Model Risk in European Union Allowance Futures and Options: From Black–76 to Institutionally Grounded Models—A Critical Structured Review

Main Article Content

Bohao Zhu
Beijing Jiaotong University, Weihai, China

DOI: https://doi.org/10.70267/icrafm.202617809818

Keywords

EU emissions trading system, EUA futures and options, model risk, risk-neutral valuation, market stability reserve

Abstract

Pricing models for European Union Allowance (EUA) derivatives are often assessed as statistical specifications even though the EU Emissions Trading System changes the payoff boundary, supply process, and intertemporal value of the underlying compliance asset. This critical structured review examines how EUA futures and options models have developed from Black–76 conventions to institutionally grounded equilibrium, structural, and Market Stability Reserve (MSR) specifications; how regulatory mechanisms enter risk-neutral valuation; and what evidence supports model robustness. Fifty-three DOI- or publisher-verified academic records were coded using an Institution–Model–Measure–Evidence (IMME) lens: 47 inform the model-level synthesis and six provide contextual triangulation. The evidence is organized into early benchmarks and deficiencies, institutionally grounded models, and MSR-era pricing and validation. Black–76 remains a transparent quotation benchmark, but evidence from physical-measure dynamics and phase boundaries limits its structural interpretation. Structural and equilibrium models make institutional channels explicit, yet add identification and numerical risks. Comparative studies provide some held-out pricing evidence, but the literature still lacks transaction-cost-aware hedging and regime-transport tests. The resulting model-selection principle is conditional adequacy: use the least complex model that is regime-aligned, measure-explicit, empirically identified, and validated for the intended pricing or hedging task.

