Abstract
AbstractIn this paper, four variants of calculating the Solvency Capital Requirement for long-tail liabilities satisfying Solvency II regulations are discussed. The merits of each metric are related to the stated objectives of Solvency II. Assumptions made in the calculations are assessed for suitability for the determination of an appropriate level of Solvency Capital. We show that two methods for calculating Solvency Capital provide insufficient capital to restore the Economic Balance Sheet in the event of distress. The standard formula referencing the Claims Development Result is shown to be too conservative when models are correctly specified.
Highlights
Solvency II regulation (European Commission, 2007, 2009b) specifies an insurer should be able to withstand a 1 in 200 years loss and still have sufficient capital for risk to be fairly transferred to a third party
The fourth example is a proxy for Solvency II Capital Requirement (SCR) given in the standard formula (European Commission, 2010, SCR.10.54.) based on the concept of the Claims Development Result (CDR) (Merz & Wüthrich, 2008; England, 2011)
As an insurer must be able to withstand a 1 in 200 year loss and still have sufficient capital for risk to be fairly transferred to a third party (European Commission, 2007, 2009b), it follows that the Best Estimate of Liabilities (BEL) and risk margin (RM), collectively known as the Technical Provisions (TPs), are the cornerstone of the Solvency II 1-year risk horizon
Summary
Solvency II regulation (European Commission, 2007, 2009b) specifies an insurer should be able to withstand a 1 in 200 years loss and still have sufficient capital for risk to be fairly transferred to a third party. The fourth example is a proxy for SCR given in the standard formula (European Commission, 2010, SCR.10.54.) based on the concept of the Claims Development Result (CDR) (Merz & Wüthrich, 2008; England, 2011). This treatment is intended to bring the crucial issues to the fore. Should the distributional assumptions be known, the 99.5th percentile of the variation in mean ultimate (VMU) is far too conservative a measure of risk capital and does not properly allow for risk diversification between the calendar years. The four measures of the SCR are related to each other and compared using a few examples
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