Shapley Value

Sharpening Shapley Allocation: from Basel 2.5 to FRTB ArXiv ID: 2511.12391 “View on arXiv” Authors: Marco Scaringi, Marco Bianchetti Abstract Risk allocation, the decomposition of a portfolio-wide risk measure into component contributions, is a fundamental problem in financial risk management due to the non-additive nature of risk measures, the layered organizational structures of financial institutions, and the range of possible allocation strategies characterized by different rationales and properties. In this work, we conduct a systematic review of the major risk allocation strategies typically used in finance, comparing their theoretical properties, practical advantages, and limitations. To this scope we set up a specific testing framework, including both simplified settings, designed to highlight basic intrinsic behaviours, and realistic financial portfolios under different risk regulations, i.e. Basel 2.5 and FRTB. Furthermore, we develop and test novel practical solutions to manage the issue of negative risk allocations and of multi-level risk allocation in the layered organizational structure of financial institutions, while preserving the additivity property. Finally, we devote particular attention to the computational aspects of risk allocation. Our results show that, in this context, the Shapley allocation strategy offers the best compromise between simplicity, mathematical properties, risk representation and computational cost. The latter is still acceptable even in the challenging case of many business units, provided that an efficient Monte Carlo simulation is employed, which offers excellent scaling and convergence properties. While our empirical applications focus on market risk, our methodological framework is fully general and applicable to other financial context such as valuation risk, liquidity risk, credit risk, and counterparty credit risk. ...

Explaining Risks: Axiomatic Risk Attributions for Financial Models ArXiv ID: 2506.06653 “View on arXiv” Authors: Dangxing Chen Abstract In recent years, machine learning models have achieved great success at the expense of highly complex black-box structures. By using axiomatic attribution methods, we can fairly allocate the contributions of each feature, thus allowing us to interpret the model predictions. In high-risk sectors such as finance, risk is just as important as mean predictions. Throughout this work, we address the following risk attribution problem: how to fairly allocate the risk given a model with data? We demonstrate with analysis and empirical examples that risk can be well allocated by extending the Shapley value framework. ...

Can I Trust the Explanations? Investigating Explainable Machine Learning Methods for Monotonic Models ArXiv ID: 2309.13246 “View on arXiv” Authors: Unknown Abstract In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain knowledge, science-informed machine learning models have demonstrated better generalization and interpretation. But do we obtain consistent scientific explanations if we apply explainable machine learning methods to science-informed machine learning models? This question is addressed in the context of monotonic models that exhibit three different types of monotonicity. To demonstrate monotonicity, we propose three axioms. Accordingly, this study shows that when only individual monotonicity is involved, the baseline Shapley value provides good explanations; however, when strong pairwise monotonicity is involved, the Integrated gradients method provides reasonable explanations on average. ...