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References

  • [1]Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1–2), 167–179. https://doi.org/10.1016/0304-405X(76)90024-6
  • [2]Cont, R. (2006). Model uncertainty and its impact on the pricing of derivative instruments. Mathematical Finance, 16(3), 519–547. https://doi.org/10.1111/j.1467-9965.2006.00281.x
  • [3]Rubin, J. D. (1996). A model of intertemporal emission trading, banking, and borrowing. Journal of Environmental Economics and Management, 31(3), 269–286. https://doi.org/10.1006/jeem.1996.0044
  • [4]Ellerman, A. D., Convery, F. J., & de Perthuis, C. (2010). Pricing carbon: The European Union Emissions Trading Scheme. Cambridge University Press. https://doi.org/10.1017/CBO9781139042765
  • [5]Chevallier, J. (2012). Econometric analysis of carbon markets: The European Union Emissions Trading Scheme and the Clean Development Mechanism. Springer. https://doi.org/10.1007/978-94-007-2412-9
  • [6]Ibikunle, G., & Gregoriou, A. (2018). Carbon markets: Microstructure, pricing and policy. Palgrave Macmillan. https://doi.org/10.1007/978-3-319-72847-6
  • [7]Snyder, H. (2019). Literature review as a research methodology: An overview and guidelines. Journal of Business Research, 104, 333–339. https://doi.org/10.1016/j.jbusres.2019.07.039
  • [8]Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., Shamseer, L., Tetzlaff, J. M., Akl, E. A., Brennan, S. E., Chou, R., Glanville, J., Grimshaw, J. M., Hróbjartsson, A., Lalu, M. M., Li, T., Loder, E. W., Mayo-Wilson, E., McDonald, S., McGuinness, L. A., … Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372, n71. https://doi.org/10.1136/bmj.n71
  • [9]Tang, L., Wang, H., Li, L., Yang, K., & Mi, Z. (2020). Quantitative models in emission trading system research: A literature review. Renewable and Sustainable Energy Reviews, 132, 110052. https://doi.org/10.1016/j.rser.2020.110052
  • [10]Bisiotis, K., Christopoulos, D., & Tzougas, G. (2026). Forecasting carbon prices: A literature review. Journal of Forecasting, 45(2), 496–529. https://doi.org/10.1002/for.70054
  • [11]Seifert, J., Uhrig-Homburg, M., & Wagner, M. (2008). Dynamic behavior of CO2 spot prices. Journal of Environmental Economics and Management, 56(2), 180–194. https://doi.org/10.1016/j.jeem.2008.03.003
  • [12]Paolella, M. S., & Taschini, L. (2008). An econometric analysis of emission allowance prices. Journal of Banking & Finance, 32(10), 2022–2032. https://doi.org/10.1016/j.jbankfin.2007.09.024
  • [13]Benz, E., & Trück, S. (2009). Modeling the price dynamics of CO2 emission allowances. Energy Economics, 31(1), 4–15. https://doi.org/10.1016/j.eneco.2008.07.003
  • [14]Daskalakis, G., Psychoyios, D., & Markellos, R. N. (2009). Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme. Journal of Banking & Finance, 33(7), 1230–1241. https://doi.org/10.1016/j.jbankfin.2009.01.001
  • [15]Çetin, U., & Verschuere, M. (2009). Pricing and hedging in carbon emissions markets. International Journal of Theoretical and Applied Finance, 12(7), 949–967. https://doi.org/10.1142/S0219024909005531
  • [16]Carmona, R., Fehr, M., & Hinz, J. (2009). Optimal stochastic control and carbon price formation. SIAM Journal on Control and Optimization, 48(4), 2168–2190. https://doi.org/10.1137/080736910
  • [17]Kijima, M., Maeda, A., & Nishide, K. (2010). Equilibrium pricing of contingent claims in tradable permit markets. Journal of Futures Markets, 30(6), 559–589. https://doi.org/10.1002/fut.20430
  • [18]Carmona, R., Fehr, M., Hinz, J., & Porchet, A. (2010). Market design for emission trading schemes. SIAM Review, 52(3), 403–452. https://doi.org/10.1137/080722813
  • [19]Carmona, R., & Hinz, J. (2011). Risk-neutral models for emission allowance prices and option valuation. Management Science, 57(8), 1453–1468. https://doi.org/10.1287/mnsc.1110.1358
  • [20]Borovkov, K., Decrouez, G., & Hinz, J. (2011). Jump-diffusion modeling in emission markets. Stochastic Models, 27(1), 50–76. https://doi.org/10.1080/15326349.2011.542726
  • [21]Chesney, M., & Taschini, L. (2012). The endogenous price dynamics of emission allowances and an application to CO2 option pricing. Applied Mathematical Finance, 19(5), 447–475. https://doi.org/10.1080/1350486X.2011.639948
  • [22]Howison, S., & Schwarz, D. (2012). Risk-neutral pricing of financial instruments in emission markets: A structural approach. SIAM Journal on Financial Mathematics, 3(1), 709–739. https://doi.org/10.1137/100815219
  • [23]Carmona, R., Delarue, F., Espinosa, G.-E., & Touzi, N. (2013). Singular forward-backward stochastic differential equations and emissions derivatives. The Annals of Applied Probability, 23(3), 1086–1128. https://doi.org/10.1214/12-AAP865
