Videos marked with an (*) contain discussion of new content in ICRFS-Plus™ 12.

If for any reason you are unable to view the training or demonstration videos, please contact our support staff at **support@insureware.com** and we will arrange to send you a copy of the videos on CD-ROM. You will be able to run the videos from the CD.

The training videos should be used for __hands on__ training. We suggest you run the videos on a separate computer using a data projector, and train as a group.

The only way you will learn all the new concepts and be able to exploit all the immense benefits is by using the system. Experiential learning is imperative.

It is important that you study the videos in sequential order as set out below.

# Table of Contents

1. Introduction to ICRFS-Plus™ 12 and modelling modules

2. Modelling using the Link Ratio Techniques and Extended Link Ratio Family modelling framework

3. Introduction to the Probabilistic Trend Family modelling framework

4. Modelling real data (CTP) in the PTF modelling framework

5. TG CS5: heteroscedasticity and varying parameters

6. TG ABC: modelling wizard, simulations, and release of capital as profit

7. Importing of data from other applications and COM Automation

8. Further PTF Modelling Examples

11. Clusters and MPTF Concepts

12. Capital Management of long tail liabilities

- 13.1 Our solution for calculating the long-tail liability Solvency II risk measures for the one-year risk horizon
- 13.2 Solvency II risk measures for a real life example involving six LOBs
- 13.3 Comparison of TP+SCR with undiscounted BEL
- 13.4 Consistency of estimates of prior accident year ultimates and Solvency II metrics on updating (*)
- 13.5 5 SII and IFRS 4 metrics excluding fungibility across LOBs and calendar years going forward, relative to assuming fungibility
- 13.6 Distressed Samples driven by process volatility and parameter volatility
- 13.7 The Ultimate Year Risk Horizon
- 13.8 Solvency II and multiple distress years

14. Other applications of the MPTF modelling framework

15. The Bootstrap: how it shows the Mack method doesn't work

## 13. Solvency II one year and ultimate year risk horizons and IFRS 4 metrics including fungibility and ring fencing: SCR, Best Estimate of Liabilities (BEL), Technical Provisions (TP) (Fair Value of Liabilities), and Market Value Margins (MVM) (Risk Margins) for the aggregate of long-tail LOBs

In the following seven videos, we present a mathematically tractable solution to the Solvency II risk metrics for the one year risk horizon that is not recursive or circular. Our solution is based on relevant **Solvency II** directives and consultation papers.

The ultimate year risk horizon is quite straightforward and is described here.

In respect of IFRS 4 we also discuss and demonstrate fungibility and ring fencing between LOBs and along calendar years (going forward).

It is only in the Probabilistic Trend Family (PTF) and Multiple PTF (MPTF) modelling frameworks that parameter uncertainty and forecast assumptions going forward are explicit, auditable, and can be monitored in a sound probabilistic framework.

The first calendar year is in distress at the 99.5th percentile, that is 1 in 200 times. Accordingly, in order to compute Solvency II metrics, it would typically be necessary to conduct 20 million simulations of the unconditional distributions of the future calendar year liability streams for which approximately a subset of 100,000 sample paths are in distress. This subset of sample paths is used to compute the conditional distributions of the payment streams from the second year onwards conditional on the first year being in distress. As our proprietary algorithms can simulate correlated lognormals conditional on the sum of lognormals (being at 99.5%), we do not take this approach. Instead, we can run 100,000 simulations unconditionally, and another 100,000 conditional simulations - a significantly faster algorithm with no loss of accuracy.

Statistical and mathematical technicalities are treated in the *first video*.

The *second video* considers a real life example comprising six LOBs. Solvency II metrics are computed (assuming full fungibility across all LOBs) for the most volatile LOB and the aggregate of all LOBs to illustrate, amongst other things, risk diversification credit of SCR and Technical Provisions.

In the *third video* it is shown that for the aggregate of the six LOBs,

**Technical Provisions + SCR = Undiscounted Reserves** (total capital at inception),

assuming a risk free rate of 4% and a spread of 6%. **This is due to risk diversification credit of writing the six LOBs that are uncorrelated**.

This result is far from true for the most volatile LOB4, were it the only one written!

