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International Regulatory Changes Actuarial Applications

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### International Regulatory ChangesActuarial Applications

### Conceivable actuarial approaches

By

Eric Lecoeur, FIA

SCOR, Group Chief Actuary

CAS 2005 Seminar on Reinsurance

Disclaimer

- The following presentation focuses on international regulatory changes in progress in the framework of IFRS phase II and Solvency II. It reflects opinions and interpretations of available material at May 2005. Positions and interpretations on any issue raised may subsequently change, according to the publication of official directives concerning certain accounting standards.
- This presentation creates no contractual relationship with SCOR.
- The participant has to be aware that, in making this presentation available, SCOR is not providing professional advice and accepts no liability arising from reliance upon this presentation.
- Any decision by a participant in this session or other readers of this presentation to rely on the opinions expressed here shall be at the participant’s own risk.

CAS 2005 Seminar on Reinsurance

Schedule

2002

2003

2004

2005

2006

IAS / IFRS

Exposure Draft for Phase I (31/07/03)

Final Phase I

Standards

IFRS 4 (31/03/04)

Phase I Balance Sheet (published at 31/12/05)

Final Phase II standard : 2007, 2008 ?

Phase II Financial Statements Published : 2009 ?

Solvency I

Müller Report in 1997

Solvency I project initiated

Solvency I

Completed

(inforce by 2004)

Directive of the European Parliament on reinsurance

Proposal for the directive (21/04/2004)

Proposal backed by the European Economic ans Social Committee

Enforcement ?

Solvency II

Sharma Report (2001) : project initiated

End of Phase I

(design of

the system)

Exposure Draft finalised for

Phase II : 2005-2006 ?

…

ICAS by FSA (UK)

CP 190 (non life) + CP 195 (life)

Integrated Prudential Sourcebook

FSA’s ICA review

CAS 2005 Seminar on Reinsurance

Content

- IAS / IFRS – Their impact on liability assessment
- Solvency II – Their impact on liability assessment
- Conceivable actuarial approaches

CAS 2005 Seminar on Reinsurance

Phase I : IAS 39 / IFRS 4

IAS / IFRS – Their impact on liability assessment

- IFRS 4 focuses on 3 points :
- Definition of an “insurance contract”
- Unbundling of deposit elements
- Separate embedded derivatives
- Enhanced disclosure
- sensitivity analyses
- risk management procedures
- Principle of “Fair Value”

IAS 39

CAS 2005 Seminar on Reinsurance

Phase I : Accounting policies

IAS / IFRS – Their impact on liability assessment

- PROHIBITED
- Catastrophe and equalization provisions
- Offsetting reinsurance assets against insurance liabilities
- MANDATED
- Liability adequacy testing

CAS 2005 Seminar on Reinsurance

Phase I : Accounting policies

IAS / IFRS – Their impact on liability assessment

- ALLOWED TO CONTINUE (but not implement)
- Undiscounted liability basis
- Deferred Acquisition Costs / Unearned Premium Reserve approach
- CAN BE IMPLEMENTED
- Use of market discount rates (if undiscounted liability is used)
- Use of shadow accounting (life insurance)

CAS 2005 Seminar on Reinsurance

Phase II – Actuarial consequences on reserving 1/3

IAS / IFRS – Their impact on liability assessment

- Catastrophe and equalization provisions are banned because they do not meet the criteria for liabilities
- Premiums and costs will no longer be smoothed over time (through deferred acquisition costs and unearned premium reserve)
- Liabilities measured at their “fair value” Interpretation : discounted anticipated value, at the closing date, of future cash flows

CAS 2005 Seminar on Reinsurance

Phase II – Actuarial consequences on reserving 2/3

IAS / IFRS – Their impact on liability assessment

- Use of discounting :
- The discount rate is likely to be the return on a risk-free asset
- Still some discussions about whether the credit quality should impact the liability recorded
- Comments on the Credit Standing of the issuer:
- From a strictly theoretical point of view, the fair value of a liability should recognize that there is some possibility of default reduction of the expected value of future cash flows and therefore the level of the liability
- Weaker insurers would reserve less than stronger players for the same liability …

CAS 2005 Seminar on Reinsurance

Phase II – Actuarial consequences on reserving 3/3

IAS / IFRS – Their impact on liability assessment

- A risk premium (Market Value Margin or MVM) must be taken into account because of the uncertainty of the liabilities
- Format of the Market Value Margin
- Adjusting the discount rate applied to expected cash flows …
- Incorporating a variability in loss reserve payment timing and then using a risk-free discount rate for the cash flows (it seems to have the preference of IASB)
- Comments on the Market Value Margin
- Making accounts more opaque (e.g. some capital may be hidden in the form of MVM) / An ability to be misused as a profit smoothing device
- Phase II is little developed. Some points are not yet solved, for instance the lack of diversification credit (the MVMs are likely to be additive between the pools or segments that they are calculated in)

