Sharpening Shapley Allocation: from Basel 2.5 to FRTB
A new survey examines risk allocation in financial institutions, focusing on the Shapley allocation method. The authors show Shapley is not only theoretically sound but also practical for large organizations, especially with Monte Carlo simulations. They address challenges like negative risk allocations and complex regulations such as Basel 2.5 and FRTB (Fundamental Review of the Trading Book). Tests reveal Shapley offers fairness and efficiency, though further validation is needed for non-market risks and interpreting negative allocations.
What it examines
This study reviews and compares major risk allocation methods in finance, focusing on how to fairly split risk across business units under regulations like Basel 2.5 and FRTB. It highlights the Shapley allocation strategy, tests its practicality using simulations, and proposes solutions for negative and multi-level risk allocations.
What it concludes
The Shapley allocation method balances fairness, accuracy, and efficiency, even for large, complex organizations. It can be used for market, credit, liquidity, and counterparty risk. The study's framework helps banks and financial firms improve risk reporting, capital management, and regulatory compliance. Future work may extend these methods to other risk types.
Evidence objects
A new survey highlights the Shapley allocation method as both theoretically robust and practical for large financial institutions, especially when combined with Monte Carlo simulations, challenging the belief that its too complex for real-world use.
key_findings bullet 1 · key_findings · validation V0
Key innovations include scalable multi-level allocation strategies that preserve additivity, novel solutions for negative risk allocations, and hybrid approaches blending Shapley with proportional methods to address high computational costs under Basel 2.5 and FRTB regulations.
key_findings bullet 2 · key_findings · validation V0
Extensive numerical tests show Shapley allocation consistently balances fairness, transparency, and efficiency, but the study notes challenges in interpreting negative allocations and calls for more empirical validation in non-market risk scenarios.
key_findings bullet 3 · key_findings · validation V0
This paper uniquely advances Quantitative Risk Management by developing and empirically testing novel solutions for negative and multi-level risk allocations under Basel 2.5 and FRTB. Its originality lies in combining practical allocation methods with efficient Monte Carlo computation for Shapley allocation, offering significant insights for regulatory compliance and risk capital allocation.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
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 syst… ▽ More 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. △ Less
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