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Testing co-volatility spillovers for natural gas spot, futures and ETF spot using dynamic conditional covariances

Author

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  • Chia-Lin Chang

    (Department of Applied Economics Department of Finance National Chung Hsing University Taichung, Taiwan.)

  • Michael McAleer

    ( Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute, Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain.)

  • Yanghuiting Wang

    (Institute of Statistics National Tsing Hua University, Taiwan.)

Abstract

There is substantial empirical evidence that energy and financial markets are closely connected. As one of the most widely-used energy resources worldwide, natural gas has a large daily trading volume. In order to hedge the risk of natural gas spot markets, a large number of hedging strategies can be used, especially with the rapid development of natural gas derivatives markets. These hedging instruments include natural gas futures and options, as well as Exchange Traded Fund (ETF) prices that are related to natural gas stock prices. The volatility spillover effect is the delayed effect of a returns shock in one physical, biological or financial asset on the subsequent volatility or co-volatility of another physical, biological or financial asset. Investigating volatility spillovers within and across energy and financial markets is a crucial aspect of constructing optimal dynamic hedging strategies. The paper tests and calculates spillover effects among natural gas spot, futures and ETF markets using the multivariate conditional volatility diagonal BEKK model. The data used include natural gas spot and futures returns data from two major international natural gas derivatives markets, namely NYMEX (USA) and ICE (UK), as well as ETF data of natural gas companies from the stock markets in the USA and UK. The empirical results show that there are significant spillover effects in natural gas spot, futures and ETF markets for both USA and UK. Such a result suggests that both natural gas futures and ETF products within and beyond the country might be considered when constructing optimal dynamic hedging strategies for natural gas spot prices.

