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Enriching the value‐at‐risk framework to ensemble empirical mode decomposition with an application to the European carbon market

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  • Bangzhu Zhu
  • Ping Wang
  • Julien Chevallier
  • Yi‐Ming Wei

Abstract

Unlike common financial markets, the European carbon market is a typically heterogeneous market, characterised by multiple timescales and affected by extreme events. The traditional value‐at‐risk (VaR) with single‐timescale fails to deal with the multi‐timescale characteristics and the effects of extreme events, which can result in the VaR overestimation for carbon market risk. To measure accurately the risk on the European carbon market, we propose ensemble empirical mode decomposition (EEMD) based multiscale VaR approach. First, the EEMD algorithm is utilised to decompose the carbon price return into several intrinsic mode functions (IMFs) with different timescales and a residue, which are modelled respectively using the ARMA‐GARCH model to obtain their conditional variances at different timescales. Furthermore, the Iterated Cumulative Sums of Squares algorithm is employed to determine the windows of an extreme event, so as to identify the IMFs influenced by an extreme event and conduct an exponentially weighted moving average on their conditional variations. Finally, the VaRs of various IMFs and the residue are estimated to reconstruct the overall VaR, the validity of which is verified later. Then, we illustrate the results by considering several European carbon futures contracts. Compared with the traditional VaR framework with single timescale, the proposed multiscale VaR‐EEMD model can effectively reduce the influences of the heterogeneous environments (such as the influences of extreme events), and obtain a more accurate overall risk measure on the European carbon market. By acquiring the distributions of carbon market risks at different timescales, the proposed multiscale VaR‐EEMD estimation is capable of understanding the fluctuation characteristics more comprehensively, which can provide new perspectives for exploring the evolution law of the risks on the European carbon market.

Suggested Citation

  • Bangzhu Zhu & Ping Wang & Julien Chevallier & Yi‐Ming Wei, 2023. "Enriching the value‐at‐risk framework to ensemble empirical mode decomposition with an application to the European carbon market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(3), pages 2975-2988, July.
    • Handle: RePEc:wly:ijfiec:v:28:y:2023:i:3:p:2975-2988
    DOI: 10.1002/ijfe.2578
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    References listed on IDEAS

    as
    1. Bangzhu Zhu & Xuetao Shi & Julien Chevallier & Ping Wang & Yi‐Ming Wei, 2016. "An Adaptive Multiscale Ensemble Learning Paradigm for Nonstationary and Nonlinear Energy Price Time Series Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(7), pages 633-651, November.
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    3. Zhu, Bangzhu & Ma, Shujiao & Chevallier, Julien & Wei, Yiming, 2014. "Modelling the dynamics of European carbon futures price: A Zipf analysis," Economic Modelling, Elsevier, vol. 38(C), pages 372-380.
    4. 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.).
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    9. Bangzhu Zhu & Julien Chevallier & Shujiao Ma & Yiming Wei, 2015. "Examining the structural changes of European carbon futures price 2005-2012," Applied Economics Letters, Taylor & Francis Journals, vol. 22(5), pages 335-342, March.
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