Portfolio risk allocation through Shapley value

Patrick S. Hagan (), Andrew Lesniewski (), Georgios E. Skoufis and Diana E. Woodward
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Patrick S. Hagan: Gorilla Science, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA
Andrew Lesniewski: Department of Mathematics, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA
Georgios E. Skoufis: Santander Corporate & Investment Banking, 2 Triton Square, Regents Place, London NW1 3AN, UK
Diana E. Woodward: Gorilla Science, Baruch College, One Bernard Baruch Way, New York, NY 10010, USA

International Journal of Financial Engineering (IJFE), 2025, vol. 12, issue 02, 1-18

Abstract: We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk. We discuss a Shapley value scheme for allocating risk to non-orthogonal greeks in a portfolio of derivatives. Such a situation arises, for example, when using a stochastic volatility model to capture option volatility smile. We also show that Shapley value allows for a natural method of interpreting components of enterprise risk measures such as VaR and ES. For all applications discussed, we derive explicit formulas and/or numerical algorithms to calculate the allocations.

Keywords: Cooperative games; Shapley value; risk factors; risk attribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S2424786323500044

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