CAS 2005 Seminar on Reinsurance

Solvency II

Assets

(market value)

Economic

net assets

Liabilities

(economic

Value)

IFRS versus Solvency IIIFRS Phase II

IAS

Fair Value

Present

Value of

Future

Cash flows

Market

Value Margin

CAS 2005 Seminar on Reinsurance

Objectives of Solvency II

SOLVENCY II – Its impact on liability assessment

- Global solvency approach
- Protect policyholders
- Provide comparability, transparency and coherency
- Enhanced risk sensitiveness
- Reflect market developments (derivatives, ALM …)
- Encourage internal risk management

CAS 2005 Seminar on Reinsurance

Organisation of Solvency II

Actuaries

IAA

Groupe Consultatif

« A global framework for

insurer solvency assessment »

(Jan. 2004)

IAIS

Solvency II

EC

CEIOPS / EIOPC

Basel II

IASB

EU States’ project

Australian

project

Canadian

project

US

project

Switzerland

APRA

OSFI

CIA

NAIC

SOA

Netherlands

CAS

«Australian capital requirements

for non-life insurers: Internal

model Based Method» (2002)

FSA

UK

CAS 2005 Seminar on Reinsurance

SOLVENCY II – Its impact on liability assessment

SOLVENCY II

Pillar I

Pillar II

Pillar III

Capital

requirements

Supervisory

Review process

Market transparency

Disclosure

A « three pillars » approach

CAS 2005 Seminar on Reinsurance

SOLVENCY II – Its impact on liability assessment

Spreads (Bonds)

Loans / Debtors

Reinsurers

Concentration

Model

Credit

Risk

Operational

Risk

Interest Rates

Economic Factors

Share Price

Catastrophes

Market

Risk

Insurance

Risk

FX

New Business

Volatility

Old Business

Liquidity

Concentration

Concentration

Model

Model

CAS 2005 Seminar on Reinsurance

SOLVENCY II – Its impact on liability assessment

Spreads (Bonds)

Loans / Debtors

Reinsurers

Concentration

Model

Credit

Risk

Operational

Risk

Interest Rates

Economic Factors

Share Price

Catastrophes

Market

Risk

Insurance

Risk

FX

New Business

Volatility

Old Business

Liquidity

Concentration

Concentration

Estimation of

the reserving risk

Model

Model

CAS 2005 Seminar on Reinsurance

Consequences on reserving

SOLVENCY II – Its impact on liability assessment

- Preservation of the equalization reserves (contrary to IFRS)
- Discount of the reserves with a risk-free rate corresponding to the average duration of the liabilities (coherent with IFRS approach)
- Necessary to replace deterministic approaches with stochastic one, in order to quantify the level of prudency. Different measures are proposed:
- the IFRS approach : best estimate + « market value margins »
- VaR / Tail-VaR
- Best-estimate loaded with a coefficient linked to the volatility of the LoB

CAS 2005 Seminar on Reinsurance

Consequences on reserving

SOLVENCY II – Its impact on liability assessment

VaR / Tail-VaR

The Value at Risk (VaR) is the alpha-% quantile of the ultimate losses’ distribution.

The Expected Shortfall (ES), or tail conditional expectation: expectation of the ultimate losses amount given that it exceeds the VaR.

ES(alpha) = E[ X | X > VaR(alpha) ]

CAS 2005 Seminar on Reinsurance

Review of regulations in Asia-Pacific

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

The Singaporean point of view

- According to the Insurance Act (Chapter 142), the valuation of insurance policy liabilities of each line of business must comprise:
- Best estimate of the premiums liabilities
- Best estimate of the claims liabilities
- Provision for adverse deviation that relates to the inherent uncertainty in the best estimate value of both the premium and claims liabilities at a minimum 75% confidence level.

