Counterparty Risk and Value Adjustments in Spark Spread Contracts: A High-Dimensional Approach
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This study focuses on the analysis of counterparty credit risk (CCR) in derivative contracts on energy commodities, with specific attention to spark spread swap contracts. These instruments are widely adopted by electricity producers and energy traders for hedging and speculative purposes, respectively, and have become central to risk management practices in energy markets. The relevance of CCR in this context was dramatically emphasized during the 2022 European energy crisis, which led to extreme market imbalances and stressed the importance of advanced valuation models . Traditionally, derivatives valuation often neglected the role of default risk. However, following the 2007–2008 financial crisis, an extensive theoretical framework of value adjustments (e.g., CVA, DVA, ColVA) was developed to incorporate counterparty and collateralization risks into pricing . While initially formulated in financial markets, such adjustments are now essential in the valuation of energy derivatives, where credit exposures can be significant. The main objective of this work is to address the challenge of valuing CCR in high-dimensional settings, where classical numerical methods fail due to the curse of dimensionality . We adopt a methodology based on backward stochastic differential equations (BSDEs) and probabilistic schemes capable of handling fully nonlinear PDEs arising in this context. Our approach replaces spatial discretization with the simulation of controlled stochastic processes and regression-based estimation of derivatives, such as gradients and Hessians. The proposed method preserves monotonicity under suitable conditions and ensures convergence to the viscosity solution, making it a robust and scalable framework for computing value adjustments in spark spread swaps. Numerical experiments confirm the effectiveness of the method in realistically complex market environments.
