04 March 2010

Published in: Capital - models, Insurance risk, Regulation - supervision

How Solvency II impacts risk calibration

For those companies interested in developing a partial or full internal model, a proper understanding of article 101 and its consequences for model architecture and calibration-related issues is crucial, explain Marc Beckers and Jürgen Wielandts

Most UK companies that have been reporting their individual capital assessments (ICAs) over the past few years are confronted with the changes Solvency II brings in the way it defines regulatory capital. Actuaries are puzzled by the one-year risk concept, and existing internal models need to be adjusted to bring them in line with the directive. Meanwhile, managers fear a theoretical framework that is not in line with the way they have been running their businesses long before Solvency II was spotted on Google.

But is Solvency II actually that different and confusing from standard business practices?

Decomposing article 101

The fair value balance sheet is one of the cornerstones of Solvency II, and its impact is not restricted only to the calculation of fair value assets and liabilities. The concept of market value margin (MVM), and the related one-year risk approach in the calculation of the solvency capital requirement (SCR), find their origin in this fair value driven approach: re/insurance companies should have enough capital on their balance sheet to cover the risks that can emerge over a 12-month timeframe, and allow for a (theoretical) transfer of all (contractual) liabilities at the end of this balance-sheet period. This means that companies have to be able to calculate the impact of such shocks on their end-of-year balance sheets, and value these in such a way that they can be transferred to a third party.

Article 101 of the Solvency II directive defines the calculation of the SCR and is written in a very concise way, but when one begins to distil the various concepts introduced, it appears to be far more challenging than at first glance. Certainly, for those companies interested in developing a partial or full internal model, a proper understanding of article 101 and its consequences on model architecture and calibration-related issues is crucial. If one reads carefully, one can separate:

• The "shock" period - this is the period over which a shock is applied to a risk. In article 101 this is defined as one year. Therefore, only shocks or risks that can occur over the preceding 12 months need to be considered, whether these are shocks that affect the investments (e.g. a change in credit defaults) or shocks that affect the liabilities (e.g. a windstorm).
• The "effect horizon" - the period over which the shock that is applied to a risk will impact the company's balance sheet. For instance, should a change in legislation become effective during the shock period, this will have a consequence on future claim payments and will impact the valuation of the liabilities. In this case, the effect horizon is the ultimate time horizon of the policy obligations.
  
  Likewise, a change in dividend yield will not only have an impact on the dividend expected for the coming 12 months, but will also impact future dividends and hence the valuation of the asset. In article 101, this definition is included in the valuation of the basic own funds, which are defined as the excess of fair-value assets over fair-value liabilities.
• The "exposure basis" - this is the exposure that one needs to take into account when applying the shock. In article 101, this is defined as the existing in-force liabilities at the opening balance sheet, plus the expected exposure from new business written over the subsequent12 months. In most cases, the exposure basis will include exposure beyond the shock period. This particular exposure does not need to be shocked any more but the possible impact from the shock occurring during the 12-month period needs to be included in the revaluation of the net assets.
• A "risk profile" - this is the distribution function from which the required capital will be derived. In article 101 this is defined as the basic own funds. In an internal model it will therefore be crucial to calculate the movement of the basic own funds over a period of 12 months, allowing for a proper valuation at the end of this 12-month period, in line with the exposure the company is expecting to write.
• A "risk measure" - this is the statistical risk measurement applied on the risk profile. This has been set to the value-at-risk approach (VaR).
• The "risk tolerance level" - 99.5%

Impact on internal model kernel

When reading the directive, it would seem that generating an internal model that models excess of assets over liabilities is straightforward, but as soon as one gets into the details, one realizes that, among the 80 consultation papers (CPs) published so far by the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS), there is very little guidance on how the requirements can actually be achieved.

A proper understanding of all these elements can make a major difference in the resulting SCR and the way the internal model can be used within the company to define a risk-limit structure and to assist in capital-related issues that management is facing.

The whole idea to focus on a balance-sheet perspective was probably welcomed by those with an accounting background, and it will also facilitate discussions between valuation-related aspects of Solvency II and future international financial reporting standard (IFRS). For most actuaries, however, this approach, and the consequences it brings in terms of calibration of risks, has come as a surprise and is still creating confusion.

Historically, actuaries have calculated premium and reserve-related risks from an ultimate perspective, considering all the shocks that might occur over the lifetime of the liabilities. Now that the regulatory regime becomes truly risk sensitive and their work becomes more important, does this approach suddenly become less appropriate?

Risk takers tend to calculate risks not only up to the end of the first year, but until the full development of risks. This is normal since the price should cover the full risk period, not only the first 12 months. The MVM is the glue that combines both visions, but this tends to be so technical that many people lose themselves in over-complicated calculation processes.

