Risk Measures Used by Insurance Regulatory Framework

The goal of this paper is to research if Expected Shortfall is a suitable risk measure for the most European insurance companies in the context of the Solvency II standard formula. The paper presents a risk measures analysis based on the properties which should be fulfilled by a risk measure in order to be considered suitable to forecast the potential loss of the future results in the context of the regulation and capital requirements. The paper focuses on the assessment of the advantages and disadvantages of Value-at-Risk (used in Solvency II insurance regulatory regime) and Expected Shortfall (applied in the Swiss Solvency Test insurance regulatory systems). Expected Shortfall presents two important theoretical advantages: it is a coherent risk measure and gives information both the frequency of insolvency losses and the severity of losses threshold of the quantile. Value-at-Risk does not give credit for diversification (is not a coherent risk measures due to the lack of subadditivity property) and does not capture the tail risk. The main advantage of the Value-at-Risk is represented by its simplicity in implementation and understanding by third parties compared to Expected Shortfall, which it is difficult to apply in practice. When selecting the risk measure that ensures a good fit for majority of insurers in the context of regulatory frameworks, an important criterion is geographical application: the Swiss Solvency Test has a limited geographical application (only Switzerland), by contrast, Solvency II covers all the entire European Union (28 Member States).