© 2017

A Forward-Backward SDEs Approach to Pricing in Carbon Markets


Part of the Mathematics of Planet Earth book series (MPE)

Also part of the SpringerBriefs in Mathematics of Planet Earth book sub series (SBMPE-WCO)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Jean-François Chassagneux, Hinesh Chotai, Mirabelle Muûls
    Pages 1-9
  3. Jean-François Chassagneux, Hinesh Chotai, Mirabelle Muûls
    Pages 11-42
  4. Jean-François Chassagneux, Hinesh Chotai, Mirabelle Muûls
    Pages 43-57
  5. Jean-François Chassagneux, Hinesh Chotai, Mirabelle Muûls
    Pages 59-74
  6. Jean-François Chassagneux, Hinesh Chotai, Mirabelle Muûls
    Pages 75-101
  7. Back Matter
    Pages 103-104

About this book


In Mathematical Finance, the authors consider a mathematical model for the pricing of emissions permits. The model has particular applicability to the European Union Emissions Trading System (EU ETS) but could also be used to consider the modeling of other cap-and-trade schemes. As a response to the risk of Climate Change, carbon markets are currently being implemented in regions worldwide and already represent more than $30 billion. However, scientific, and particularly mathematical, studies of these carbon markets are needed in order to expose their advantages and shortcomings, as well as allow their most efficient implementation.

This Brief reviews mathematical properties such as the existence and uniqueness of solutions for the pricing problem, stability of solutions and their behavior. These fit into the theory of fully coupled forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. The authors present a numerical algorithm to compute the solution to these non-standard FBSDEs. They also carry out a case study of the UK energy market. This involves estimating the parameters to be used in the model using historical data and then solving a pricing problem using the aforementioned numerical algorithm.

The Brief is of interest to researchers in stochastic processes and their applications, and environmental and energy economics. Most sections are also accessible to practitioners in the energy sector and climate change policy-makers.


60H30, 91G80 EU ETS stochastic analysis forward-backward stochastic differential equations commodity prices environmental finance parameter estimation pricing in carbon markets carbon markets emissions permits energy economics environmental economics

Authors and affiliations

  1. 1.U.F.R. de MathématiquesUniversité Paris Diderot, LPMAParisUnited Kingdom
  2. 2.Department of MathematicsImperial CollegeLondonUnited Kingdom
  3. 3.Grantham InstituteImperial CollegeLondonUnited Kingdom

Bibliographic information