Skip to main content
Log in

Pricing and valuation of carbon swap in uncertain finance market

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

It has become a consensus in the international community to actively address global climate change issues and strive to achieve carbon reduction. For this purpose, carbon finance market plays a significant role in reducing carbon emissions by providing financial mechanisms to support and incentivize emission reduction projects. As a type of carbon finance derivative, carbon swap is an agreement between two parties whereby a floating price is exchange for a fixed price for carbon emission right over a specified period. How to price carbon swap before signing, i.e., determine the fixed price in the swap contract, and valuate carbon swap during the life of the swap contract are key issues. Noting the fact that the underlying asset of carbon swap is carbon price, the primary task is to model carbon price reasonably. Due to the inherent challenges and uncertainties associated with pricing carbon, frequency stability is often not guaranteed, resulting in the failure of probability based methods. Thus, this paper characterizes the carbon price using uncertain differential equation under the framework of uncertainty theory, and derives swap pricing and valuation formulas. Estimations for unknown parameters in the proposed model are given. Finally, with carbon spot price in European Energy Exchange, real data analyses are documented to illustrate our proposed methods in details.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. https://www.eex.com/en/market-data/environmentals/spot..

References

  • Chevallier, J. (2010). Volatility forecasting of carbon prices using factor models. Economics Bulletin, 30(6), 1642–1660.

    Google Scholar 

  • Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, 9(1), 69–81.

    Article  MathSciNet  Google Scholar 

  • Chen, X., & Gao, J. (2013). Uncertain term structure model of interest rate. Soft Computing, 17, 597–604.

    Article  Google Scholar 

  • Daskalakis, G., Psychoyios, D., & Markellos, R. (2009). Modeling C02 emission allowance prices and derivatives: Evidence from the European trading scheme. Journal of Banking and Finance, 33(7), 1230–1241.

    Article  Google Scholar 

  • Lin, L. (2012). Research on international carbon finance market development and risk in low carbon economy. Contemporary Finance Economics, 2, 51–58.

    Google Scholar 

  • Liu, B. (2007). Uncertainty Theory (2nd ed.). Berlin: Springer.

    Google Scholar 

  • Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.

    Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

    Google Scholar 

  • Liu, B. (2015). Uncertainty Theory (4th ed.). Berlin: Springer.

    Book  Google Scholar 

  • Liu, Y., & Liu, B. (2022). Residual analysis and parameter estimation of uncertain differential equations. Fuzzy Optimization and Decision Making, 21(4), 513–530.

    Article  MathSciNet  Google Scholar 

  • Liu, Y., & Liu, B. (2022). Estimating unknown parameters in uncertain differential equation by maximum likelihood estimation. Soft Computing, 26(6), 2773–2780.

    Article  Google Scholar 

  • Liu, Y., Tian, L., Sun, H., Zhang, X., & Kong, C. (2022). Option pricing of carbon asset and its application in digital decision making of carbon asset. Applied Energy, 310(15), 118375.

    Article  Google Scholar 

  • Liu, Y., & Liu, B. (2023). Estimation of uncertainty distribution function by the principle of least squares. Communications in Statistics-Theory and Methods. https://doi.org/10.1080/03610926.2023.2269451

    Article  Google Scholar 

  • Liu, Z., & Huang, S. (2021). Brownian motion optimized by GARCH model in carbon emission trading. North American Journal of Economics and Finance, 55, 101307.

    Article  Google Scholar 

  • Lu, T. (2016). Study on development status of China carbon finance market, international experience and counter measures. Meteorological and Environmental Research, 7, 32–35.

    Google Scholar 

  • Luo, C., & Wu, D. (2016). Environment and economic risk: An analysis of carbon emission market and portfolio management. Environmental Research, 149(5), 297–301.

    Article  Google Scholar 

  • Pei, Q., Liu, L., & Zhang, D. (2013). Carbon emission right as a new property right: Rescue CDM developers in China from 2012. International Environmental Agreements: Politics, Law and Economics, 13, 307–320.

    Article  Google Scholar 

  • Yang, X., & Ke, H. (2023). Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption. Fuzzy Optimization and Decision Making, 22, 447–462.

    Article  MathSciNet  Google Scholar 

  • Yang, X., Jia, W., Wang, K., & Peng, G. (2024). Does the National Carbon Emissions Trading Market Promote Corporate Environmental Protection Investment? Evidence from China. Sustainability, 16(1), 402.

    Article  Google Scholar 

  • Yang, L., & Liu, Y. (2024). Solution method and parameter estimation of uncertain partial differential equation with application to China’s population. Fuzzy Optimization and Decision Making, 23, 155–177.

    Article  MathSciNet  Google Scholar 

  • Ye, T., & Liu, B. (2023). Uncertain hypothesis test for uncertain differential equations. Fuzzy Optimization and Decision Making, 22(2), 195–211.

    Article  MathSciNet  Google Scholar 

  • Ye, T., & Zheng, H. (2023). Analysis of birth rates in China with uncertain statistics. Journal of Intelligent and Fuzzy Systems, 44(6), 10621–10632.

    Article  Google Scholar 

  • Ye, T. (2024). Partial derivatives of uncertain fields and uncertain partial differential equations. Fuzzy Optimization and Decision Making. https://doi.org/10.1007/s10700-023-09417-3

    Article  MathSciNet  Google Scholar 

  • Zhang, X., Yang, K., Lu, Q., Wu, J., Yu, L., & Lin, Y. (2023). Predicting carbon futures prices based on a new hybrid machine learning: Comparative study of carbon prices in different periods. Journal of Environmental Management, 346, 118962.

    Article  Google Scholar 

  • Zhang, K., & Liu, B. (2024). Higher-order derivative of uncertain process and higher-order uncertain differential equation. Fuzzy Optimization and Decision Making. https://doi.org/10.1007/s10700-024-09422-0

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Social Science Funds of China (23BJL006).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yanbin Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Li, Y. Pricing and valuation of carbon swap in uncertain finance market. Fuzzy Optim Decis Making 23, 319–336 (2024). https://doi.org/10.1007/s10700-024-09423-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-024-09423-z

Keywords

Navigation