Skip to main content
Log in

Extreme Risk Measurement of Carbon Market Considering Multifractal Characteristics

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Influenced by the global economy, politics, energy and other factors, the price of carbon market fluctuates sharply. It is of great practical significance to explore a suitable measurement method of extreme risk of carbon market. Considering that the return series of carbon market has the characteristics of leptokurtosis, fat tail, skewness and multifractal, and there maybe many extreme risk values in the carbon market, this paper introduces the Skewed-t distribution which can describe the characteristics of leptokurtosis, fat tail and skewness of return series into MSM model which can describe multifractal characteristic of return series to model volatility of carbon market. On the basis, based on the extreme value theory, this paper constructs Skewed-t-MSM-EVT model to measure extreme risk of carbon market. This paper chooses EUA market as the object to study extreme risk of carbon market, and draws the following conclusions: Skewed-t-MSM-EVT model has significantly higher prediction accuracy for carbon market’s VaR than MSM-EVT models under other distributions (including normal distribution, t distribution, GED distribution); Skewed-t-MSM-EVT model is superior to traditional Skewed-t-FIGARCH-EVT and Skewed-t-GARCH-EVT models in predicting carbon market’s VaR. This research has important practical significance for accurately grasping the risk of carbon market and promoting energy conservation and emission reduction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Zhang C, Wu Y Q, and Yang Y, The influencing factors of scer price dynamics under the clean development mechanism: Theory and econometric analysis, Journal of Systems Science & Complexity, 2018, 31(5): 1244–1272.

    Article  MathSciNet  MATH  Google Scholar 

  2. Koch N, Fuss S, Grosjean G, et al., Causes of the EU ETS price drop: Recession, CDM, renewable policies or a bit of everything? — New evidence, Energy Policy, 2014, 73: 676–685.

    Article  Google Scholar 

  3. Keppler J H and Mansanet-Bataller M, Causalities between CO2, electricity, and other energy variables during phase I and phase II of the EU ETS, Energy Policy, 2010, 38(7): 3329–3341.

    Article  Google Scholar 

  4. Sousa R, Aguiar-Conraria L, and Soares M J, Carbon financial markets: A time-frequency analysis of CO2 prices, Physica A: Statistical Mechanics and Its Applications, 2014, 15: 118–127.

    Article  Google Scholar 

  5. BalciLar M, Demirer R, Hammoudeh S, et al., Risk spillovers across the energy and carbon markets and hedging strategies for carbon risk, Energy Economics, 2016, 54: 159–172.

    Article  Google Scholar 

  6. Tu Q and Mo J L, Coordinating carbon pricing policy and renewable energy policy with a case study in China, Computers & Industrial Engineering, 2017, 113: 294–304.

    Article  Google Scholar 

  7. Paolella M and Taschini L, An econometric analysis of emission trading allowances, Swiss Finance Institute, 2006, 3: 6–26.

    Google Scholar 

  8. Zhang C, Yang Y, and Yun P, Risk measurement of international carbon market based on multiple risk factors heterogeneous dependence, Finance Research Letters, 2018, 32: 101083.

    Article  Google Scholar 

  9. Zhang C, Yun P, and Wagan Z A, Study on the wandering weekday effect of the international carbon market based on trend moderation effect, Finance Research Letters, 2018, 28: 319–327.

    Article  Google Scholar 

  10. Palao F and Pardo A, Assessing price clustering in European carbon markets, Applied Energy, 2012, 92(2): 51–56.

    Article  Google Scholar 

  11. Zeitlberger A and Brauneis A, Modeling carbon spot and futures price returns with GARCH and Markov switching GARCH models, Central European Journal of Operations Research: CEJOR, 2016, 24(1): 149–176.

    Article  MathSciNet  MATH  Google Scholar 

  12. Chevallier J, Carbon futures and macroeconomic risk factors: A view from the EU ETS, Energy Economics, 2009, 31(4): 614–625.

    Article  Google Scholar 

  13. Gil-Alana L A, Gupta R, and Gracia F D, Modeling persistence of carbon emission allowance prices, Renewable and Sustainable Energy Reviews, 2016, 55: 221–226.

    Article  Google Scholar 

  14. Dutta A, Modeling and forecasting the volatility of carbon emission market: The role of outliers, time-varying jumps and oil price risk, Journal of Cleaner Production, 2018, 172: 2773–2781.

    Article  Google Scholar 

  15. Zhuang X Y, Wei Y, and Zhang B Z, Multifractal detrended cross-correlation analysis of carbon and crude oil markets, Physica A: Statistical Mechanics and Its Applications, 2014, 399: 113–125.

