## Best Estimate under Solvency II

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- Category: Poles of competences

Under Solvency II, important changes are proposed to the evaluation of technical provisions and the impact on reserving processes will be marked. While some of the approaches and techniques applied under Solvency II will be similar to those followed currently, there are other areas where significant changes will be required.

Insurer, will have to calculate technical provisions for each year-end and mid-year during the dry run process. The best estimate of technical provision calculation should allow various causes of uncertainty in the future cash flows, and for this reason, the company must be able to demonstrate: the robustness of the valuation process; the appropriateness of the level of technical provisions held; the applicability and relevance of the methods applied; and the adequacy of the underlying data used.

A managing agent is responsible for applying appropriate methods to calculate the technical provisions of each of its managed company, selecting from the continuum of methods available, taking into account the nature, scale and complexity of the risks. In mathematical terms, the nature of the risks underlying the insurance contracts could be described by the probability distribution of the future cash flows arising from the contracts.

###### Base on his experience, Brainmize can help you to choose the most appropriate method to increase the robustness of the assessment process, demonstrate that the assumptions used are appropriate, realistic and have been validated and reviewed, and the adequacy of statistical and financial data underlying used.

Article 101 of the Solvency II Directive states, "The Solvency Capital Requirement (SCR) shall correspond to the Value-at-Risk (VaR) of the basic own funds of an insurance or reinsurance undertaking subject to a confidence level of 99.5% over a one-year period."

Essentially, the basic own funds are defined as the excess of assets over liabilities, under specific valuation rules. So it seems straightforward to estimate the SCR using a simulation-based model: Simply create a simulated distribution of the basic own funds over a one-year period, then calculate the VaR at the 99.5th percentile. But the thousands of pages of requirements offer little implementation guidance when details matter.

A principal problem is the capital market-consistent value of insurance liabilities, which requires a best estimate (defined as the expected present value of future cash flows under Solvency II) plus a risk margin calculated using a cost-of-capital approach.

So to calculate the SCR using simulation-based internal capital models, an opening balance sheet is required using discounted expected liabilities with a risk margin, along with a simulated balance sheet on the same basis after one year. That one-year balance sheet requires the expected value of liabilities with a risk margin for each simulation, producing a distribution of expected values.

## Need of a stochastic Model

The method for calculation of best estimate shall correspond to the probability-weighted average of future cash flows taking account of the time value of money, using the relevant risk-free interest rate term structure.

This in effect acknowledges that the best estimate calculation shall allow for the uncertainty in the future cash-flows used for the calculation of the best estimate.

Technical provisions in respect of insurance liabilities will in the future be based on discounted best estimates of expected future cash flows, with assets and non-insurance liabilities included on a market consistent value. This comprises the economic balance sheet (EBS) against which the components are stressed to assess the SCR requirements.

Importantly, Solvency II requires an assessment of the balance sheet’s ability to withstand a 1-in-200-year event, so the EBS becomes the cornerstone of all Solvency II reporting.

When insurance or reinsurance undertakings use an economic scenario generator (ESG) for the stochastic modelling of the technical provisions, they should be able to demonstrate to the relevant supervisory authorities the accuracy, robustness and market consistency properties of the ESG. A measure of the accuracy of the ESG (at least a Monte Carlo error analysis) should be assessed.

## Our Advantage: Increase your robustness of the techniques and assumptions

Our actuary team are expert to make an internal model proper to the company, to generate the best estimate of technical provision using stochastic method behind chain ladder or Mack’s model for example. The idea is to define:

- Which method for taking account of inflation best reflects the exposure (e.g. eliminating past inflation from data and projecting future inflation)
- What effect does monitoring of reserves have on methodology and underlying assumptions (e.g. subsequent reserving behavior, especially for business with long run off periods)?
- How can large and catastrophe losses be assessed (e.g. analyses of individual losses or scenarios)?
- What effect does large losses have on the projection of the run off triangles (elimination of large and catastrophe losses from data)?

The values of these options should be taken into account in the value of the technical provisions.

Otherwise, the financial leverage would be underestimates and thus the overall insolvency risk underestimated as well when assessing the sensitivity of the value of these options should of course also be taken into account.