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In this paper we study the distribution of a product of two continuous random variables. We derive formulas for the probability density functions and moments of the products of the Gaussian, log-normal, Student's t and Pareto random…

Probability · Mathematics 2021-11-29 Julia Adamska , Łukasz Bielak , Joanna Janczura , Agnieszka Wyłomańska

The accurate prediction of short-term electricity prices is vital for effective trading strategies, power plant scheduling, profit maximisation and efficient system operation. However, uncertainties in supply and demand make such…

Econometrics · Economics 2023-04-20 Mira Watermeyer , Thomas Möbius , Oliver Grothe , Felix Müsgens

This paper employs machine learning algorithms to forecast German electricity spot market prices. The forecasts utilize in particular bid and ask order book data from the spot market but also fundamental market data like renewable infeed…

Applications · Statistics 2022-09-20 Simon Schnürch , Andreas Wagner

The recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits…

Statistical Finance · Quantitative Finance 2018-02-20 Noufel Frikha , Vincent Lemaire

Electricity markets are highly complex, involving lots of interactions and complex dependencies that make it hard to understand the inner workings of the market and what is driving prices. Econometric methods have been developed for this,…

Machine Learning · Computer Science 2025-06-26 Antoine Pesenti , Aidan OSullivan

Virtual bidding plays an important role in two-settlement electric power markets, as it can reduce discrepancies between day-ahead and real-time markets. Renewable energy penetration increases volatility in electricity prices, making…

Machine Learning · Computer Science 2024-12-03 Xuesong Wang , Sharaf K. Magableh , Oraib Dawaghreh , Caisheng Wang , Jiaxuan Gong , Zhongyang Zhao , Michael H. Liao

Electricity price forecasting supports decision-making in energy markets and asset operation. Probabilistic forecasts are increasingly adopted to explicitly quantify uncertainty, typically issued as quantile predictions or ensembles of the…

Statistical Finance · Quantitative Finance 2026-04-22 Simon Hirsch , Florian Ziel

In this paper we propose a regularization approach for network modeling of German power derivative market. To deal with the large portfolio, we combine high-dimensional variable selection techniques with dynamic network analysis. The…

Statistical Finance · Quantitative Finance 2020-09-22 Shi Chen , Wolfgang Karl Härdle , Brenda López Cabrera

We examine the problem of modeling and forecasting European Day-Ahead and Month-Ahead natural gas prices. For this, we propose two distinct probabilistic models that can be utilized in risk- and portfolio management. We use daily pricing…

Applications · Statistics 2023-02-13 Jonathan Berrisch , Florian Ziel

In wholesale electricity markets, prices fluctuate widely from hour to hour and electricity generators price-hedge their output using longer-term contracts, such as monthly base futures. Consequently, the incentives they face to drive up…

General Economics · Economics 2025-06-05 Alice Lixuan Xu , Jorge Sánchez Canales , Chiara Fusar Bassini , Lynn H. Kaack , Lion Hirth

Since the 1990s, widespread introduction of central (wholesale) electricity markets has been seen across multiple continents, driven by the search for efficient operation of the power grid through competition. The increase of renewables has…

Systems and Control · Electrical Eng. & Systems 2025-10-15 Pål Forr Austnes , Matthieu Jacobs , Lu Wang , Mario Paolone

In electricity markets, futures contracts typically function as a swap since they deliver the underlying over a period of time. In this paper, we introduce a market price for the delivery periods of electricity swaps, thereby opening an…

Pricing of Securities · Quantitative Finance 2022-06-13 Annika Kemper , Maren D. Schmeck , Anna Kh. Balci

Accurate electricity price forecasting (EPF) is crucial for effective decision-making in power trading on the spot market. While recent advances in generative artificial intelligence (GenAI) and pre-trained large language models (LLMs) have…

Machine Learning · Computer Science 2025-08-21 Timothée Hornek Amir Sartipi , Igor Tchappi , Gilbert Fridgen

The participation of consumers and producers in demand response programs has increased in smart grids, which reduces investment and operation costs of power systems. Also, with the advent of renewable energy sources, the electricity market…

Machine Learning · Computer Science 2022-07-29 Nafise Rezaei , Roozbeh Rajabi , Abouzar Estebsari

Intra-day price variations in financial markets are driven by the sequence of orders, called the order flow, that is submitted at high frequency by traders. This paper introduces a novel application of the Sequence Generative Adversarial…

Statistical Finance · Quantitative Finance 2021-09-29 Ye-Sheen Lim , Denise Gorse

While deep learning gradually penetrates operational planning, its inherent prediction errors may significantly affect electricity prices. This letter examines how prediction errors propagate into electricity prices, revealing notable…

Machine Learning · Computer Science 2023-11-14 Vladimir Dvorkin , Ferdinando Fioretto

Accurate price predictions are essential for market participants in order to optimize their operational schedules and bidding strategies, especially in the current context where electricity prices become more volatile and less predictable…

Computational Engineering, Finance, and Science · Computer Science 2025-09-26 Naga Venkata Sai Jitin Jami , Juraj Kardoš , Olaf Schenk , Harald Köstler

In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices…

Economics · Quantitative Finance 2023-03-03 Naoya Yamaguchi , Maiya Hori , Yoshinari Ideguchi

Accurate forecasts of electricity spot prices are essential to the daily operational and planning decisions made by power producers and distributors. Typically, point forecasts of these quantities suffice, particularly in the Nord Pool…

Statistical Finance · Quantitative Finance 2018-12-07 Gunnhildur H. Steinbakk , Alex Lenkoski , Ragnar Bang Huseby , Anders Løland , Tor Arne Øigård

Coordination of distributed energy resources is critical for electricity grid management. Although nodal pricing schemes can mitigate congestion and voltage deviations, the resulting prices are not necessarily equitable. In this work, we…

Optimization and Control · Mathematics 2023-12-15 Emmanuel Balogun , Sonia Martin , Anthony Degleris , Ram Rajagopal
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