Reinsurance as a Mechanism for Optimizing Capital Requirements Under the Solvency II Regime: An Empirical Analysis of a Ten-Year Insurance Portfolio

Abstract

The Solvency II regulatory framework (Directive 2009/138/EC) defines the Solvency Capital Requirement (Solvency Capital Requirement, SCR) using a value-at-risk (VaR) approach, with a confidence level of 99.5% and a one-year time horizon. This structure makes regulatory capital extremely sensitive to the characteristics of the right tail of the loss distribution and, consequently, to the effectiveness of risk transfer mechanisms. This study analyzes the impact of the five main types of reinsurance contracts quota share, surplus, quota–surplus, excess-of-loss (XoL), and stop-loss on the transformation of the net loss distribution and the resulting dynamics of the SCR. The empirical analysis is based on a computational experiment using real data from a ten-year insurance portfolio covering the period 2016–2025. The results show that the use of reinsurance leads to a reduction in the total capital requirement in the range of 18.4–23.4% on an annual basis, with the effect exhibiting an approximately linear relationship with the size of the cession quota. The stratified comparative analysis conducted identifies significant differences in the effectiveness of individual contract structures with regard to the reduction of tail risk. In particular, XoL contracts demonstrate the strongest effect on the extreme quantiles of the loss distribution, with a reduction reaching −52.5% at the 99.5% VaR level and −68.6% at the 99.9% VaR level. In contrast, quota-share contracts result in a practically proportional scaling of risk, characterized by a symmetric reduction of approximately −40% across all confidence levels. The results further show that multi-tiered reinsurance programs combining quota share, excess, catastrophe XoL, and stop-loss components provide the highest degree of capital relief, reaching 48.8%, which indicates the presence of significant nonlinear diversification and complementarity effects among the individual risk transfer mechanisms. A waterfall decomposition is applied to identify the main factors determining the difference between the standard formula and the internal model. The analysis finds that the dominant drivers of the observed capital relief are the effect of precise risk calibration (on average −8.3%) and the effect of diversification (−4.7%). These results underscore the importance of adequately modeling the interdependencies among risk modules and the limitations of standardized regulatory parameterizations. In addition, a “wrong-way risk” stress scenario is developed, involving the simultaneous occurrence of a catastrophic risk and the insolvency of two key reinsurers. Under this scenario, the effectiveness of risk transfer is reduced to −27.3%, and the solvency ratio falls below the minimum capital requirement (12.5%). This result empirically confirms the cautious regulatory stance of the European Insurance and Occupational Pensions Authority regarding the limited recognition of capital reliefs that do not demonstrate resilience under extreme stress conditions. This study provides a quantitatively grounded framework for optimizing reinsurance programs under the Solvency II regime. The main conclusion is that capital efficiency is not a function of a single “optimal” reinsurance contract, but rather results from the strategic combination of various reinsurance mechanisms capable of simultaneously reducing tail risk, improving diversification, and limiting vulnerability to systemic stress events.