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

The Australian point of view

- Extract of the Australian Prudential Standard GPS 210 :
- “Insurance liabilities include both the insurer’s Outstanding Claims Liabilities, and its Premiums Liabilities.”
- “The Approved Actuary must provide advice on the valuation of insurance liabilities at a given level of sufficiency – that level is 75% (or, in some circumstances, the central estimate plus one half of the coefficient of variation).”
- “Insurance liabilities are to be valued on a discounted basis. The rate to be used in discounting is the risk-free rate; i.e. the gross redemption yield of a portfolio of sovereign risk securities with a similar expected payment profile to the insurance liabilities”

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

The Australian point of view

- Claims liability
- “Stand alone” risk margins for the Net Outstanding Claims Liabilities for Primary Insurers
- “Stand alone” risk margins for the Net Outstanding Claims Liabilities for Inwards Reinsurance:
- - For proportional inwards reinsurance : same coefficients
- - for non-proportional inwards reinsurance : coefficient to be applied to direct risk margin (about 2)

Coefficients for the risk margin computation from the report of Bateup&Reed

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

The Australian point of view

- Premium liability
- “Stand alone” risk margins for the Net Premium Liability :
- The recommended multiples of the net outstanding claims liability risk margin to be applied for determining premium liability risk margins, are as follows :
- - 1.75 for short tail lines of business
- - 1.25 for long tail lines of business

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

The Australian point of view

- Diversification:
- “Rule of thumb”:
- Diversification discount = f (C, N, S)
- Where:
- C = coefficient of concentration = (Net insurance liability for largest LoB) / (Total net insurance liability)
- N = number of lines of business
- S = size of the insurer’s total insurance liabilities in $ million

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Risk Margin Estimation

Risk margin estimation under some classical underlying distribution assumptions :

Let X be the random variable “Ultimate Aggregate Loss” with average m (which is the best estimate) and standard deviation σ. What is the loading Lα to be applied to the best estimate to achieve a level of confidence of α percent?

Notation: we will name AlphaEst the new estimate.

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Risk Margin Estimation

Assumption of log-normality :

Let X follow a lognormal distribution with parameters μ and σ

The random variable Y defined as ln X follows a N(M,S), with :

Introducing the variation coefficient of X, , we have :

which leads to the loading

Note: under an assumption of normality, the loading is

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Bootstrapping the Chain Ladder (simplified)

Definitions

Assume that the data consist of a triangle of incremental claims:

The cumulative claims are defined by:

and the loss development factors (LDF) of the chain-ladder technique are denoted by :

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Bootstrapping the Chain Ladder (simplified)

- Obtain the standard chain-ladder development factors
- Obtain incremental fitted values by backwards recursion
- Calculate the unscaled Pearson residuals and the scale parameter Ф
- Resample with replacement the adjusted residuals
- Obtain pseudo data
- Use chain ladder and estimate future incremental payments

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Bootstrapping the Chain Ladder (simplified)

- Simulate future payments from process distribution assuming the mean is the incremental value obtained
- Repeat many times, storing the reserve estimates, giving a predictive distribution
- Prediction error (variability in the data and variability due to the estimation) is then standard deviation of results

Where SEbs(Ri) is the bootstrap standard error of the reserve estimate and p is the number of parameters estimated

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Improving bootstrapping

- Variability often changes across in triangle. The idea is to divide the triangle into “zones” for simulation.
- Use of correlations between LoBs
- use of rank correlations between the simulations of the triangles for each Line Of Business (see Kirschner, “Two approaches to calculating correlated reserve indications across multiple lines of business”)

ZONE 1

ZONE 2

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Mack’s model

The Mack’s model reproduces chain-ladder estimates. The model is distribution-free and only specifies the first two moments of the distribution.

The hypothesis are similar to those of the Chain Ladder method, with in addition that the variance of Dij is equal to

And consequently :

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Mack’s model

Under the assumption of independence between the accident years, the model provides estimators for λj (Loss Development Factors of the chain ladder method) and

For 1 ≤ j ≤ n – 2 :

The mean squared error of the estimated reserve Ri can be estimated by :

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Example

- In this example, we use the same data as Verrall (1990, 1991) and Mack (1993) :
- Run-off triangle (accumulated figures)

CAS 2005 Seminar on Reinsurance

Conceivable actuarial approaches

Example

- Bootstrapping the reserves allows to obtain the distribution (outputs from RESQ® of EMB) :

Cumulative distribution

Density function

CAS 2005 Seminar on Reinsurance

Selected references

- England P.D., Verrall R.J. (1999) : « Analytic Bootstrap estimates of prediction error in claims reserving » Insurance : Math. And Econ. Vol. 25, 281-293
- Mack T. (1993) : « Distribution free calculation of the standard error of Chain Ladder reserve estimates » Astin Bull. Vol. 23, 213-225
- Prudential Standard GPS 210 : « Liability Valuation for General Insurers » www.apra.gov.au
- FitchRatings (May 2004) : « Mind the GAAP: Fitch’s view on Insurance IFRS » www.fitchratings.com
- www.iasplus.com - Deloitte
- R. Bateup and I. Reed, (November 2001) : « Research and data analysis relevant to the development of standards and guidelines on Liability valuation for General Insurance »

CAS 2005 Seminar on Reinsurance

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