AA4 – Energy and Markets



Stochastic modeling of intraday electricity markets

Project Heads

Dörte Kreher, Markus Reiß

Project Members

Cassandra Milbradt (HU) 

Project Duration

01.01.2019 – 31.12.2021

Located at

HU Berlin


This project aims at developing infinite dimensional, stochastic models for intraday electricity markets with continuous trading, with a special focus on the newly launched integrated European intraday electricity market XBID. Starting from a microscopic description of the market model, we will derive heavy traffic approximations of the system dynamics yielding a tractable description of the volumes, prices, and available transmission capacities via stochastic (partial) differential equations.


In a first step, we study the dynamics for the volumes and prices of a single electricity contract traded on national limit order market. Second, we will look at a single contract being traded in an integrated market network, exhibiting limited transmission capacities. Third, we will look at several contracts simultaneously, constructing an underlying term structure model. Furthermore, we shall develop statistical methods to estimate the model’s parameters and to provide uncertainty quantification via confidence statements, for which explicit limit distributions of the estimators and test statistics will be derived.


As opposed to the existing structural energy market models, we develop analytically tractable, mathematical models for intraday electricity markets based on their observable market microstructure and therefore on statistically measurable input factors. This may presumably be useful to gain not only qualitative, but also quantitative insights into the German Intraday Electricity Market as well as the XBID market project.

Project Webpages

Selected Publications

  • U. Horst and D. Kreher. Second order approximations for limit order book. Finance and Stochastics, 22(4):827–877, 2018.
  • U. Horst and D. Kreher. A diffusion approximation for limit order book models. Stochastic Processes and their Applications, 129(11):4431-4479, 2019.
  • U. Horst and D. Kreher. A weak law of large numbers for a limit order book model with fully state dependent order dynamics. SIAM J. Financial Mathematics, 8:314–343, 2017.
  • M. Bibinger, M. Jirak, and M. Reiß. Volatility estimation under one-sided errors with applications to limit order books. Annals of Applied Probability, 26:2754–2790, 2016.

Selected Pictures

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