Skip to main content Accessibility help

Equilibrium Price Dynamics of Emission Permits

  • Steffen Hitzemann and Marliese Uhrig-Homburg


This article presents a stochastic equilibrium model for environmental markets that allows us to study the characteristic properties of emission permit prices induced by the design of today’s cap-and-trade systems. We characterize emission permits as highly nonlinear contingent claims on economy-wide emissions and reveal their hybrid nature between investment and consumption assets. Our model makes predictions about the dynamics and volatility structure of emission permit prices, the forward price curve, and the implications for option pricing in this market. Empirical evidence from existing emissions markets shows that the model explains the stylized facts of emission permit prices and related derivatives.


Corresponding author

*Hitzemann (corresponding author),, Rutgers Business School Department of Finance and Economics; Uhrig-Homburg,, Karlsruhe Institute of Technology Institute for Finance.


Hide All

We thank Antje Berndt, René Carmona, Marc Chesney, Karl-Martin Ehrhart, Sang Baum Kang, Rüdiger Kiesel, Dominik Möst, Paulo Pereira, Christian Schlag, Philipp Schuster, Siegfried Trautmann, Michael Triskatis, Clemens Völkert, and Volker Vonhoff, as well as participants at the 2009 International Ruhr Energy Conference, the 2010 Campus for Finance Research Conference, the 2010 Industrial-Academic Forum on Commodities, Energy Markets, and Emission Trading at the Fields Institute (Toronto), the 2010 World Congress of Environmental and Resource Economists, the 2010 Energy Finance Conference, the 2011 Annual Conference of the Swiss Society for Financial Market Research, the 2011 Financial Management Association European Conference, the 2011 European Financial Management Association Annual Meetings, the 2011 International Congress on Industrial and Applied Mathematics, the 2011 Annual Meeting of the German Finance Association, the 2011 Financial Management Association Annual Meeting, the 2013 Annual Meeting of the German Academic Association for Business Research, the 2013 Applicable Semiparametrics Conference, and the Universities of Duisburg-Essen and Zurich for valuable discussions and helpful comments and suggestions. The article greatly benefited from comments by Hendrik Bessembinder (the editor) and Gurdip Bakshi and Bryan Routledge (associate editors and referees). Financial support by the Graduate School 895 “Information Management and Market Engineering” at the Karlsruhe Institute of Technology (KIT), funded by Deutsche Forschungsgemeinschaft (DFG), is gratefully acknowledged. An earlier version of this article was circulated under the title “Understanding the Price Dynamics of Emission Permits: A Model for Multiple Trading Periods.”



