A note on the appropriate choice of risk measures in the solvency assessment of insurance companies

Abstract

Purpose – The concept of value at risk is used in the risk-based calculation of solvency capital requirements in the Basel II/III banking regulations and in the planned Solvency II insurance regulation framework planned in the European Union. While this measure controls the ruin probability of a financial institution, the expected policyholder deficit (EPD) and expected shortfall (ES) measures, which are relevant from the customer's perspective as they value the amount of the shortfall, are not controlled at the same time. Hence, if there are variations in or changes to the asset-liability situation, financial companies may still comply with the capital requirement, while the EPD or ES reach unsatisfactory levels. This is a significant drawback to the solvency frameworks. The paper aims to discuss these issues. Design/methodology/approach – The author has developed a model framework wherein the author evaluates the relevant risk measures using the distribution-free approach of the normal power approximation. This allows the author to derive analytical approximations of the risk measures solely through the use of the first three central moments of the underlying distributions. For the case of a reference insurance company, the author calculates the required capital using the ruin probability and EPD approaches. For this, the author performs sensitivity analyses considering different asset allocations and different liability characteristics. Findings – The author concludes that only a simultaneous monitoring of the ruin probability and EPD can lead to satisfactory results guaranteeing a constant level of customer protection. For the reference firm, the author evaluates the relative changes in the capital requirement when applying the EPD approach next to the ruin probability approach. Depending on the development of the assets and liabilities, and in the cases the author illustrates, the reference company would need to provide substantial amounts of additional equity capital. Originality/value – A comparative assessment of alternative risk measures is relevant given the debate among regulators, industry representatives and academics about how adequately they are used. The author borrows the approach in parts from the work of Barth. Barth compares the ruin probability and EPD approach when discussing the RBC formulas of the US National Association of Insurance Commissioners introduced in the 1990s. The author reconsiders several of these findings and discusses them in the light of the new regulatory frameworks. More precisely, the author first performs sensitivity analyses for the risk measures using different parameter configurations. Such analyses are relevant since in practice parameter values may differ from estimates used in the model and have a significant impact on the values of the risk measures. Second, the author goes beyond a simple discussion of the outcomes for each risk measure, by deriving the firm conclusion that both the frequency and magnitude of shortfalls need to be controlled.

Solvency II solvency capital requirement for life insurance companies based on expected shortfall

“…Historical simulations are used in the calibration of solvency II. Other authors that claim that the ES is more appropriate to determine capital buffers are Beder [ 10 ], Acerbi and Tasche 3 , [ 44 ], Frey and McNeil [ 28 ], Yamai and Yoshiba [ 46 ], and Wagner [ 45 ]. CEIOPS [ 12 ] acknowledges the theoretical advantages of using the expected shortfall to calculate the SCR.…”

“…Instead, we exemplary analyze the effects on three main risk factors of the total SCR for a fictitious life annuity insurer if the solvency II SCR calibration is based on expected shortfall instead of value-at-risk. The use of expected shortfall for insurance stress testing is also suggested by CEIOPS [ 12 ], Sandström [ 40 ], and Wagner [ 45 ]. We hereby consider this hypothetical change in regulation for three major risk classes: equity risk, interest rate risk, and longevity risk.…”

How has Italian insurers' asset book value evolved from 1998 to 2012?

“…National and international regulations have attempted to control and monitor the many risks inherent in insurance business. Controls applied on the insurance market have focused in particular on relationships between risk and solvency, reflected in the Solvency project and its last update, Solvency II, now being completed (Wagner, 2014;Schumacher and Barnhill, 2011). This issue has been investigated from several viewpoints (Gryglewicz, 2011;Sherris, 2006;Butsic, 1994), dedicating particular attention to insurers' economic capital, i.e., Solvency Capital Requirements, and many observers have focused on evaluating insurers' balance sheets to verify compliance with the necessary capital requirements (Meyers, 2003;Mildenhall, 2002;Meyers and Read, 2001); the financial stability of insurers between different continents has also been verified (Siegel, 2013).…”

Solvency II Solvency Capital Requirement for Life Insurance Companies Based on Expected Shortfall

“…Historical simulations are used in the calibration of solvency II. Other authors that claim that the ES is more appropriate to determine capital buffers are Beder [10], Acerbi and Tasche 3, [44], Frey and McNeil [28], Yamai and Yoshiba [46], and Wagner [45]. CEIOPS [12] acknowledges the theoretical advantages of using the expected shortfall to calculate the SCR.…”

“…In the European Union, there are ongoing discussions about applying such a framework to all European pension funds as well [23]. For instance, see Doff [17], Eling et al [19], Sandström [40], Steffen [43], and Wagner [45] for an overview and critical discussion of the solvency II framework.…”