  • [24]Barrieu, P., & Fehr, M. (2014). Market-consistent modeling for cap-and-trade schemes and application to option pricing. Operations Research, 62(2), 234–249. https://doi.org/10.1287/opre.2013.1242
  • [25]Yang, S. S., Huang, J.-W., & Chang, C.-C. (2016). Detecting and modelling the jump risk of CO2 emission allowances and their impact on the valuation of option on futures contracts. Quantitative Finance, 16(5), 749–762. https://doi.org/10.1080/14697688.2015.1059953
  • [26]Trück, S., & Weron, R. (2016). Convenience yields and risk premiums in the EU-ETS—Evidence from the Kyoto commitment period. Journal of Futures Markets, 36(6), 587–611. https://doi.org/10.1002/fut.21780
  • [27]Segnon, M., Lux, T., & Gupta, R. (2017). Modeling and forecasting the volatility of carbon dioxide emission allowance prices: A review and comparison of modern volatility models. Renewable and Sustainable Energy Reviews, 69, 692–704. https://doi.org/10.1016/j.rser.2016.11.060
  • [28]Hitzemann, S., & Uhrig-Homburg, M. (2018). Equilibrium price dynamics of emission permits. Journal of Financial and Quantitative Analysis, 53(4), 1653–1678. https://doi.org/10.1017/S0022109018000297
  • [29]Hitzemann, S., & Uhrig-Homburg, M. (2019). Empirical performance of reduced-form models for emission permit prices. Review of Derivatives Research, 22(3), 389–418. https://doi.org/10.1007/s11147-018-09152-7
  • [30]Perino, G., & Willner, M. (2017). EU-ETS Phase IV: Allowance prices, design choices and the market stability reserve. Climate Policy, 17(7), 936–946. https://doi.org/10.1080/14693062.2017.1360173
  • [31]Tietjen, O., Lessmann, K., & Pahle, M. (2021). Hedging and temporal permit issuances in cap-and-trade programs: The Market Stability Reserve under risk aversion. Resource and Energy Economics, 63, 101214. https://doi.org/10.1016/j.reseneeco.2020.101214
  • [32]Chassagneux, J.-F., Chotai, H., & Crisan, D. (2023). Modelling multiperiod carbon markets using singular forward–backward SDEs. Mathematics of Operations Research, 48(1), 463–497. https://doi.org/10.1287/moor.2022.1269
  • [33]Fang, M., Tan, K. S., & Wirjanto, T. S. (2024). Valuation of carbon emission allowance options under an open trading phase. Energy Economics, 131, 107351. https://doi.org/10.1016/j.eneco.2024.107351
  • [34]Chen, L., Feng, L., Wu, W., Jin, C., & Zhang, Y. (2026). Deep carbon option: A transfer learning method for carbon derivatives valuation based on option pricing theory. Journal of Cleaner Production, 560, 148318. https://doi.org/10.1016/j.jclepro.2026.148318
  • [35]Chevallier, J., Ielpo, F., & Mercier, L. (2009). Risk aversion and institutional information disclosure on the European carbon market: A case-study of the 2006 compliance event. Energy Policy, 37(1), 15–28. https://doi.org/10.1016/j.enpol.2008.07.030
  • [36]Hitzemann, S., Uhrig-Homburg, M., & Ehrhart, K.-M. (2015). Emission permits and the announcement of realized emissions: Price impact, trading volume, and volatilities. Energy Economics, 51, 560–569. https://doi.org/10.1016/j.eneco.2015.07.007
  • [37]Chevallier, J. (2013). Variance risk-premia in CO2 markets. Economic Modelling, 31, 598–605. https://doi.org/10.1016/j.econmod.2012.12.017
  • [38]Viteva, S., Veld-Merkoulova, Y. V., & Campbell, K. (2014). The forecasting accuracy of implied volatility from ECX carbon options. Energy Economics, 45, 475–484. https://doi.org/10.1016/j.eneco.2014.08.005
  • [39]Byun, S. J., & Cho, H. (2013). Forecasting carbon futures volatility using GARCH models with energy volatilities. Energy Economics, 40, 207–221. https://doi.org/10.1016/j.eneco.2013.06.017
  • [40]Chevallier, J., & Sévi, B. (2014). On the stochastic properties of carbon futures prices. Environmental and Resource Economics, 58(1), 127–153. https://doi.org/10.1007/s10640-013-9695-2
  • [41]Kim, J., Park, Y. J., & Ryu, D. (2017). Stochastic volatility of the futures prices of emission allowances: A Bayesian approach. Physica A: Statistical Mechanics and Its Applications, 465, 714–724. https://doi.org/10.1016/j.physa.2016.08.036
  • [42]Dutta, A. (2018). Modeling and forecasting the volatility of carbon emission market: The role of outliers, time-varying jumps and oil price risk. Journal of Cleaner Production, 172, 2773–2781. https://doi.org/10.1016/j.jclepro.2017.11.135
  • [43]Bruninx, K., Ovaere, M., & Delarue, E. (2020). The long-term impact of the market stability reserve on the EU emission trading system. Energy Economics, 89, 104746. https://doi.org/10.1016/j.eneco.2020.104746