Each year, Solvency II metrics are recomputed. In the *fourth video*, we discuss conditions under which estimates of prior year ultimates and related solvency II metrics are statistically consistent on updating.

In the *fifth video* we compare SII and IFRS 4 metrics, namely, SCR, Risk Margins and Fair Value of Liabilities, not allowing for 'surpluses' (total calendar year loss less than the mean) in one LOB to pay for a high loss (greater than the mean) in another LOB. That is, the 'surplus' is ring fenced within the LOB, so that there is no fungibility.

Indeed, portfolios of LOBs can be set up so that there is complete fungibility across LOBs in the same portfolio, but no fungibility (surplus sharing) between LOBs in different portfolios. That is, each portfolio is ring fenced.

We also consider another option and that is fungibility along calendar years going forward. That is, if the total loss in a calendar year (2+) is less than the mean, then the surplus can be used to pay for losses in future calendar years that exceed the mean.

In the *sixth video* we look at distressed samples, that is samples for which the first calendar year is in "distress" at the 99.5 percentile, including a situation where we remove all process variability and only have parameter uncertainty (volatility).

The *seventh video* considers the SII Ultimate year risk horizon with all the possible scenarios in respect of ring fencing defined portfolios and along calendar years going forward.

# 13.1 Our solution for calculating the long-tail liability Solvency II risk measures for the one-year risk horizon

This video discusses Best Estimates of Liabilities (BEL), Market Value Margins (or Risk Margins), Technical Provisions (TP) (or Fair Value of Liabilities), and Solvency Capital Requirements (SCR). It is emphasized that calendar year loss distributions and their correlations are necessary to compute any solvency II risk measure.

Our solution to the one-year risk horizon is shown to arise directly out of relevant directives and consultation papers. Our solution is not recursive or circular contrary to other proposed solutions.

For the one-year risk horizon, risk capital is raised at the beginning of each year. The cost of raising the risk capital, the Market Value Margin (MVM) or premium on the risk capital, is paid to the capital providers at the end of each year along with any unused risk capital. The sum of the MVMs and the Best Estimate of Liabilities (BELs) for each calendar year is the Technical Provision (also referred to as Fair Value of Liabilities).

We show that based on the directives and definition of the first calendar year being in distress that SCR is given by the equation,

SCR = VaR(1) + ΔTP,

where VaR(1) is the VaR_{99.5%} for the first calendar year and ΔTP is the additional technical provisions for the subsequent years if the first year is in distress.

The SCR is required to cover the losses for the distressed year (VaR_{99.5%}) and to restore the Fair Value of Liabilities (Technical Provisions) of the balance sheet at the beginning of the second year. The ΔTP is allocated to each year as required to ensure that there is sufficient monies to meet the additional BEL and sufficient MVM to raise the risk capital in the event of the first (next) calendar year being a distressed year.

Powerpoint slides referenced in this video are available here.

# 13.2 Solvency II risk measures for a real life example involving six LOBs

The second video considers a real life example comprising six LOBs. Solvency II metrics are computed for the most volatile LOB and the aggregate of all LOBs to illustrate, amongst other things, risk diversification credit of SCR and Market Value Margins (a component of the Technical Provisions).

The most volatile LOB (LOB 4) possesses much process variability and a large degree of parameter uncertainty. The base development year trend is not negative until development year six. As a result of this, and a high calendar trend assumption going forward, it takes ten years before 50% of the total reserves are paid out. More importantly, the high correlations of the calendar year paid loss distributions have a large impact on the additional technical provisions required if the first (calendar) year is in distress, resulting in an SCR that is a high proportion of BEL.

By contrast, for the aggregate of the six LOBs, 50% of the total reserves are paid out in the next two years and the paid loss calendar year correlations are comparatively low. Furthermore, there is only significant (low) process correlation between two LOBs. Accordingly, there is significant diversification credit in respect of SCR and risk capital allocation by writing the six LOBs instead of just the single, most volatile LOB.

It is also important to point out that the most volatile LOB4 comprises only 11.2% of the total mean reserve across the six LOBs. Next year in distress is principally driven by the largest LOB3 which comprises 66% of the total mean reserve.