Is there actually so much difference between this one-year and ultimate approach? This really depends from which angle you look at the problem. Capital requirements calculated from a one-year risk approach will in most cases be lower than when calculated on an ultimate perspective. However, when one looks at the problem from a calculation point of view, the approach taken between a one-year or ultimate basis does not necessarily need to be that different.

The AISAM-ACME study on non-life long-tail liabilities in October 2007 raised the alarm that only a few members were aware of the inconsistency that existed between their assessment on an ultimate basis and the Solvency II one-year approach. Since then a number of algorithms have been described in actuarial literature to calculate risks from a one-year perspective. This seems to give the impression that ultimate and one-year are two different approaches. A much more logical approach is to calculate the risks to ultimate and then introduce a second process: how much of the risk (=deviation from the expected value) can be realistically measured over the first 12 months, over the first 24 months, etc., until, at ultimate, all the risk can be measured.

This second process is called the emergence of risk process. Take for example a reinsurer writing long-tail business. The change in the view of the expected ultimate cost of claims over one year could be negligible, but the actual ultimate cost of claims after all liabilities have been extinguished could be very different from the opening view. In this case, the SCR covers the risks emerging during the first 12 months and the implications these might have on the end-of- year valuation, but the MVM covers the risks associated with the settling of liabilities beyond this 12-month period. Or, to be even more precise, the SCR covers the capital required to cushion the risk for the first 12 months, whereas the MVM covers the cost to attract capital to cushion the risk beyond the 12-month period.

The above table shows the various ultimate loss ratio calculations (measured at different positions in time) per development period for a reinsurer who writes non-proportional business. When considering only the risk that emerges over the first 12 months, the loss-ratio seems to be quite stable across the various accounting years. This probably finds its reason in the fact that not much information is available, and most is based on estimates. Only through the development, information becomes available and the true ultimate loss-ratio (and its movement over time) becomes visible.

As an example the (premium risk) standard deviation suggested in CP75 (method 1) was calculated based on the observed ultimate loss-ratio in its first year of development (13.97%) and based on the last known ultimate loss-ratio (19.51%). Clearly the risk that emerges over the first 12 months is much lower than when considered from an ultimate perspective. The example clearly demonstrates the importance of the various definitions introduced by the fair value concept, not only on the calculation of the SCR but also on the MVM. Needless to say, proper MVM calculation will be important for those companies writing long-tail re/insurance.

Risk emergence patterns

Using risk emergence patterns to bridge the link between one-year and ultimate is probably welcomed not only by actuaries but also by management. Actuaries do not have to change their traditional way of working. In order to come up with one-year risk parameters for reserve or premium calculation they can remain working on an ultimate basis, but an additional process will need to be added to derive appropriate parameter inputs for a Solvency II-type calculation. In their expression of the risk appetite, management might not only be interested in covering the capital for the one-year period, but might also be interested in the level of capital required to cover the full run-off.

The above example shows the emergence of risk at the end of various 12-month periods, each showing the position of the ultimate view of loss given a certain "state of the world".

Impact on calibration

The Solvency II framework has been established to protect policyholders, and the one-year SCR + MVM approach is an appropriate way of doing so. Companies should be aware, however, that calculating SCR based on an ultimate perspective will lead to a much higher than required capital requirement that provides greater policyholder protection than the regulator is aiming for. Calibration of insurance risk on a total balance sheet approach itself is a quite challenging exercise - certainly in the case where one tries to cover all aspects of the technical insurance both on a gross and net level:

• Premium modelling: large loss, attritional loss, nat-cat loss, man-made cat;
• Reserve modelling: large loss, attritional;
• Counterparty default modelling.

The one-year approach and the implications it has on the calibration process creates an additional requirement. But certainly from a use-test perspective, it is much better to re-use existing processes (which mostly deal with ultimate calculations) and append these to introduce the one-year risk approach. The aspects of risk emergence are not restricted to reserve risk only (as is currently discussed in most actuarial literature) but also have important implications on attritional and large loss premium risk modeling, certainly because the emergence of reserving risk between these different capabilities needs to be undertaken on a consistent basis. The icing on the cake is deriving a proper net-of-reinsurance position of the SCR where a clear link with all ultimate calculations is still auditable.

The impact that reinsurance has on the risk profile of a company will therefore need to be reconsidered since it will have an effect on multiple levels:

• The SCR - this will be the effect that will be most visible in future Solvency II related capital calculations;
• MVM - reinsurance can protect the business for the full run-off of the claim, and hence will also have an impact on the MVM calculation;
• ORSA (own risk and solvency assessment) - management should not only look at the capital required to cover the first 12 months but assume a going-concern point of view. In the end, besides some small examples, the insurer tends to take the risk on its balance sheet until it is settled.

Marc Beckers is head of Aon Benfield Analytics Europe, Middle East and Africa, and Jürgen Wielandts is a senior actuary at Aon Benfield

 

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