Shapley allocation, diversification and services in operational risk

Peter Mitic; Bertrand Hassani

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Allocation of a total amount of costs, expenses, resources etc. to business units has to be done in a way that is seen as ‘fair’ by those business units.
The Shapley allocation method ensures fairness through cooperation between business units, but the results of that cooperation are rarely available in the context of operational risk losses.
In this paper we examine how the Shapley method may be applied to operational risk loss allocations by making simple assumptions about the results of potential cooperation.
The results are given in terms of simple formulae, and are compared with the easier Pro-Rata allocation.

Abstract

In this paper, a method of allocating operational risk regulatory capital using a closed-form Shapley method, applicable to a large number of business units (BUs), is proposed. It is assumed that if BUs form coalitions, the value added to a coalition by a new entrant is a simple function of the value of that entrant. This function represents the diversification that can be achieved by combining operational risk losses. Two such functions are considered. The calculations account for a service that further reduces the capital payable by BUs. The results derived are applied to recent loss data.

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