Kybernetika 53 no. 6, 1071-1085, 2017

Which carbon derivatives are applicable in practice? A case study of a European steel company

Martin Šmíd, František Zapletal and Jana HančlováDOI: 10.14736/kyb-2017-6-1071


This paper constructs and analyses a model for optimal production and emission covering of a real-life European steel company. The emissions may be covered by a combination of EUA and CER allowances and their derivatives. The company is assumed to be risk-averse, maximizing the Mean-CVaR criterion. The problem is analysed given continuum of risk-aversion coefficients and three scenarios of the demand. It is found that the production does not depend on the risk aversion and is always maximal, but the optimal composition of the (spot) allowances and their derivatives depends non-trivially on both the risk aversion and the demand. Out of all the derivatives, only futures are used. Surprisingly, options are never used.


optimization, carbon allowances, carbon derivatives, mean-CVaR


90B30, 91B28


  1. P. Artzner, F. Delbaen, J.-M. Eber and D. Heath: Coherent measures of risk. Math. Finance 9 (1999), 3, 203-228.   DOI:10.1111/1467-9965.00068
  2. E. A. Benz and J. Hengelbrock: Liquidity and price-discovery in the european co2 futures market: An intraday analysis (working paper). University of Bonn, 2009.   CrossRef
  3. J. Chevallier: Econometric analysis of carbon markets: the European Union emissions trading scheme and the clean development mechanism. Springer Science and Business Media, 2011.   DOI:10.1007/978-94-007-2412-9
  4. European Comission: Use of international credits. \url{}   CrossRef
  5. EU Commission et al.: Directive 2003/87/ec of the european parliament and of the council of 13 october 2003 establishing a scheme for greenhouse gas emission allowance trading within the community and amending council directive 96/61/ec. Union, European 46 (2003), 32-46.   DOI:10.1017/cbo9780511610851.034
  6. G. Daskalakis, D. Psychoyios and R. N. Markellos: Modeling co 2 emission allowance prices and derivatives: Evidence from the european trading scheme. J. Banking Finance 33 (2009), 7, 1230-1241.   DOI:10.1016/j.jbankfin.2009.01.001
  7. X. Gong and S. X. Zhou: Optimal production planning with emissions trading. Oper. Res. 61 (2013), 4, 908-924.   DOI:10.1287/opre.2013.1189
  8. J. C. Hull and S. Basu: Options, Futures, and Other Derivatives. Prentice Hall, New Jersey 2016.   DOI:10.23874/amber/2016/v7/i1/121351
  9. P. Mazza and M. Petitjean: How integrated is the european carbon derivatives market? Finance Res. Lett. 15 (2015), 18-30.   DOI:10.1016/
  10. R. T. Rockafellar and S. Uryasev: Conditional value-at-risk for general loss distributions. J. Banking Finance 26 (2002), 7, 1443-1471.   DOI:10.1016/s0378-4266(02)00271-6
  11. Bao-jun Tang, Cheng Shen and Chao Gao: The efficiency analysis of the european co 2 futures market. Applied Energy 112 (2013), 1544-1547.   DOI:10.1016/j.apenergy.2013.02.017
  12. M. Uhrig-Homburg and M. Wagner: Futures price dynamics of co2 emission allowances: An empirical analysis of the trial period. J. Derivatives 17 (2009), 2, 73-88.   DOI:10.3905/jod.2009.17.2.073
  13. F. Zapletal and M. Šmíd: Mean-risk optimal decision of a steel company under emission control. Central Europ. J. Oper. Res. 24 (2016), 2, 435-454.   DOI:10.1007/s10100-015-0430-7