IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v219y2014i1p333-35710.1007-s10479-011-0900-9.html
   My bibliography  Save this article

Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model

Author

Listed:
  • Xun Lu
  • Kin Lai
  • Liang Liang

Abstract

This paper combines copula functions with GARCH-type models to construct the conditional joint distribution, which is used to estimate Value-at-Risk (VaR) of an equally weighted portfolio comprising crude oil futures and natural gas futures in energy market. Both constant and time-varying copulas are applied to fit the dependence structure of the two assets returns. The findings show that the constant Student t copula is a good compromise for effectively fitting the dependence structure between crude oil futures and natural gas futures. Moreover, the skewed Student t distribution has a better fit than Normal and Student t distribution to the marginal distribution of each asset. Asymmetries and excess kurtosis are found in marginal distributions as well as in dependence. We estimate VaR of the underlying portfolio to be 95% and 99%, by using the Monte Carlo simulation. Then using backtesting, we compare the out-of-sample forecasting performances of VaR estimated by different models. Copyright Springer Science+Business Media, LLC 2014

Suggested Citation

  • Xun Lu & Kin Lai & Liang Liang, 2014. "Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model," Annals of Operations Research, Springer, vol. 219(1), pages 333-357, August.
    • Handle: RePEc:spr:annopr:v:219:y:2014:i:1:p:333-357:10.1007/s10479-011-0900-9
    DOI: 10.1007/s10479-011-0900-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0900-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0900-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vaz de Melo Mendes, Beatriz & Martins de Souza, Rafael, 2004. "Measuring financial risks with copulas," International Review of Financial Analysis, Elsevier, vol. 13(1), pages 27-45.
    2. Bastianin, Andrea, 2009. "Modelling Asymmetric Dependence Using Copula Functions: An Application to Value-at-Risk in the Energy Sector," Sustainable Development Papers 50452, Fondazione Eni Enrico Mattei (FEEM).
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    5. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    7. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    8. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    9. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    10. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    11. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    12. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    13. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    14. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    15. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    16. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173, March.
    17. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    18. Huard, David & Evin, Guillaume & Favre, Anne-Catherine, 2006. "Bayesian copula selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 809-822, November.
    19. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fousekis, Panos & Grigoriadis, Vasilis, 2017. "Price co-movement and the crack spread in the US futures markets," Journal of Commodity Markets, Elsevier, vol. 7(C), pages 57-71.
    2. Sebastián Cano-Berlanga & José-Manuel Giménez-Gómez, 2018. "On Chinese stock markets: How have they evolved over time?," Annals of Operations Research, Springer, vol. 266(1), pages 499-510, July.
    3. Wenming Shi & Kevin X. Li & Zhongzhi Yang & Ganggang Wang, 2017. "Time-varying copula models in the shipping derivatives market," Empirical Economics, Springer, vol. 53(3), pages 1039-1058, November.
    4. Zhou, Wei & Chen, Yan & Chen, Jin, 2022. "Risk spread in multiple energy markets: Extreme volatility spillover network analysis before and during the COVID-19 pandemic," Energy, Elsevier, vol. 256(C).
    5. AlShelahi, Abdullah & Wang, Jingxing & You, Mingdi & Byon, Eunshin & Saigal, Romesh, 2020. "Data-driven prediction for volatile processes based on real option theories," International Journal of Production Economics, Elsevier, vol. 226(C).
    6. Sabri Boubaker & Zhenya Liu & Yaosong Zhan, 2022. "Risk management for crude oil futures: an optimal stopping-timing approach," Annals of Operations Research, Springer, vol. 313(1), pages 9-27, June.
    7. Bai, Xiwen & Kavussanos, Manolis G., 2022. "Hedging IMO2020 compliant fuel price exposure using futures contracts," Energy Economics, Elsevier, vol. 110(C).
    8. E. Allevi & L. Boffino & M. E. Giuli & G. Oggioni, 2019. "Analysis of long-term natural gas contracts with vine copulas in optimization portfolio problems," Annals of Operations Research, Springer, vol. 274(1), pages 1-37, March.
    9. Zied Ftiti & Kais Tissaoui & Sahbi Boubaker, 2022. "On the relationship between oil and gas markets: a new forecasting framework based on a machine learning approach," Annals of Operations Research, Springer, vol. 313(2), pages 915-943, June.
    10. Nguyen, Quynh Nga & Bedoui, Rihab & Majdoub, Najemeddine & Guesmi, Khaled & Chevallier, Julien, 2020. "Hedging and safe-haven characteristics of Gold against currencies: An investigation based on multivariate dynamic copula theory," Resources Policy, Elsevier, vol. 68(C).
    11. Shim Jeungbo & Lee Seung-Hwan, 2017. "Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 11(1), pages 1-29, January.
