Deep Learning for Energy Market Contracts: Dynkin Game with Doubly RBSDEs

This paper examines a Contract for Difference (CfD) with early exit options, a key risk management tool in electricity markets. The contract, involving a producer and a regulatory entity, is modeled as a two-player Dynkin game with mean-reverting electricity prices and penalties for early termination. We formulate the strategic interaction using Doubly Reflected Backward Stochastic Differential Equations (DRBSDEs), which characterize the fair contract value and optimal stopping strategies. We show that the first component of the DRBSDE solution represents the value of the Dynkin game, and that the first hitting times correspond to a Nash equilibrium. Additionally, we link the problem to a Skorokhod problem with time-dependent boundaries, deriving an explicit formula for the Skorokhod adjustment processes. To solve the DRBSDE, we develop a deep learning-based numerical algorithm, leveraging neural networks for efficient computation. We analyze the convergence of the deep learning algorithm, as well as the value function and optimal stopping rules. Numerical experiments, including a CfD model calibrated on French electricity prices, highlight the impact of exit penalties, price volatility, and contract design. These findings offer insights for market regulators and energy producers in designing effective risk management strategies.