  • [44]Borghesi, S., Pahle, M., Perino, G., Quemin, S., & Willner, M. (2023). The Market Stability Reserve in the EU Emissions Trading System: A critical review. Annual Review of Resource Economics, 15, 131–152. https://doi.org/10.1146/annurev-resource-111820-030145
  • [45]Maulberger, A., & Rathgeber, A. W. (2026). Disentangling supply and demand shocks in the EU ETS—Before and after the introduction of the Market Stability Reserve. Resource and Energy Economics, 87, 101575. https://doi.org/10.1016/j.reseneeco.2026.101575
  • [46]Chen, T.-F., Chiu, H.-Y., & Shen, C. (2026). Modeling EUA price dynamics: A multistage PDE framework with Market Stability Reserve mechanisms. International Review of Economics & Finance, 110, 105626. https://doi.org/10.1016/j.iref.2026.105626
  • [47]Liang, X., & Pan, Y. (2026). Research on pricing of carbon options based on an improved jump test method. Finance Research Letters, 90, 109406. https://doi.org/10.1016/j.frl.2025.109406
  • [48]Chevallier, J. (2010). Modelling risk premia in CO2 allowances spot and futures prices. Economic Modelling, 27(3), 717–729. https://doi.org/10.1016/j.econmod.2010.01.012
  • [49]Chevallier, J., & Sévi, B. (2011). On the realized volatility of the ECX CO2 emissions 2008 futures contract: Distribution, dynamics and forecasting. Annals of Finance, 7(1), 1–29. https://doi.org/10.1007/s10436-009-0142-x
  • [50]Bredin, D., & Parsons, J. (2016). Why is spot carbon so cheap and future carbon so dear? The term structure of carbon prices. The Energy Journal, 37(3), 83–108. https://doi.org/10.5547/01956574.37.3.dbre
  • [51]Hinz, J., & Novikov, A. (2010). On fair pricing of emission-related derivatives. Bernoulli, 16(4), 1240–1261. https://doi.org/10.3150/09-BEJ242
  • [52]Kollenberg, S., & Taschini, L. (2016). Emissions trading systems with cap adjustments. Journal of Environmental Economics and Management, 80, 20–36. https://doi.org/10.1016/j.jeem.2016.09.003
  • [53]Perino, G., & Willner, M. (2016). Procrastinating reform: The impact of the Market Stability Reserve on the EU ETS. Journal of Environmental Economics and Management, 80, 37–52. https://doi.org/10.1016/j.jeem.2016.09.006
  • [54] Appendix A. Corpus Classification and IMME Coding Protocol
  • [55] Corpus classification. The 53-record evidence matrix contains 47 records used in the model-level synthesis and six contextual records retained for triangulation. The latter comprise Chevallier's risk-premium analysis [48], Chevallier and Sévi's realized-volatility forecast [49], Bredin and Parsons' cost-of-carry and term-structure evidence [50], Hinz and Novikov's fair-pricing principles [51], Kollenberg and Taschini's cap-adjustment design [52], and Perino and Willner's analysis of delayed MSR reform [53]. They support pricing-measure, term-structure, or institutional interpretation but do not add an independent cross-model option-validation or hedging test; none was treated as a duplicate or quality exclusion.
  • [56] Coding protocol. Institution codes record regime boundaries and policy state; Model codes identify processes, state variables, payoffs, parameters, and numerical methods; Measure codes distinguish P, Q, transformations, and incomplete-market pricing principles; Evidence codes record data, filters, validation splits, losses, hedging costs, and regime tests. For example, Fang et al. [33] is coded as Phase III–IV open trading with inter-phase banking (Institution); LN, SKM, and MLN-2 futures-option specifications (Model); risk-neutral calibration to option prices (Measure); and weekly cross-sections with training/testing MSE, MAE, and MAPE but no dynamic-hedging or regime-transport test (Evidence).
  • [57] Illustrative evidence links. Risk-neutral modelling in [19] illustrates Level 1 coherence; option-price calibration in [33] illustrates a Level 2 component; and next-month pricing in [29] illustrates the chronological holdout component of Level 3. These links identify particular evidence requirements rather than formal ratings of whole studies; neither empirical example establishes the combined hedging and cross-regime validation required at Level 4.

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Oct 19, 2026
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Vol. 17 (2026): Proceedings of the International Conference on Research in Accounting, Finance and Management (ICRAFM 2026)
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How to Cite

Zhu, Bohao. “Model Risk in European Union Allowance Futures and Options: From Black–76 to Institutionally Grounded Models—A Critical Structured Review”. Exploring Science Academic Conference Series, vol. 17, Oct. 2026, pp. 809-18, https://doi.org/10.70267/icrafm.202617809818.