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Concurrent Session: Update on a Global Risk Based Capital Standard

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Solvency II in Europe and Internal Risk ModellingN. Savelli - nino.savelli@unicatt.itCatholic University of Milan Member IAA Solvency Sub-Committee

Concurrent Session:

”Update on a Global Risk Based

Capital Standard”

Agenda

- The new Solvency Regimes adopted by some European Supervisory Authorities
- Solvency II Project: the state-of-art
- Some Results of capital requirements by a Risk-Theory Simulation Model
- Final comments

Solvency II in Europe and IRM

The new Solvency Regimes adopted by some European Supervisory Authorities

Solvency II in Europe and IRM

The FSA approach

- Financial Services Authority (FSA) – UK:

ECR (Enhanced Capital Requirement): is calculated using a standardized formula with different charges (in %) on assets (for asset risk), on liabilities (for reserving risk) and on premiums (for pure underwriting risk).

ICA (Individual Capital Assessment): Insurers are additionally required to develop their own view on their capital requirements using simple Stress & Scenario testing or Internal Models.

Time horizon = 1 year confidence level = 99.5% .

These ICA results are submitted and discussed with regulator, and an individual capital requirement then is agreed.

These tests are currently “soft”. They should become “hard” in the near future.

Solvency II in Europe and IRM

The FSA Approach: the structure of ECR

Total Capital Requirement (TCR) = AC + RC + UC

- AC = Asset charge = by applying factors to various categories of assets (Form 13 – FSA Returns) where more risky assets are attracting higher factors. Further, they include credit risks such as reinsurance recoverables.
- RC = Reserve charge = by applying factors to the net of reinsurance reserves for each class of business (for a total of 24 classes of business: 8 LoB for each of direct&facultative, proportional treaty and non-proportional treaty). Reserves include outstanding claims, IBNR, unearned premium reserve (undiscounted and excluding equalisation reserves)
- UC = Underwriting charge = by applying factors to the net premium for each class of business (the same 24 classes of business are used as for Reserve Charge).

Solvency II in Europe and IRM

8 Lines of Business:

- Accident & Health, - Motor - Aviation - Marine

- Transport - Property - Liability - Miscellaneous

& Pecuniary loss

- 3 different reinsurance covers:

Direct & Facult. / Proportional Treaty / Non-Proportional Treaty

- 8 overall sets of risk factors:

Timescale:

T=1 and T=5 years

Probability Capital Requirement to be insufficient:

1/40=2.5% 1/100=1% 1/200=0.5% 1/500=0.2%

- Data available: for all major UK insurers and for many of the smaller insurers (Lloyd’s not included) 1985-2001fin. years.

Solvency II in Europe and IRM

Optimised RISK FACTORS based on

ALL INSURERS

(T=1 year and PoF=1%)

Asset Factors

- Debt securities approved2.8%

- Land & Buildings: 6.1%

- Equities: insurance dependents0%

- Equities: group&non-ins. dependents6.1%

- Equities: other12.8%

Reserve Factors

Property:

8.0% 10.5% 10.5% (Dir./Prop./Non-Prop.)

Liability:

12.1% 12.1% 12.1% (Dir./Prop./Non-Prop.)

Underwriting Factors

Property:

8.6% 19.1% 45.3% (Dir./Prop./Non-Prop.)

Liability:

12.4% 12.4% 12.4% (Dir./Prop./Non-Prop.)

Optimised RISK FACTORS based on

ALL INSURERS

(T=1 year and PoF=0.5%)

Asset Factors

- Debt securities approved3.4%

- Land & Buildings:7.4%

- Equities: insurance dependents0%

- Equities: group&non-ins. dependents: 7.4%

- Equities: other15.5%

Reserve Factors

Property:

9.7% 12.1% 12.1% (Dir./Prop./Non-Prop)

Liability:

14.2% 14.2% 14.2% (Dir./Prop./Non-Prop)

Underwriting Factors

Property:

10.2% 23.1% 53.6% (Dir./Prop./Non-Prop)

Liability:

13.9% 13.9% 13,9% (Dir./Prop./Non-Prop)

Solvency II in Europe and IRM

The above results have been optimised using All Insurers in the market (a larger weight is placed on the larger insurers)

- Then in order to fit the factors to smaller Insurers, the optimisation has been also based on:

- All Insurers except the largest 10

- All Insurers with net premium in 2001 below 10 million (GBP)

- Higher measures are clearly obtained forsmaller Insurers (e.g. small Insurers often show a greater degree of volatility than large insurers)
- For T=1and PoF = 0.5% the results show a capital requirement equal to 50-60% of net premiums.

For T=1and PoF = 1,0% the results show a capital requirement equal to 40-50% of net premiums.

