Economic Capital and Solvency II
Solvency II aims to establish a solvency regime that is better matched to the true risks of an insurance company.
ICRFS-Plus™ is the only Enterprise Risk Management system in the world that affords the user the unique benefit of designing models that reflect the true risks in the company's long tail LOBs. It is also extremely efficient, flexible and innovative in supporting Solvency II Requirements and Economic Capital determination.
The 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 remainder of the current page covers the following topics related to Solvency II Capital Requirements (SCR) in respect of the aggregate of all long tail LOBs and each long tail LOB.
- Solvency Capital Requirement (SCR), Technical Provisions, Market Value Margins, and Cost of Capital based on one year and ultimate year risk horizons and VaRs or T-VaRs. See details below and here.
- Excess risk capital if the first (next) calendar year is in distress. See details below and here.
- Variation in ultimates (conditional on next calendar years' paid losses). See details below and here - this page is related to the paper of François Morin of Towers Perrin and this is discussed in further detail.
The identification (design) of a single composite model for all long tail LOBs that succinctly describes the volatility of each LOB and their correlations is a necessary requirement of Solvency Capital. The single composite model possesses easily interpretable parameters. The forecast probability distributions for accident year reserves and calendar year liability streams by LOB and the aggregate of all LOBs are based on explicit, transparent, auditable assumptions.
The probability distributions of calendar year liability streams and their correlations are required to compute SCR one year horizon and SCR ultimate horizon.
According to a PDF article on the CEIOPS web site the "best estimate" is a mean of a (derived) probability distribution of future paid losses.
"In particular, this Article requires that:
[...] the best estimate shall be equal to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure."
Ann Hagen of PWC in the article Solvency II: Brave new world also argues for "projected payment patterns".
"Doing the job
Under Solvency II, the way that work is carried out will change.
For example, Solvency II is likely to require different actuarial techniques from the ones currently used. Technical provisions will be estimated as a probability-weighted average of expected future cash flows, taking into account the time-value of money and including a risk margin. Many
of us are estimating claims reserves using traditional deterministic actuarial techniques, primarily relying on incurred claims data. Under Solvency II, not only will we need to discount these reserve estimates, requiring projected payment patterns, we will also need to demonstrate a deep
understanding of the uncertainty of those reserves. We will additionally be required to apply the same approach to evaluating unexpired risk liabilities currently allowed for in the unearned premium reserves."
An accurate assessment of the probability distributions can only be obtained by modelling the incremental paid losses in the Probabilistic Trend Family (PTF) modelling framework. It is calendar year trends jointly with development year trends that are the important determinants of liability streams. That calendar year trends project onto development years and accident years is as axiomatic as 2+3=5. See, amongst numerous other references on this web site, the paper "Best Estimate for Reserves" that is on the CAS Syllabus of examinations.
The Multiple Probabilistic Trend Family (MPTF) modelling framework facilitates the design of a single composite model for multiple LOBs.
The distribution of the liability, alternatively future paid losses is not the same as the distribution of the mean.
A liability distribution is the probability distribution of the possible outcomes of the liability (loss reserve) or future paid losses. 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. An identified PTF 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 variance and parameter uncertainty.
The aggregate liability distribution for a number of LOBs 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 years, and aggregates for each LOB.
The table below shows the calendar year liability stream's means, standard deviations and CVs of their probability distributions for the aggregate of multiple lines (15 in this case), along with the corresponding table for a particular line (B ReA).
All risk measures required for Economic Capital determination are driven by the volatility in the data and can be obtained from (Tail) Value@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 COM enabled software such as Excel. Note that some articles in the literature refer to VaR as economic capital.
Solvency II Risk Capital (SCR), One Year and Ultimate Year Risk Horizons, Technical Provisions, Market Value Margin (MVM) and Cost of Capital (CoC) approach
A detailed treatment of Technical Provisions (TP) and MVMs for Solvency Capital Requirement (SCR), incorporating the concepts of Fair Value and Cost of Capital can be found by clicking on the link below. In particular, we show the differences between one-year risk horizon and ultimate year risk horizon. Solvency II mandates a one-year risk horizon at the 99.5% level.
ICRFS-Plus™ Excel Macros can be downloaded from the one-year and ultimate year risk horizon pages. These macros enable ICRFS-Plus™ users to apply these calculations to their own single composite models for multiple LOBs (and associated forecast scenarios).
For a discussion of SCR, Technical Provisions, MVM and Cost of Capital for one year risk horizon and ultimate risk horizon click here.
Excess Risk Capital requirement conditional on the first calendar year being in distress
The basic idea for this calculation is to examine the impact on future calendar years' paid losses (reserves) means, given that the first (next) calendar year falls into a distress percentile - e.g.: 99.5%. The mean (total) losses are computed for calendar years subsequent to the first one, given that the first calendar year is in distress.
The Excess Risk Capital (ERC) represents the risk capital requirement for the first calendar year in distress plus the excess mean capital above the (unconditional) mean for subsequent calendar years. That is, the first calendar year's contribution to ERC is VaR (or T-VaR) and the subsequent years contributions are the additional mean reserves (conditional on the first calendar year being in distress). This calculation is heavily dependent on parameter uncertainty relative to process variability. In the absence of parameter uncertainty ERC is the same VaR(1), the VaR for the first calendar year.
This is discussed in further detail here.
Variation in Ultimates and Solvency II
In the presentation, "Integrating Reserve Risk Models into Economic Capital Models" by François Morin of Towers Perrin, the Solvency II one-year risk horizon is measured as the sample variance of the difference between estimates of ultimates today and one year from now. Morin provides several methods of calculating the variance of the change in estimate.
We discuss François Morin's approach for computing the variation in estimates of ultimates here and compare with our analytical approach that is formulated in a sound consistent probabilistic framework. Moreover, our approach also applies to the aggregate of multiple LOBs.
For further information...
Click here to view our flyer on Economic Capital. (Approx 1.5MB)
To view a demonstration video on Capital Management of all long tail liabilities click here.
Please view the online demonstration videos to appreciate the full capability of ICRFS-Plus™.
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.