    12. Palma, Alessia & Paltrinieri, Andrea & Goodell, John W. & Oriani, Marco Ercole, 2024. "The black box of natural gas market: Past, present, and future," International Review of Financial Analysis, Elsevier, vol. 94(C).
    13. Andrei Rusu, 2020. "Multivariate VaR: A Romanian Market study," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 12(1), pages 79-95, June.
    14. Dariusz Gołȩbiewski & Tomasz Barszcz & Wioletta Skrodzka & Igor Wojnicki & Andrzej Bielecki, 2022. "A New Approach to Risk Management in the Power Industry Based on Systems Theory," Energies, MDPI, vol. 15(23), pages 1-19, November.
    15. Fernandes, Mário Correia & Dias, José Carlos & Nunes, João Pedro Vidal, 2021. "Modeling energy prices under energy transition: A novel stochastic-copula approach," Economic Modelling, Elsevier, vol. 105(C).
    16. Yanlin Shi, 2023. "Long memory and regime switching in the stochastic volatility modelling," Annals of Operations Research, Springer, vol. 320(2), pages 999-1020, January.
    17. Emmanuel Afuecheta & Saralees Nadarajah & Stephen Chan, 2021. "A Statistical Analysis of Global Economies Using Time Varying Copulas," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1167-1194, December.
    18. Tan, Sook-Rei & Li, Changtai & Yeap, Xiu Wei, 2022. "A time-varying copula approach for constructing a daily financial systemic stress index," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    19. Emilio Cardona & Andrés Mora-Valencia & Daniel Velásquez-Gaviria, 2019. "Testing expected shortfall: an application to emerging market stock indices," Risk Management, Palgrave Macmillan, vol. 21(3), pages 153-182, September.
    20. Zhou, Wei & Chen, Yan & Chen, Jin, 2024. "Dynamic volatility spillover and market emergency: Matching and forecasting," The North American Journal of Economics and Finance, Elsevier, vol. 71(C).
    21. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2019. "Quantifying Risk in Traditional Energy and Sustainable Investments," Sustainability, MDPI, vol. 11(3), pages 1-22, January.
    22. Guo, Zi-Yi, 2022. "Risk management of Bitcoin futures with GARCH models," Finance Research Letters, Elsevier, vol. 45(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-78, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Mario Cerrato & John Crosby & Minjoo Kim & Yang Zhao, 2015. "Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula," Working Papers 2015_15, Business School - Economics, University of Glasgow.
    3. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," SIRE Discussion Papers 2015-78, Scottish Institute for Research in Economics (SIRE).
    4. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 120-135.
    5. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    6. Krzysztof Echaust & Małgorzata Just, 2021. "Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic," Energies, MDPI, vol. 14(14), pages 1-21, July.
    7. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    8. Tong, Bin & Wu, Chongfeng & Zhou, Chunyang, 2013. "Modeling the co-movements between crude oil and refined petroleum markets," Energy Economics, Elsevier, vol. 40(C), pages 882-897.
    9. Lin, Chu-Hsiung & Changchien, Chang-Cheng & Kao, Tzu-Chuan & Kao, Wei-Shun, 2014. "High-order moments and extreme value approach for value-at-risk," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 421-434.
    10. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    11. Mensah, Jones Odei & Premaratne, Gamini, 2014. "Dependence patterns among Banking Sectors in Asia: A Copula Approach," MPRA Paper 60119, University Library of Munich, Germany.
    12. Udichibarna Bose & Ronald MacDonald & Serafeim Tsoukas, 2014. "The role of education in equity portfolios during the recent financial crisis," Working Papers 2014_17, Business School - Economics, University of Glasgow.
    13. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    14. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2014. "Modeling Dependence Structure and Forecasting Portfolio Value-at-Risk with Dynamic Copulas," SIRE Discussion Papers 2015-25, Scottish Institute for Research in Economics (SIRE).
    15. Jin Zhang & Dietmar Maringer, 2010. "Asset Pair-Copula Selection with Downside Risk Minimization," Working Papers 037, COMISEF.
    16. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2017. "Relation between higher order comoments and dependence structure of equity portfolio," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 101-120.
    17. Peter Christoffersen & Kris Jacobs & Xisong Jin & Hugues Langlois, 2013. "Dynamic Diversification in Corporate Credit," CREATES Research Papers 2013-46, Department of Economics and Business Economics, Aarhus University.
    18. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    19. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2014. "Modeling Dependence Structure and Forecasting Portfolio Value-at-Risk with Dynamic Copulas," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-25, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    20. Lorán Chollete & Andréas Heinen & Alfonso Valdesogo, 2009. "Modeling International Financial Returns with a Multivariate Regime-switching Copula," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 437-480, Fall.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:219:y:2014:i:1:p:333-357:10.1007/s10479-011-0900-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.