Total Capital Requirements implied by

each of the three optimisation methods

Solvency II in Europe and IRM

The PV approach

- Pensioen Verzekeringskamer (PV) – Netherlands:

Financial Assessment Framework (it will be gradually implemented until 2008)

This system consists of 2 tests:

- FIRST TEST: reported liabilities > actual value of liabilities

where “actual” liabilities = PV expected cash flow + risk margin. Furthermore, insurers are required to extend this test to show that in 1-year time, with 99.5% confidence level:

actual value of resources > actual value of liabilities

(assuming no new business)

- SECOND TEST (continuity test): it concerns long-term survival of the insurer. It is performed over a 3-5 years time horizon and new business and proposed policy are considered.

For both tests, a choice of methods is available, ranging from simplified versions with input by regulators to internal Models.

Solvency II in Europe and IRM

The SFOPI approach

- Swiss Federal Office of Private Insurance (SFOPI) – Switzerland:

Swiss Solvency Test (currently under consultation but due for implementation in 2006)

Insurers are required to show that they hold sufficient capital to the extent that in an unlikely negative scenario (e.g. 1%), assets and liabilities can be transferred to a third party.

The regulator will provide a standard model for insurance, market and credit risk, which insurers can deviate from previous authorization of the regulator.

Alternatively, insurers can use internal models, if they can prove that their model reflects risks more appropriately.

Assets and liabilities must be reported at their market-consistent value.

Solvency II in Europe and IRM

Solvency II Project:

the state-of-art

(Pillar I Non-Life Working Group:

Solvency II – Issues paper, February 2005)

Solvency II in Europe and IRM

The Solvency II structure

Who is involved in Solvency II project:

- Insurance Commission (IC): European Commission’s regulatory and legislative policy body ultimately responsible for drafting the new directives. IC members are appointed from the insurance supervisory authorities of the 25 member states;
- Committee of European Insurance and Occupational Pension Supervisors (CEIOPS): advisory body within the European Commission who advices the IC on technical aspects of Solvency II. It is composed by high-level representatives of the (insurance and pension) EU supervisory authorities

Timetable:

- by December 2005: it is expected a proposal for framework directive key principles
- by December 2009: measures implementation.

Solvency II in Europe and IRM

Pillar I:it focuses on quantitative aspects of solvency, mainly calculating the capital requirement (MCR and SCR)

- Pillar II:it is mainly concerned with qualitative measures regarding the Supervisory review
- Pillar III: concerns disclosure requirements. The aim is to reinforce market discipline and risk-based supervision (Note: many European insurers are not listed and then at the moment are not subject to a very high degree of public disclosure).

Solvency II in Europe and IRM

Risks and Capital Measures under Pillar I

- In Pillar I are contained all the components of the “Insurance Risk” that can be measured quantitatively:

- underwriting risk (pricing risk and reserving risk)

- market risk

- credit risk,

- liquidity risk

- operational risk

- Total Balance-Sheet approach: target capital and technical provisions to be covered by high quality assets

Solvency II in Europe and IRM

Two capital measures likely to be introduced:

- MCR(Minimum Capital Requirement)

- SCR(Solvency Capital Requirement or Target Capital)

andan Early Warning indicator(set above SCR and calibrated over a longer time horizon, likely to be used for supervisory intervention level)

- The EU Insurance Commission would like to keep a simple formula forMCR as it is now for Solvency I (roughly the maximum between 16%-18% of net premiums and 23-26% of net claims amount). It should include an absolute floor expressed in euros.

Solvency II in Europe and IRM

A capital below MCR represents an unacceptable risk for policyholders and then immediate supervisory action is required

- Alternative options for determining MCR are:

- extending present Solvency I formula to capture

asset risks;

- using SCR as a reference;

- establishing a simple risk margin over and above

liabilities

Solvency II in Europe and IRM

As to SCR, it should reflect the level of capital that an insurer would need to operate with a “rather” low probability of failure for a fixed time horizon. In principle it should be calculated on a going-concern basis.

- This low level has not yet been defined, but at the moment the low probability might be 0.5% for 1 yeartime span.
- The Risk Measure has not yet been defined, but VaR or TVaR are good candidates (the choice will be likely linked to the desired safety level and the actual capital ratios of the market).

On this matter, IAA has suggested TVaR as a more appropriate risk measure for insurers.

Solvency II in Europe and IRM

Standard Formula vs Internal Model for calculating SCR

- The approach for calculating SCR:

- Standard Formula: it should be technically feasible for all firms, but clearly no standard formula would be able to capture the complete risk profile of the company.

Two main methodologies:

a) Factor-Based Capital Models

b) Scenario-Based Approaches.

