Economic Capital and Solvency II

For further information click here to view our flyer on Economic Capital. (Approx 1.5MB)

 

ICRFS-Plus™, a long tail liability Enterprise Risk Management system, is simply the key to a new innovative paradigm for measuring and managing long tail liability risks in a unique integrated relational database. Data input, updating, monitoring and testing the adequacy of claims provisions, and reporting are all done within one integrated system. Communication with other software or other databases can be automated using COM scripts.

Solvency II aims to establish a solvency regime that is better matched to the true risks of  an insurance company. Knowing the probability distributions of reserves for the long-tail lines of business and their inter relationships is crucial to better management of risk and capital.

More information on Solvency 2 can be found at
http://www.fsa.gov.uk/pages/About/What/International/solvency/index.shtml,
http://ec.europa.eu/internal_market/insurance/solvency_en.htm and
http://www.hm-treasury.gov.uk/Documents/Financial_Services/eu_financial_services/fin_eufs_solvency.cfm.

The ICRFS-Plus™ relational database facilitates the understanding of the significant long tail liability risks of the enterprise in a quantifiable and integrated manner. It is effortless to navigate the database so that each actuary has access to the same information with just a few mouse clicks. 

The relational database can contain any classification variables designed by the user, such as line of business, territory, currency, profit centre, etc.

Models are designed, built or identified, from the data (using a modelling Wizard), that represent the true volatility in the lines of business and their inter relationships. Models are validated to ensure that assumptions carried by the models are supported by the data. For each line of business and the aggregate of all lines, a (saved) composite (integrated) model gives forecast probability distributions by accident period, calendar period and aggregate. Capital allocation by line of business is also computed (using a covariance formula). Models for individual lines of business are designed in the PTF modelling framework and for the composite of multiple lines of business the composite model is designed in the MPTF modelling framework.

The composite model includes the two different types of correlations between any two long tail lines of business.

All risk measures required for Economic Capital determination are driven by the volatility in the data and can be obtained from Value-at-Risk tables and percentiles in the PALD module or from the simulated values (of aggregates) that can be exported into any other application effortlessly, including seamless communication with a COM enabled software such as Excel.

There are also applications to pricing future underwriting years, designing optimal outgoing and incoming reinsurance both retrospective and prospective and credibility modelling.

Please view the online demonstration videos.

Solvency II & Economic Capital - you need ICRFS-Plus™

• Key requirements of Solvency II are the management of all the inter-related long tail liability risks, calculation of liability distributions, correlations between lines of business and transparency.

• ICRFS-Plus™ is the only Enterprise Risk Management system for long tail liabilities in the world that satisfies these key requirements within a sound statistical framework.

• Standard Actuarial Techniques (link ratios or any derivative) are incapable of meeting this requirement.

Solvency II - liability distributions

In the paper Solvency II: a new framework for prudential regulation of insurance in the EU the requirements for reserving are given as a margin above the best estimate (where the best estimate is the mean or expected value of the liability distribution).

The principle that valuation of insurance liabilities should be based on the best estimate is widely accepted. The European Commissions initial proposal is that the valuation should be the best estimate plus a margin and Member States have endorsed this.
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The key point to be noted is the liability distribution.

Benefits of using ICRFS-Plus™

ICRFS-Plus™ provides sound statistical modelling frameworks for forecasting the reserve distributions of individual lines of business and their aggregates. The distributions include both process variability and parameter uncertainty. The aggregate distribution incorporates the two types of correlations (parameter and process) between Lines of Business. Models are transparent and assumptions are explicit. Each model is represented by four graphs that are easily interpretable.

The distributions are based on probabilistic models that describe the volatility in the past data. Assumptions for the future are explicit and can be related to past experience. Additional benefits are percentiles and Value@Risk tables for each Line of Business and for the aggregate.

The PTF modelling framework is used to design, build, or identify a model for a Line of Business that describes the trend structure and volatility about the trends in the Paid Losses. The MPTF modelling framework is used to design a model for the aggregate of Lines of Business that also describes the two types of correlations (parameter and process) between the lines.

For PTF, the PALD module calculates the underlying liability distribution by accident period, calendar period, and aggregate. The PALD module in MPTF calculates the underlying distribution for the aggregate of the Lines of Business - also by accident period, calendar period, and aggregate. A quantile (percentile) summary is also provided detailing the Value@Risk for a given provision (eg the mean of the liability distribution).

What is a liability distribution?

There seems to be a lot of confusion in the industry on what a liability distribution is. Much of this confusion is generated by an unsound paradigm for calculating loss reserves.

A liability distribution is the probability distribution of the possible outcomes of the liability (loss reserve). It is not the distribution of the best estimate. The distribution of the best estimate has a smaller variance than the (estimated) liability distribution as it does not include process variance (see the paper on Variability and Uncertainty).

The only sound way of estimating the liability distribution is from the volatility in the past Paid Losses. A good model describes the volatility in the past paid losses and forecasts that volatility into the future using explicit, easily interpretable assumptions. The estimated liability distribution includes both process variability and parameter uncertainty.

The aggregate liability distribution for a number of Lines of Business also includes parameter and process correlations that are computed from the data. The latter two correlations induce correlations in the aggregate reserve (liability) distributions between accident periods, calendar periods, and aggregates for each Line.

Deficiency of standard actuarial techniques

Standard actuarial techniques based on link ratios (and any derivatives thereof) do not provide an estimate of the reserve distribution - they only produce a 'point estimate'. In any case, this point estimate is often wrong and misleading.

Standard actuarial techniques cannot capture the volatility in real data. This has been demonstrated extensively in many technical papers.

Moreover, fitting a distribution to a set of answers based on different methods is similarly incorrect. Volatility based on different methods has nothing to do with the volatility in the data and accordingly nothing to do with distribution of the liability (reserve).

Standard actuarial techniques cannot meet Solvency II requirements.