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

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  • 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

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  • 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
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    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).

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