They could be combined in the SCR standard formula.

- Internal Model: likely Solvency II will allow partial modelsinitially (FSA and PV allow the use of internal models for their own new solvency regime, and SFOPI permits its use as approved alternative tool only).

Solvency II in Europe and IRM

Standard Formula

- Factor-Based Approach: formulaic relationship between risk measures and capital requirements. The parameters in any formula can be either identical for all firms or tailored to reflect individual aspects, or a combination. The RBC in US and the Swiss Solvency Test adopt a personalised factor-based model.
- Criticism:

- weak ability to capture interaction of risks

- opacity

- lack of dynamism

- low predictive power

Solvency II in Europe and IRM

Scenario-Based Approach:

- it can be used to analyse the impact of adverse scenarios on the firm, defined for each category of risk (underwriting, market, credit, etc. …).

- Static or Dynamic scenarios (in the latter case, the assumption of management’s inertia is relaxed).

- Scenarios may be used to model extreme events where the factor-based approach may fail because these events may be either absent from the data or may have to be smoothed out in the calibration process;
- e.g. in the SST a separate treatment for catastrophic underwriting risk is made by scenarios capturing the impact of extreme events.

Solvency II in Europe and IRM

In principle, a third approach might be the Probabilistic Approach (usually via Monte Carlo simulation), but it requires intensive use of data and computing power and therefore it is not useful for a standard formula.

Solvency II in Europe and IRM

Internal Model

- Internal Models : they can be used to represent the business of an individual firm much more closely than the standard formula, with capital requirements more significantly aligned to the effective risk of the company.
- Internal Model could also be used as an effective risk management tool within the firm, and then it would be desirable to encourage firms to move from the standard formula to internal models through capital or other incentives.
- Internal models may also be a relevant tool for the capital requirements at the group level.

Solvency II in Europe and IRM

Firms would only seek approval of internal models if they lead to a reduction in capital requirements compared with the standard formula

- The model’s approval process will require considerable effort and expertise from the supervisor
- Internal Models can be highly sensitive to the underlying assumptions and parameters: sensitivity testing as part of the validation process needed
- Cherry-picking risk: firms should not have the option of switching back to the standard formula simply because this leads to a minor capital requirement

Solvency II in Europe and IRM

Potentially, internal models might be used only for some risks (or for the main lines of business) whilst the standardised formula is used for the remaining (e.g. operational risk, where less data are available)

- Anyhow, partial use of internal models would be a temporary solution (to avoid cherry-picking again)

Solvency II in Europe and IRM

Some Results from a

Risk-Theory Simulation Model

see paper byRytgaard & Savelli

”Risk-Based Capital requirements for property and liability insurers according to different reinsurance strategies and the effect on profitability”,

(presented at XXXV ASTIN Colloquium 2004 in Bergen)

Solvency II in Europe and IRM

General framework of the model

- Company: General Insurance
- Lines of Business:Casualty and Property (separately)
- Time Horizon:T=3 years
- Total Claim amount:Compound Mixed Poisson Process
- Number of Claims:Neg. Binomial distrib.for non-CAT claims

Poisson distrib. for CAT claims

- Claim Size:LogNormal distrib. for non-CAT claims

Pareto distrib. for CAT claims

- Dynamic Ins. Portfolio: Volume of premiums increases annually according to real growth and claim inflation
- Reinsurance strategy:Traditional Quota Share, Surplus, XL (and CAT XL only for Property)
- Investment Return:Stochastic (AR model), only 1 asset category
- Monte Carlo approach:400.000 simulations
- Risks not considered:Reserving, CreditandOperational Risks

Solvency II in Europe and IRM

Ut = Risk Reserve at the end of year t

Bt = Gross premiums in year t

Xt = Aggregate claims amount

Et = Actual total expenses of year t

BRE= Premiums ceded to reinsurers

XRE = Claims amount recovered by reins

CRE= Reinsurance Commissions

j = Investment return (annual rate)

LR = Loss Reserve amount

TXt = Taxation amount

DVt = Dividends of the year

The Risk-Reserve process (Ut)Solvency II in Europe and IRM

Total Claims Amount (Xt)

- kl,t= non-CAT Claim Number of year t (for the line l)

is assumed to be Negative Binomialdistributed (i.e. Poisson distribution with a stochastic parameter n*q, where q is a multiplicative random structure variable with mean 1 and distributed as a Gamma(h,h) - only short-term fluctuations and no systematic changes are assumed).

