Price formation and optimal trading in intraday electricity markets

Féron, Olivier; Tankov, Peter; Tinsi, Laura

doi:10.1007/s11579-021-00307-z

Cited by 16 publications

(12 citation statements)

References 29 publications

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“…Another approach is to impose the market clearing condition but the demand of the asset is assumed to be given by an exogenous function of price without considering the optimization problem among the agents. See [1,9,14,15,16,23,39,12,13] as interesting applications to, optimal trading, optimal liquidation, optimal oil production, and price formation in electricity markets etc., using the phenomenological approaches explained above. A notable exception directly dealing with the market clearing equilibrium is [22], where the market price process becomes deterministic due to the absence of the common noise.…”

Section: Introductionmentioning

confidence: 99%

A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

Fujii

Takahashi

2020

SSRN Journal

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We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown, in the accompanying paper (Fujii & Takahashi) [19], that the solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit. In this work, we prove the existence of a unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the strong convergence to the corresponding mean-field limit given in [19] under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit.

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Section: Introductionmentioning

confidence: 99%

A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

Fujii

Takahashi

2020

SSRN Journal

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“…Contrary to the recent work of Féron et al. (2020) where the Samuelson's effect is obtained in a mean‐field Nash equilibrium model of intraday trading, we do not need to resolve to strategic interactions to find conditions for the effect. We show that if all agents are identical, the price volatility monotonicity is fully determined by the volatility of the demand forecasts.…”

Section: Introductionmentioning

confidence: 71%

Equilibrium price in intraday electricity markets

Aïd

Cosso

Pham

2021

Mathematical Finance

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We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity. Forecasts are prone to idiosyncratic noise and common noise (weather). Agents production capacities are subject to independent random outages, which are each modeled by a Markov chain. The equilibrium price is defined as the price that minimizes trading cost plus imbalance cost of each agent and satisfies the usual market clearing condition. Existence and uniqueness of the equilibrium are proved, and we show that the equilibrium price and the optimal trading strategies are martingales. The main economic insights are the following: (i) when there is no uncertainty on generation, it is shown that the market price is a convex combination of forecasted marginal cost of each agent, with deterministic weights. Furthermore, the equilibrium market price is consistent with Almgren and Chriss's model, and we identify the fundamental part and the permanent market impact. It turns out that heterogeneity across agents is a necessary condition for Samuelson's effect to hold. We show that when heterogeneity lies only on costs, Samuelson's effect holds true. A similar result stands when heterogeneity lies only on market access quality. (ii) When there is production uncertainty only, we provide an approximation of the equilibrium for large number of players. The resulting price exhibits increasing volatility with time.

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“…Using a linearquadratic structure, the authors obtained a market price depending on the average position of the agents and the position of the major agent. The successive work [20] proposed a MFG model with common noise, with numerical results for the EPEX intraday electricity market. A MFG of optimal stopping was introduced in [2] to model the transition from traditional to renewable means of energy production.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning architectures for price formation models

Gomes¹,

Gutiérrez²,

Laurière³

2022

Preprint

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Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min-max characterization of the optimal control and price variables. Our main theoretical contribution is the development of a posteriori estimates as a tool to evaluate the convergence of the training process. We illustrate our results with numerical experiments for a linear-quadratic model.

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Price formation and optimal trading in intraday electricity markets

Cited by 16 publications

References 29 publications

A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

Equilibrium price in intraday electricity markets

Machine Learning architectures for price formation models

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