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.

Keywords: Risk allocation, Shapley value, Basel 2.5 / FRTB regulations, Coherent risk measures, Monte Carlo simulation, Market Risk (Multi-asset)

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced game theory and mathematical properties (e.g., Shapley values, Euler theorems) for risk allocation, indicating high math complexity, while it uses a structured testing framework with realistic portfolios under Basel 2.5 and FRTB regulations, focusing on computational aspects and Monte Carlo methods, demonstrating high empirical rigor and backtest readiness.

  flowchart TD
    A["Research Goal<br>Systematic Review &<br>Optimization of Risk<br>Allocation Strategies"] --> B["Methodology<br>Comparative Analysis &<br>Novel Solution Development"]
    
    B --> C["Input Data<br>Simplified Settings &<br>Realistic Portfolios<br>(Basel 2.5 / FRTB)"]
    
    C --> D["Computational Process<br>Efficient Monte Carlo<br>Simulation for Shapley"]
    
    D --> E["Key Findings & Outcomes<br>Shapley Value = Best<br>Compromise (Simplicity,<br>Properties, Cost)<br>Negative/Multi-level<br>Solutions Preserved"]