Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Applied and Computational Mathematics (ACM)

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Bilateral German-Portuguese Project

PRISEMA - Pricing of Financial Instruments in Emission Markets

financed by DAAD and FCT- Fundação Para a Ciência e a Tecnologia

(05/2024 - 04/2026)

Scientific goals

The aim of this project is to develop new models and methods for the pricing of carbon emission allowances and renewable energy certificates. We will focus on stochastic structural models based on the underlying economic factors that determine the price of carbon credits. Our goal is to derive a forward-backward stochastic differential equation (FBSDE) for the emission allowance pricing process and numerically solve the associated partial differential equations (PDEs). We will extend the basic model for risk-neutral pricing of carbon emission certificates by considering more general processes for the electricity demand process and for the processes modeling cumulative emissions and the interaction between the electricity and emissions markets. In particular, we will consider the following extensions:

  1. In the demand process, we will introduce feedback effects between the price process and demand, explicit time dependence for the drift function, seasonality, and truncation effects;
  2. in the stochastic differential equations modeling the demand process, we will introduce appropriate nonlinear terms and jump diffusion processes;
  3. we will also consider multiple stochastic fuel prices.
In the generalized models, we will first derive the corresponding FBSDE, which is the risk-neutral price of carbon emission certificates. Then, we investigate the problem of well-posedness and existence/uniqueness of solutions for this FBSDE.

In the proposed modified models, we will generalize the PDE approach of Howison and Schwarz. In particular, we will study the following problems:

  1. derive properties of the solutions of the pricing PDE in particular asymptotic cases (e.g. near maturity);
  2. develop efficient numerical methods for solving the pricing PDE, testing the methods based on semi-Lagrangian schemes, Lagrange-Galerkin methods, and alternating direction (ADI) finite difference schemes, among others;
  3. obtain pricing PDEs for financial derivatives and options depending on the emission certificates, and testing appropriate numerical methods for solving these PDEs;
  4. extend the methodology to the pricing of renewable energy certificates (RECs).
We believe that this project will make significant contributions to the emerging field of environmental (green) finance. The new models and methods developed will be of interest to researchers/practitioners in the field.

Strategic and Educational Aims

We will further strengthen the academic relations between the two working groups, but also between the two universities. Right in this context we will establish a new german-portuguese subgroup in our ECMI special interest group on computational finance and an active student and staff exchange in the framework of the ERASMUS programme. Here we plan jointly supervised theses and compact courses offered by the staff of the partner group with the vision of a truly European education and qualification on a high academic level, also with the emphasis to train fellows to work in multi-cultural research teams.

German team:

Portuguese team:

German institutions:

Portuguese institutions:

Publications related to the Project

2024

2025 2026

Talks related to the Project

2024

2025 2026

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

Last modified:   Disclaimer   ehrhardt@math.uni-wuppertal.de