The expected number of claims is increasing with the real rate of growth: nt=n0*(1+g)t

- kCAT,t= CAT Claim Number of year t (affecting only property lines) is assumed to be Poissondistributed. The Poisson parameter is kept constantover the chosen time horizon

non-CAT claims

CAT claims

(for Property only)

Solvency II in Europe and IRM

Zl,k,t= non-CAT claim Size for the k-th non-CAT claim of year t (for the line l):

is assumed to be LogNormaldistributed, with values increasing annually according to the deterministic claim inflation (i) only.

- Wk,t= CAT claim Size for the k-th CAT claim of year t (affecting only property lines):

is assumed to be Paretodistributed, with values increasing every year according to the joint (deterministic) effect of real growth (g) and claim inflation (i) rates.

Solvency II in Europe and IRM

For each line, non-CAT claim size random variables Z are here assumed to be i.i.d.;

- In case of a CAT claim, the CAT claim sizes affecting each line are clearly not independent
- Here random variables Xt are assumed time independent. In reality, however, long-term cycles are present and therefore auto-correlation might be significant (especially for medium/long-term analyses).

Solvency II in Europe and IRM

General assumptions

- Real growth rate (g): 5% (for every line)
- Claims inflation rate (i):
- Liability 5%
- Property 2%
- Loss reserve ratio (LR/B):
- Liability 120%
- Property 30%
- Expenses loading coefficient (c): 25%
- Risk loading coefficient (λ):Motor Liability: λ = 2.1 %

Commercial Liability: λ =14.7 %

Property (Homeowners, Agriculture, Commercial): λ = 17.5 %

(having fixed b=35%)

- Investment return process (j): expected rate 4% and std 2%(approx.)
- Taxation flat rate (tx): 35% gross profit of the year
- Dividends flat rate (div): 20% net profit of the year

Solvency II in Europe and IRM

Liability multi-line insurer (most relevant input parameters)

NOTE: Parameters as Var(q), E(Z) and CV(Z) are derived from the IAA-SWP Report (2004)

Solvency II in Europe and IRM

Property Multi-line Insurer(most relevant input parameters)

Solvency II in Europe and IRM

Simulation steps

- Start simulations with u0=0
- Calculate risk measure rbc for a time horizon T=1,2,3 (gross and net of reinsurance)
- Useu0=rbc(TVaR; 99%,T=1) as initial capital ratio
- Compute expected RoE

Solvency II in Europe and IRM

Alternative Reinsurance Strategies

At the moment we consider the only reinsurance strategies available on the market, which are:

Liability Multil. Insurer

- Noreinsurance
- Q/S 10% with commission 25% (cRE=c)

Property Multil. Insurer

- No reinsurance
- Q/S 40% with commission 27% (cRE=c+2%) andCat XL protecting retention

Solvency II in Europe and IRM

Results of 400.000 simulationsNo reinsurance (Strategy 1)

Solvency II in Europe and IRM

Results of 400.000 simulationsWith reinsurance (Strategy 2)

Solvency II in Europe and IRM

Alternative Reinsurance Strategies(Liability Multiline Insurer)

Now we assume that the following reinsurance strategies are available on the market:

- Noreinsurance
- Q/S 10% with commission 25% (cRE=c)
- Q/S 20% with commission 25% (cRE=c)
- Unlim. xs 730.000 @ 7.57%

Solvency II in Europe and IRM

Alternative Reinsurance Strategies(Property Multiline Insurer)

- No reinsurance
- Q/S40% with commission 27% (cRE=c+2%) and Cat XL protecting retention
- Surplus treaty after € 300.000 (i.e. retention = 100% for househ., 75% for agric. and 25% for comm.) with commission 26% (cRE=c+1%) and Cat XL protecting retention. This coverage corresponds approx. to cede the same amount of premiums as QS 40%.
- RiskXL € 840.000 xs 360.000 @ 7.51% and Cat XL protecting retention
- Cat XLonly (XL 369,9 mill xs 14,1 mill - RoL 6.27%)

Solvency II in Europe and IRM

rbc(TVaR 99%)according to different retentionsT = 1 year

Strategy 1

Strategy 1

o

o

o

Strategy 2

Strategy 2

Solvency II in Europe and IRM

Liability Multi-line insurer – Results (400.000 simul.)

Solvency II in Europe and IRM

Property Multi-line insurer - Results (400.000 simul.)

Solvency II in Europe and IRM

Final Comments

- Prominent role of Internal Modelling in the future
- Quantitative Tools are strongly necessary for this task (with special reference to extreme events and dependencies)
- Nowadays the minimum EU solvency ratio for a P&C Insurers is roughly 16-20% of net premiums, and the results of many studies show how the minimum capital ratio should be significantly increased (at least 35-40% of premiums)
- Attention must be paid to excessive capital requirements with undesirable effects on a higher cost of capital for the insurance market

Solvency II in Europe and IRM

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