IDEAS home Printed from https://ideas.repec.org/p/boc/bocoec/952.html
   My bibliography  Save this paper

Stochastic volatility, jumps and leverage in energy and stock markets: evidence from high frequency data

Author

Listed:
  • Christopher F Baum

    () (Boston College
    German Institute for Economic Research (DIW Berlin)
    CESIS, Royal Institute of Technology, Stockholm)

  • Paola Zerilli

    () (University of York)

  • Liyuan Chen

    () (University of York)

Abstract

In this paper, we propose a model for futures returns that has the potential to provide both individual investors and firms who have positions in financial and energy commodity futures a valid tail risk management tool. In doing so, we also aim to explore the commonalities between these markets and the degree of financialization of energy commodities. Unlike most of the existing studies in energy derivative markets based on daily data, our empirical analysis makes use of high-frequency (tick-by-tick) data from the futures markets, aggregated to 10-minute intervals during the trading day. The intraday variation is then utilized to generate daily time series of prices, returns and realized variance. We estimate stochastic volatility models using a GMM approach based on the moment conditions of the Integrated Volatility derived from high frequency data. While existing empirical studies in energy markets embed either leverage or jumps in the futures return dynamics, we show that the introduction of both features improves the ability to forecast volatility as an indicator for risk for both the S&P500 and natural gas futures markets using both the RMSE and MAE criteria. Our analysis also shows that overall, the introduction of both leverage and jumps in the SVJL model provides the best forecast for risk in both a VaR and a CVaR sense for investors who have any position in natural gas futures regardless of their degree of risk aversion. In the S&P500 market, the SVJL model provides the most precise forecast of risk in a CVaR sense for risk-averse investors with any position in futures, regardless of their degree of risk aversion. Focusing on a firm's internal risk management, the introduction of both jumps and leverage in the SVJL model would benefit speculative firms who are short natural gas futures aiming at minimizing tail risk in a VaR sense, as well as speculative firms who are long S&P500 futures and use either VaR or CVaR as financial risk management criteria while wanting to minimize the opportunity cost of capital.

Suggested Citation

  • Christopher F Baum & Paola Zerilli & Liyuan Chen, 2018. "Stochastic volatility, jumps and leverage in energy and stock markets: evidence from high frequency data," Boston College Working Papers in Economics 952, Boston College Department of Economics, revised 29 May 2019.
  • Handle: RePEc:boc:bocoec:952
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/EC-P/wp952.pdf
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    as
    1. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    2. Kerkhof, Jeroen & Melenberg, Bertrand, 2004. "Backtesting for risk-based regulatory capital," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1845-1865, August.
    3. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    4. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    5. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    6. Mason, Charles F. & A. Wilmot, Neil, 2014. "Jump processes in natural gas markets," Energy Economics, Elsevier, vol. 46(S1), pages 69-79.
    7. Youssef, Manel & Belkacem, Lotfi & Mokni, Khaled, 2015. "Value-at-Risk estimation of energy commodities: A long-memory GARCH–EVT approach," Energy Economics, Elsevier, vol. 51(C), pages 99-110.
    8. Pindyck, Robert S, 1991. "Irreversibility, Uncertainty, and Investment," Journal of Economic Literature, American Economic Association, vol. 29(3), pages 1110-1148, September.
    9. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    10. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    11. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    12. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    13. repec:eee:eneeco:v:79:y:2019:i:c:p:111-129 is not listed on IDEAS
    14. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    15. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    16. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    17. Jaime Casassus & Pierre Collin‐Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, vol. 60(5), pages 2283-2331, October.
    18. Fan, Ying & Zhang, Yue-Jun & Tsai, Hsien-Tang & Wei, Yi-Ming, 2008. "Estimating 'Value at Risk' of crude oil price and its spillover effect using the GED-GARCH approach," Energy Economics, Elsevier, vol. 30(6), pages 3156-3171, November.
    19. Askari, Hossein & Krichene, Noureddine, 2008. "Oil price dynamics (2002-2006)," Energy Economics, Elsevier, vol. 30(5), pages 2134-2153, September.
    20. Nomikos, Nikos & Andriosopoulos, Kostas, 2012. "Modelling energy spot prices: Empirical evidence from NYMEX," Energy Economics, Elsevier, vol. 34(4), pages 1153-1169.
    21. Robert S. Pindyck, 2004. "Volatility and commodity price dynamics," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(11), pages 1029-1047, November.
    22. Ben S. Bernanke, 1983. "Irreversibility, Uncertainty, and Cyclical Investment," The Quarterly Journal of Economics, Oxford University Press, vol. 98(1), pages 85-106.
    23. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    24. Chen, Liyuan & Zerilli, Paola & Baum, Christopher F., 2019. "Leverage effects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications," Energy Economics, Elsevier, vol. 79(C), pages 111-129.
    25. Vo, Minh T., 2009. "Regime-switching stochastic volatility: Evidence from the crude oil market," Energy Economics, Elsevier, vol. 31(5), pages 779-788, September.
    26. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    27. Joshua C. C. Chan & Angelia L. Grant, 2016. "On the Observed-Data Deviance Information Criterion for Volatility Modeling," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(4), pages 772-802.
    28. Baum, Christopher F. & Zerilli, Paola, 2016. "Jumps and stochastic volatility in crude oil futures prices using conditional moments of integrated volatility," Energy Economics, Elsevier, vol. 53(C), pages 175-181.
    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. repec:gam:jeners:v:12:y:2019:i:4:p:618-:d:206208 is not listed on IDEAS

    More about this item

    Keywords

    stochastic volatility; leverage effect; energy markets; high frequency data; VaR; CVaR;

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:boc:bocoec:952. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F Baum). General contact details of provider: http://edirc.repec.org/data/debocus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.