Suggested Citation

  • Chia-Lin Chang & Michael McAleer & Yanghuiting Wang, 2016. "Testing co-volatility spillovers for natural gas spot, futures and ETF spot using dynamic conditional covariances," Documentos de Trabajo del ICAE 2016-10, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:1610
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    1. Chia-Lin Chang & Yiying Li & Michael McAleer, 2018. "Volatility Spillovers between Energy and Agricultural Markets: A Critical Appraisal of Theory and Practice," Energies, MDPI, vol. 11(6), pages 1-19, June.
    2. Chang, C-L. & McAleer, M.J. & Tansuchat, R., 2010. "Analyzing and Forecasting Volatility Spillovers and Asymmetries in Major Crude Oil Spot, Forward and Futures Markets," Econometric Institute Research Papers EI 2010-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    4. Chang, Chia-Lin & McAleer, Michael & Tansuchat, Roengchai, 2011. "Crude oil hedging strategies using dynamic multivariate GARCH," Energy Economics, Elsevier, vol. 33(5), pages 912-923, September.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Chia-Lin Chang & Yu-Pei Ke, 2014. "Testing Price Pressure, Information, Feedback Trading, And Smoothing Effects For Energy Exchange Traded Funds," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 1-26.
    7. Michael McAleer, 2014. "Asymmetry and Leverage in Conditional Volatility Models," Econometrics, MDPI, vol. 2(3), pages 1-6, September.
    8. Chang, Chia-Lin & McAleer, Michael & Tansuchat, Roengchai, 2010. "Analyzing and forecasting volatility spillovers, asymmetries and hedging in major oil markets," Energy Economics, Elsevier, vol. 32(6), pages 1445-1455, November.
    9. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    10. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "How are VIX and Stock Index ETF Related?," Documentos de Trabajo del ICAE 2016-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    11. Hammoudeh, Shawkat & Li, Huimin & Jeon, Bang, 2003. "Causality and volatility spillovers among petroleum prices of WTI, gasoline and heating oil in different locations," The North American Journal of Economics and Finance, Elsevier, vol. 14(1), pages 89-114, March.
    12. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
    13. Karali, Berna & Ramirez, Octavio A., 2014. "Macro determinants of volatility and volatility spillover in energy markets," Energy Economics, Elsevier, vol. 46(C), pages 413-421.
    14. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    15. Chia-Lin Chang & Michael McAleer & Chien-Hsun Wang, 2017. "An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors," IJFS, MDPI, vol. 6(1), pages 1-24, December.
    16. Massimiliano Caporin & Michael McAleer, 2008. "Scalar BEKK and indirect DCC," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 537-549.
    17. Michael S. Haigh & Matthew T. Holt, 2002. "Crack spread hedging: accounting for time-varying volatility spillovers in the energy futures markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(3), pages 269-289.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. Caporin, Massimiliano & Fontini, Fulvio, 2017. "The long-run oil–natural gas price relationship and the shale gas revolution," Energy Economics, Elsevier, vol. 64(C), pages 511-519.
    20. Krause, Timothy & Tse, Yiuman, 2013. "Volatility and return spillovers in Canadian and U.S. industry ETFs," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 244-259.
    21. Sadorsky, Perry, 2012. "Correlations and volatility spillovers between oil prices and the stock prices of clean energy and technology companies," Energy Economics, Elsevier, vol. 34(1), pages 248-255.
    22. Christian M. Hafner & Michael McAleer, 2014. "A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process," Documentos de Trabajo del ICAE 2014-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    23. Balcilar, Mehmet & Gupta, Rangan & Miller, Stephen M., 2015. "Regime switching model of US crude oil and stock market prices: 1859 to 2013," Energy Economics, Elsevier, vol. 49(C), pages 317-327.
    24. Milunovich, George & Thorp, Susan, 2006. "Valuing volatility spillovers," Global Finance Journal, Elsevier, vol. 17(1), pages 1-22, September.
    25. Scholtens, Bert & Yurtsever, Cenk, 2012. "Oil price shocks and European industries," Energy Economics, Elsevier, vol. 34(4), pages 1187-1195.
    26. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(1), pages 232-261, February.
    27. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    28. Efimova, Olga & Serletis, Apostolos, 2014. "Energy markets volatility modelling using GARCH," Energy Economics, Elsevier, vol. 43(C), pages 264-273.
    29. J. -H. Chen & C. -Y. Huang, 2010. "An analysis of the spillover effects of exchange-traded funds," Applied Economics, Taylor & Francis Journals, vol. 42(9), pages 1155-1168.
    30. Chang, Chia-Lin & McAleer, Michael & Wang, Yu-Ann, 2018. "Modelling volatility spillovers for bio-ethanol, sugarcane and corn spot and futures prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1002-1018.
    31. Lee, Bi-Juan & Yang, Chin Wei & Huang, Bwo-Nung, 2012. "Oil price movements and stock markets revisited: A case of sector stock price indexes in the G-7 countries," Energy Economics, Elsevier, vol. 34(5), pages 1284-1300.
    32. Chang, C-L. & McAleer, M.J. & Wang, Y-A., 2016. "Modelling Volatility Spillovers for Bio-ethanol, Sugarcane and Corn," Econometric Institute Research Papers EI2016-15, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    33. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    34. Lin, Sharon Xiaowen & Tamvakis, Michael N., 2001. "Spillover effects in energy futures markets," Energy Economics, Elsevier, vol. 23(1), pages 43-56, January.
    35. Ewing, Bradley T. & Malik, Farooq & Ozfidan, Ozkan, 2002. "Volatility transmission in the oil and natural gas markets," Energy Economics, Elsevier, vol. 24(6), pages 525-538, November.
    36. Cunado, Juncal & Perez de Gracia, Fernando, 2014. "Oil price shocks and stock market returns: Evidence for some European countries," Energy Economics, Elsevier, vol. 42(C), pages 365-377.
    37. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    38. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1554-1583, December.
    39. Jones, Charles M & Kaul, Gautam, 1996. "Oil and the Stock Markets," Journal of Finance, American Finance Association, vol. 51(2), pages 463-491, June.
    40. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-170, March.
    41. Jo-Hui Chen, 2011. "The spillover and leverage effects of ethical exchange traded fund," Applied Economics Letters, Taylor & Francis Journals, vol. 18(10), pages 983-987.
    42. Elyasiani, Elyas & Mansur, Iqbal & Odusami, Babatunde, 2011. "Oil price shocks and industry stock returns," Energy Economics, Elsevier, vol. 33(5), pages 966-974, September.
    43. Sukcharoen, Kunlapath & Zohrabyan, Tatevik & Leatham, David & Wu, Ximing, 2014. "Interdependence of oil prices and stock market indices: A copula approach," Energy Economics, Elsevier, vol. 44(C), pages 331-339.
    44. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    45. Narayan, Paresh Kumar & Sharma, Susan Sunila, 2011. "New evidence on oil price and firm returns," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3253-3262.
    46. Shao, Chengwu & Bhar, Ramaprasad & Colwell, David B., 2015. "A multi-factor model with time-varying and seasonal risk premiums for the natural gas market," Energy Economics, Elsevier, vol. 50(C), pages 207-214.
    47. Ghoddusi, Hamed, 2016. "Integration of physical and futures prices in the US natural gas market," Energy Economics, Elsevier, vol. 56(C), pages 229-238.
    48. Roger D. Huang & Ronald W. Masulis & Hans R. Stoll, 1996. "Energy shocks and financial markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(1), pages 1-27, February.
    49. Ciner Cetin, 2001. "Energy Shocks and Financial Markets: Nonlinear Linkages," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(3), pages 1-11, October.
    50. Ergen, Ibrahim & Rizvanoghlu, Islam, 2016. "Asymmetric impacts of fundamentals on the natural gas futures volatility: An augmented GARCH approach," Energy Economics, Elsevier, vol. 56(C), pages 64-74.
    51. 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.
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    More about this item

    Keywords

    Energy; Natural gas; Spot; Futures; ETF; NYMEX; ICE; Optimal hedging strategy; Covolatility spillovers; Diagonal BEKK.;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products

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