Indeed, if only the most volatile line was written, then the SCR as a percentage of BEL, is close to 100%! For the aggregate, however, the SCR as a percentage of BEL is only 11%.

Also see video chapter 13.3 for a comparison of total capital and undiscounted reserves.

# 13.3 Comparison of TP+SCR with undiscounted BEL- Risk diversification of SCR and MVM

In the third video it is shown that for the aggregate of the six LOBs,

**Technical Provisions + SCR = Undiscounted Reserves**,

assuming a risk free rate of 4% and a spread of 6%. This is due to risk diversification credit of writing the six LOBs that are uncorrelated.

This result is far from true for the most volatile LOB4, were it the only one written!

In practice, we conclude that Solvency II capital requirements are not expected to be a burden on insurers or reinsurers with good diversification between LOBs, even when highly volatile lines are written as part of their portfolio.

# 13.4 Consistency of estimates of prior accident year ultimates and Solvency II metrics on updating

It is first explained using a simulation example that calendar year trends project onto development years and accident years. Consequently, estimates of prior accident year ultimates and Solvency II risk measures are statistically consistent on updating only if assumptions going forward are consistent.

One does not want to be in a position where the distress situation in the next calendar year is due to model error distress rather than outcomes in the tail of the projected loss distributions.

A real life example is considered involving updating that illustrates the importance of explicit assumptions going forward and shows consistency of estimates of prior accident year ultimates and Solvency II metrics.

# 13.5 SII and IFRS 4 metrics excluding fungibility across LOBs and calendar years going forward, relative to assuming fungibility

In respect of IFRS 4 exposure draft Exposure Draft (2010), BC119 the level of aggregation of Risk Margins is considered in the context of degree of fungibility.

Ring fencing and fungibility are also discussed in QIS5, SCR11.

In this video we compare SII and IFRS 4 metrics, namely, SCR, Risk Margins and Fair Value of Liabilities, not allowing for 'surpluses' (total calendar year loss less than the mean) in one LOB to pay for a high loss (greater than the mean) in another LOB. That is, the 'surplus' is ring fenced within the LOB.

It turns out that for the specific example under consideration involving the six LOBs there is very little loss in diversification by ring fencing.

We also consider another option and that is fungibility along calendar years going forward. That is, if the total loss in a calendar year (2+) is less than the mean, then the surplus can be used to pay for losses in future calendar years that exceed the mean.

# 13.6 Distressed Samples driven by process volatility and parameter volatility

One of the conditions of Solvency II one-year risk horizon is that the metrics are all based on the first year (next calendar year) being in distress at the 99.5% percentile.

The next calendar year is in distress based on two (related) drivers, namely, process volatility, parameter volatility (uncertainty) or both.

In this video we study distressed samples, that is samples for which the first calendar year is in "distress" at the 99.5 percentile, including a situation where we remove all process volatility and only have parameter volatility (uncertainty).

# 13.7 The Ultimate Year Risk Horizon

The Solvency II regulatory Capital Requirements are based on the one-year risk horizon.

However, in respect of running the business the company may decide to consider the ultimate year risk horizon.

In this video we compute the SII and IFRS 4 metrics for the aggregate of the six LOBs considered in video chapters 13.2 and 13.3 for the ultimate year risk horizon and compare the metrics with those obtained for the one-year risk horizon. Naturally, the ultimate year risk horizon is much more onerous in respect of Risk Capital and Risk Margins than the one-year risk horizon.

Four possible scenarios for fungibility by LOB and calendar year are also considered.

# 13.8 Solvency II and multiple distress years

In this video we explore the ability of the ICRFS-Plus Solvency II module to take into account more than one future year in distress. This applies in cases where the Solvency II paradigm includes the consideration that future years will also need to be adjusted for the requirement of rebalancing after the following twelve months turns out to suffer losses at a distress level corresponding to the 99.5th percentile.

Solvency II output is compared for a sample dataset with 1, 2, 3 and 4 future years in distress. Changes are seen to occur only in the MVM, these changes are traced through the tables and explained.

For additional information on ICRFS-Plus™ features - click here.

Solvency II Capital requirements for each LOB and the aggregate of all LOBs are only met by ICRFS-Plus™ in a sound statistical framework.