Hide All
Baker, S. D.; Hollifield, B.; and Osambela, E.. “Disagreement, Speculation, and Aggregate Investment.” Journal of Financial Economics, 119 (2016), 210225.
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 20032049.
Bansal, R.; Kiku, D.; and Ochoa, M.. “Price of Long-Run Temperature Shifts in Capital Markets.” NBER Working Paper No. 22529 (2017).
Black, F.Studies of Stock Price Volatility Changes.” In Proceedings of the 1976 Meetings of the American Statistical Association (1976), 177181.
Brennan, M. J.The Supply of Storage.” American Economic Review, 48 (1958), 5072.
Calel, R., and Dechezleprêtre, A.. “Environmental Policy and Directed Technological Change: Evidence from the European Carbon Market.” Review of Economics and Statistics, 98 (2016), 173191.
Carmona, R.; Delarue, F.; Espinosa, G.-E.; and Touzi, N.. “Singular Forward–Backward Stochastic Differential Equations and Emissions Derivatives.” Annals of Applied Probability, 23 (2013), 10861128.
Carmona, R., and Fehr, M.. “The Clean Development Mechanism and Joint Price Formation for Allowances and CERs.” In Progress in Probability, Vol. 63, Seminar on Stochastic Analysis, Random Fields and Applications (2011), 341383.
Carmona, R.; Fehr, M.; and Hinz, J.. “Optimal Stochastic Control and Carbon Price Formation.” SIAM Journal on Control and Optimization, 48 (2009), 21682190.
Carmona, R.; Fehr, M.; Hinz, J.; and Porchet, A.. “Market Design for Emission Trading Schemes.” SIAM Review, 52 (2010), 403452.
Carmona, R., and Hinz, J.. “Risk-Neutral Models for Emission Allowance Prices and Option Valuation.” Management Science, 57 (2011), 14531468.
Casassus, J., and Collin-Dufresne, P.. “Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates.” Journal of Finance, 60 (2005), 22832331.
Cetin, U., and Verschuere, M.. “Pricing and Hedging in Carbon Emissions Markets.” International Journal of Theoretical and Applied Finance, 12 (2009), 949967.
Chesney, M., and Taschini, L.. “The Endogenous Price Dynamics of Emission Allowances and an Application to CO2 Option Pricing.” Applied Mathematical Finance, 19 (2012), 447475.
Chevallier, J.Modelling the Convenience Yield in Carbon Prices Using Daily and Realized Measures.” International Review of Applied Financial Issues and Economics, 1 (2009), 5673.
Christie, A. A.The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects.” Journal of Financial Economics, 10 (1982), 407432.
Cline, W. R. Carbon Abatement Costs and Climate Change Finance. Washington DC: Peterson Institute for International Economics (2011).
Coase, R. H.The Problem of Social Cost.” Journal of Law and Economics, 3 (1960), 144.
Cronshaw, M. B., and Kruse, J.. “Regulated Firms in Pollution Permit Markets with Banking.” Journal of Regulatory Economics, 9 (1996), 179189.
Daskalakis, G.; Psychoyios, D.; and Markellos, R. N.. “Modeling CO2 Emission Allowance Prices and Derivatives: Evidence from the European Trading Scheme.” Journal of Banking and Finance, 33 (2009), 12301241.
Ellerman, A. D., and Buchner, B. K.. “Over-Allocation or Abatement? A Preliminary Analysis of the EU ETS Based on the 2005-06 Emissions Data.” Environmental and Resource Economics, 41 (2008), 267287.
Geske, R.The Valuation of Compound Options.” Journal of Financial Economics, 7 (1979), 6381.
Hahn, R. W.Market Power and Transferable Property Rights.” Quarterly Journal of Economics, 99 (1984), 753765.
Hitzemann, S., and Uhrig-Homburg, M.. “Empirical Performance of Reduced-Form Models for Emission Permit Prices.” SSRN Working Paper No. 2297121 (2018).
Jarrow, R. A.Convenience Yields.” Review of Derivatives Research, 13 (2010), 2543.
Joskow, P. L.; Schmalensee, R.; and Bailey, E. M.. “The Market for Sulfur Dioxide Emissions.” American Economic Review, 88 (1998), 669685.
Kijima, M.; Maeda, A.; and Nishide, K.. “Equilibrium Pricing of Contingent Claims in Tradable Permit Markets.” Journal of Futures Markets, 30 (2010), 559589.
Klepper, G., and Peterson, S.. “Marginal Abatement Cost Curves in General Equilibrium: The Influence of World Energy Prices.” Resource and Energy Economics, 28 (2006), 123.
Kossoy, A., and Guigon, P.. State and Trends of the Carbon Market. Washington, DC: The World Bank (2012).
Litzenberger, R. H., and Rabinowitz, N.. “Backwardation in Oil Futures Markets: Theory and Empirical Evidence.” Journal of Finance, 50 (1995), 15171545.
Montgomery, W. D.Markets in Licenses and Efficient Pollution Control Programs.” Journal of Economic Theory, 5 (1972), 395418.
Nauclér, T., and Enkvist, P.-A.. Pathways to a Low-Carbon Economy. Version 2 of the Global Greenhouse Gas Abatement Cost Curve. New York, NY: McKinsey & Company (2009).
Rittler, D.Price Discovery and Volatility Spillovers in the European Union Emissions Trading Scheme: A High-Frequency Analysis.” Journal of Banking and Finance, 36 (2012), 774785.
Routledge, B. R.; Seppi, D. J.; and Spatt, C. S.. “Equilibrium Forward Curves for Commodities.” Journal of Finance, 55 (2000), 12971338.
Rubin, J. D.A Model of Intertemporal Emission Trading, Banking, and Borrowing.” Journal of Environmental Economics and Management, 31 (1996), 269286.
Schennach, S.The Economics of Pollution Permit Banking in the Context of Title IV of the 1990 Clean Air Act Amendments.” Journal of Environmental Economics and Management, 40 (2000), 189210.
Schmalensee, R.; Joskow, P. L.; Ellerman, A. D.; Montero, J. P.; and Bailey, E. M.. “An Interim Evaluation of Sulfur Dioxide Emissions Trading.” Journal of Economic Perspectives, 12 (1998), 5368.
Schwartz, E. S.The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging.” Journal of Finance, 52 (1997), 923973.
Seifert, J.; Uhrig-Homburg, M.; and Wagner, M. W.. “Dynamic Behavior of CO2 Spot Prices.” Journal of Environmental Economics and Management, 56 (2008), 180194.
Stavins, R. N.Transaction Costs and Tradeable Permits.” Journal of Environmental Economics and Management, 29 (1995), 133148.
Trolle, A. B., and Schwartz, E. S.. “Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives.” Review of Financial Studies, 22 (2009), 44234461.
Uhrig-Homburg, M., and Wagner, M.. “Futures Price Dynamics of CO2 Emission Allowances: An Empirical Analysis of the Trial Period.” Journal of Derivatives, 17 (2009), 7388.
Type Description Title
Supplementary materials

Hitzemann and Uhrig-Homburg supplementary material
Hitzemann and Uhrig-Homburg supplementary material 1

 Unknown (268 KB)
268 KB

Equilibrium Price Dynamics of Emission Permits

  • Steffen Hitzemann and Marliese Uhrig-Homburg


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed