. (2016). Medición del riesgo de la cola en el mercado del petróleo mexicano aplicando la teoría de valores extremos condicional, EconoQuantum, vol. 13, no. 2, pp. 77-98. https://doi.org/10.18381/eq.v13i2.6022
De Jesús-Gutiérrez, R. & Santillán, R.J. (2019). Conditional Extreme Values Theory and Tail-related Risk Measures: Evidence from Latin American Stock Markets, International Journal of Economics and Financial Issues, vol. 9, no. 3, pp. 127-141. https://doi.org/10.32479/ijefi.7596
De Jesús-Gutiérrez, R. y Sosa, M. (2019). Predicción de la volatilidad en los mercados del petróleo mexicano a través de modelos CGARCH asimétricos bajo dos supuestos distribucionales, Cuadernos de Economía, vol. 42, no. 120, pp. 253-267. https://doi.org/10.32826/cude.v42i120.88
Dimitrakopoulos, D.N., Kavussanos, M. & Spyrou, S. (2010). Value at risk for volatile emerging markets equity portfolio, The Quarterly Review of Economics and Finance, vol. 50, no. 4, pp. 515–526. https://doi.org/10.1016/j.qref.2010.06.006
Lee, G.G. y Engle, R. (1999). A Permanent and transitory component model of stock return volatility, in R. Engle and H. White (eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger, Oxford: Oxford University Press, pp. 475-497.
Ewing, B.T., Malik, F. y Anjum, H. (2019). Forecasting value at risk in oil prices in the presence of volatility shifts, Review of Financial Economics, vol. 37, no. 3, pp. 341-351. https://doi.org/10.1002/rfe.1047
Embrechts, P., Klüppelberg, C. y Mikosch, T. (1997), Modelling Extremal Events, Berlin: Springer Verlag.
Fan, Y., Zhang, Y.J., Tsai, H.T. & Wei, Y.M. (2008). Estimating value at risk of crude oil price and its spillover effect using the GED-GARCH approach, Energy Economics, vol. 30, no. 6, pp. 3156-3171. https://doi.org/10.1016/j.eneco.2008.04.002
Furió, D. & Climent, F.J. (2014). Extreme value theory versus traditional GARCH approaches applied to financial data: A comparative evaluation, Quantitative Finance, vol. 13, no., pp. 45-63. https://doi.org/10.1080/14697688.2012.696679
Ghorbel, A. y Trabelsi, A. (2014). Energy portfolio risk management using time-varying extreme value copula methods, Economic Modelling, vol. 38, February, pp. 470-485. https://doi.org/10.1016/j.econmod.2013.12.023
Karmakar, M. (2013). Estimation of tail-related risk measures in the Indian stock market: An extreme value approach, Review of Financial Economics, vol. 22, no. 3, pp. 79-85. https://doi.org/10.1016/j.rfe.2013.05.001
Karmakar, M. & Shukla, G.K. (2015). Managing extreme risk in some major stock markets: An extreme value approach, International Review of Economics and Finance, vol. 35, pp. 1-25. https://doi.org/10.1016/j.iref.2014.09.001
Krehbiel, T. & Adkins, L.C. (2005). Price risk in the NYMEX energy complex: An extreme value approach. The Journal of Futures Markets, vol. 25, no. 4, pp. 309-337. https://doi.org/10.1002/fut.20150
Kupiec, P.H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, vol. 3, no. 2, pp. 73-84. https://doi.org/10.3905/jod.1995.407942
Liew, V. (2004). Which lag length selection criteria should we employ? Economics Bulletin, vol. 3, no. 33, pp. 1–9. http://www.economicsbulletin.com/2004/volume3/EB−04C20021A.pdf
Li, Y.X., Lian, J.G. y Hang, H. (2016). Forecast and backtesting of VaR models in crude oil market, Research & Reviews: Journal of Statistics and Mathematical Sciences, vol. 2, no. 1, pp. 131–140. https://www.rroij.com/open-access/forecast-and-backtesting-of-var-models-in-crude-oil-market-.php?aid=75292
Marimoutou, V., Raggad, B. & Trabelsi, A. (2009). Extreme value theory and value at risk: application to oil market. Energy Economics, vol. 31, no. 4, pp. 519-530. https://doi.org/10.1016/j.eneco.2009.02.005
Maheu, J.M. (2005). Can GARCH models capture long-range dependence? Studies in Nonlinear Dynamics & Econometrics, vol. 9, no. 4, pp. 1-41. https://doi.org/10.2202/1558-3708.1269
McNeil, A.J. & Frey, R. (2000). Estimation of tail-related risk measures for heteroscedasticity financial time series: An extreme value approach, Journal of Empirical Finance, vol. 7, no. 3-4, pp. 271–300. https://doi.org/10.1016/S0927-5398(00)00012-8
Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3 (1), 119–131. https://doi.org/10.1214/aos/1176343003
Ren, F. & Giles, D.E. (2010). Extreme value analysis of daily Canadian crude oil prices, Applied Financial Economics, vol. 20, no. 12, pp. 941-954. https://doi.org/10.1080/09603101003724323
Serrano, R. y Núñez, J.A. (2020). Valor en riesgo en el sector petrolero: un análisis de la eficiencia en la medición del riesgo de la distribución α-estable versus las distribuciones t-Student generalizada asimétrica y normal, Contaduría y Administración, Vol. 65 (2), 1-19. http://dx.doi.org/10.22201/fca.24488410e.2019.2021
Sowgagur, V. & Narsoo, J. (2017). Forecasting value at risk using GARCH and extreme value theory approaches for daily returns, International Journal of Statistics and Applications, vol. 7, no. 2, pp. 137-151. 10.5923/j.statistics.20170702.10
Weru, S.K., Waititu, A. & Ngunyi, A. (2019). Modelling energy market volatility using GARCH models and estimating value at risk, Journal of Statistics and Actuarial Research, vol. 2, no. 1, pp. 1-32. https://www.iprjb.org/journals/index.php/JSAR/article/view/902
Zikovic, S. (2011). Measuring risk of crude oil at extreme quantiles, Journal of Economics and Business, vol. 29, no. 1, pp. 9-31. https://hrcak.srce.hr/69459
Youssef, M., Belkacem, L. & Mokni, K. (2015). Value-at-risk estimation of energy commodities: A long-memory GARCH-EVT approach, Energy Economics. vol. 51, September, pp. 99-110. https://doi.org/10.1016/j.eneco.2015.06.010
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Published
2021-09-01
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How to Cite
Español. (2021). Análisis Económico, 36(93), 81-98. https://doi.org/10.24275/uam/azc/dcsh/ae/2021v36n93/De-jesus