    Article  Google Scholar 

  16. Feng Z H, Wei Y M, and Wang K, Estimating risk for the carbon market via extreme value theory: An empirical analysis of the EU ETS, Applied Energy, 2012, 99: 97–108.

    Article  Google Scholar 

  17. Tang B J and Qian X Y, Research on risk measurement of EUA carbon market based on extreme value theory, Energy of China, 2016, 38(4): 40–43.

    Google Scholar 

  18. Yang C, Li G L, and Men M, Risk measure of the international carbon trading market and enlightenment to China, The Journal of Quantitative & Technical Economics, 2011, 28(4): 94–109, 123.

    Google Scholar 

  19. Calvet L E and Fisher A J, How to forecast long-run volatility: Regime switching and the estimation of multifractal processes, Journal of Financial Econometric, 2004, 1: 49–83.

    Article  Google Scholar 

  20. Zhang L, Yu C L, and Sun J Q, Generalized Weierstrass-Mandelbrot function model for actual stocks markets indexes with nonlinear characteristics, Fractals, 2015, 23(2): 1550006.

    Article  MathSciNet  Google Scholar 

  21. Onali E and Goddard J, Unifractality and multifractality in the Italian stock market, International Review of Financial Analysis, 2009, 18(4): 154–163.

    Article  Google Scholar 

  22. Mandelbrot B, Fisher A, and Calvet L, A Multifractal Model of Asset Returns, Cowles Foundation Discussion Paper, No.1164, 1997, available at: http://cowles.econ.yale.edu/P/cd/d11b/d1164.pdf.

  23. Muzy J F and Bacry E, Multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws, Physical Review E, 2002, 66(5): 056121.

    Article  Google Scholar 

  24. Lux T and Morales-Arias L, Forecasting volatility under fractality, regime-switching, long memory and student-t innovations, Computational Statistics & Data Analysis, 2010, 54(11): 2676–2692.

    Article  MathSciNet  MATH  Google Scholar 

  25. Tang Z P, Huang Y P, Chen W H, et al., Forecasting volatility of Shanghai composite index using Markov-switching multifractal model with fat-tailed innovation distributions, Chinese Journal of Management Science, 2014, S1: 313–317.

    Google Scholar 

  26. Hansen B E, Autoregressive conditional density estimation, International Economic Review, 1994, 35(3): 705–730.

    Article  MATH  Google Scholar 

  27. Lambert P and Laurent S, Modelling financial time series using GARCH-type models with a Skewed student distribution for the innovations, Stat discussion, Universite Catholique de Louvain, 2001.

  28. Yu W H, Comparative study on measurement precision of different time-varying Copula-EVT-ES models, Journal of Management Sciences in China, 2015, 18(5): 32–45.

    MathSciNet  Google Scholar 

  29. Mcneil A J and Frey R, Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach, Journal of Empirical Finance, 2000, 7(3): 271–300.

    Article  Google Scholar 

  30. Pickands L J, Statistical inference using extreme order statistics, The Annals of Statistics, 1975, 3(1): 119–131.

    MathSciNet  MATH  Google Scholar 

  31. Kupiec P H, Techniques for verifying the accuracy of risk measurement models, Social Science Electronic Publishing, 1995, 3(2): 73–84.

    Google Scholar 

  32. Yang K, Yu W H, and Wei Y, Dynamic measurement of extreme risk among various crude oil markets based on R-vine copula, Chinese Journal of Management Science, 2017, 25(8): 19–29.

    Google Scholar 

  33. Shen L, Statistical comparison of foreign exchange risk measurement methods based on GARCH-VaR model, Statistics & Decision, 2018, 34(21): 163–166.

    Google Scholar 

  34. Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, et al., Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and Its Applications, 2002, 316(1–4): 87–114.

    Article  MATH  Google Scholar 

  35. Ran M, Tang Z P, and Yu X H, Analysis of Markov-switching multifractal model, Logistics Engineering and Management, 2018, 40(4): 142–144, 149.

    Google Scholar 

  36. Dumouchel W H, Estimating the stable index α in order to measure tail thickness: A critique, Annals of Statistics, 1983, 11(4): 1019–1031.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chen Zhang.

Ethics declarations

The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 71971071.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, D., Zhang, C. & Pan, D. Extreme Risk Measurement of Carbon Market Considering Multifractal Characteristics. J Syst Sci Complex 36, 2497–2514 (2023). https://doi.org/10.1007/s11424-023-1471-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-023-1471-y

Keywords

Navigation