Assessment of Insurance Group Capital Requirements Taking into Account the Lack of Fungibility between Legal Entities

Abstract

The current development of Solvency frameworks in Europe (e.g. Solvency 2 for the European Union, Swiss Solvency Test in Switzerland) focuses on capital requirements for stand-alone legal entities. The solvency assessment of insurance groups or conglomerates involves additional elements that are not visible on the balance sheets of stand-alone non-consolidated legal entities including, in particular, the issue of fungibility of capital between different legal entities running business in different jurisdictions. These additional elements also include optimal capital allocation between the different companies of one group and the theoretical option to allow the bankruptcy of one subsidiary when it is hit by a major catastrophic event (hereinafter the “run-off option”).

In order to estimate the impact of these supplementary elements, this article introduces a case study of one insurance group made of three daughter companies. For this group, optimal capital allocation is proposed taking into account the potential lack of capital fungibility between the three daughter companies. In addition, the value of the “run-off option” for each subsidiary is calculated on the basis of the Black&Scholes model. Using these results, the capitalization ratio of the group is then estimated.

Keywords: Fungibility of capital, Copula, Aggregation, Solvency capital requirement, Minimum capital requirement, Diversification benefit, Expected shortfall, Option pricing, Capitalization ratio

JEL Classification: G22