june 6-7, 2005 cas 2005 seminar on reinsurance 1 international regulatory changes actuarial...

June 6-7, 2005

CAS 2005 Seminar on Reinsurance1

International Regulatory Changes

Actuarial Applications

By

Eric Lecoeur, FIA

SCOR, Group Chief Actuary

June 6-7, 2005


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.

June 6-7, 2005


Schedule2002 2003 2004 2005 2006

Solvency I

Müller Report in 1997Solvency 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

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

IAS / IFRS

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 ?

…

June 6-7, 2005


Content

IAS / IFRS – Their impact on liability assessment

Solvency II – Their impact on liability assessment

Conceivable actuarial approaches

June 6-7, 2005


IAS / IFRS

Their impact on liability assessment

June 6-7, 2005


Phase I : IAS 39 / IFRS 4

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


June 6-7, 2005


Phase I : Accounting policies

PROHIBITED

Catastrophe and equalization provisions

Offsetting reinsurance assets against insurance liabilities

MANDATED

Liability adequacy testing


June 6-7, 2005


Phase I : Accounting policies

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)


June 6-7, 2005


Phase II – Actuarial consequences on reserving 1/3

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


June 6-7, 2005



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 …


June 6-7, 2005



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)


June 6-7, 2005


IFRS versus Solvency II

Assets (market value)

IFRS / Solvency II

Liabilities(economic

Value)

Economicnet assets

Solvency II

IAS Fair Value

IFRS Phase II

MarketValue Margin

Present Value ofFuture

Cash flows

June 6-7, 2005


Solvency II

Their impact on liability assessment

June 6-7, 2005


Objectives of Solvency II

Global solvency approach

Protect policyholders

Provide comparability, transparency and coherency

Enhanced risk sensitiveness

Reflect market developments (derivatives, ALM …)

Encourage internal risk management

SOLVENCY II – Its impact on liability assessment

June 6-7, 2005


Organisation of Solvency II

Solvency IIEC

CEIOPS / EIOPC

Actuaries IAA Groupe Consultatif

Canadianproject

EU States’ project

Basel II

IAIS

IASB

USproject

Australianproject

APRA CIAOSFI

CAS

SOANAIC

« A global framework for insurer solvency assessment »

(Jan. 2004)

«Australian capital requirements for non-life insurers: Internal model Based Method» (2002)

Switzerland

Netherlands

UKFSA

June 6-7, 2005


A « three pillars » approach

Cap

ital

req

uir

emen

ts

Su

per

viso

ryR

evie

w p

roce

ss

Mar

ket

tran

spar

ency

Dis

clo

sure

Pillar I Pillar II Pillar III

SOLVENCY II


June 6-7, 2005


Distribution of results over 3 years

-100 000

-80 000

-60 000

-40 000

-20 000

0

20 000

40 000

SOLVENCY II – Its impact on liability assessmentFinal output

June 6-7, 2005


Spreads (Bonds)

MarketRisk

Insurance Risk

Credit Risk

Operational Risk

Share Price

Interest Rates

FX

Volatility

Liquidity

Concentration

Model

Economic Factors

Catastrophes

New Business

Old Business

Concentration

Model

Loans / Debtors

Reinsurers

Model

Concentration


June 6-7, 2005


Spreads (Bonds)

MarketRisk

Insurance Risk

Credit Risk

Operational Risk Economic Factors

Catastrophes

New Business

Old Business

Concentration

Model

Loans / Debtors

Reinsurers

Model

Concentration

Share Price

Interest Rates

FX

Volatility

Liquidity

Concentration

Model


Estimation of the reserving risk

June 6-7, 2005


Consequences on reserving

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


June 6-7, 2005


Consequences on reserving


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) ]

June 6-7, 2005



Review of regulations in Asia-Pacific

June 6-7, 2005



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.

The Singaporean point of view

June 6-7, 2005



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”

The Australian point of view

June 6-7, 2005



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)

Net Central EstimateOSC Liability

$M

DomMotor

FireWorkers's

CompLiability

100 6,70% 8,50% 12,70% 12,70%200 6,00% 7,70% 11,60% 11,60%400 5,50% 7,20% 11,00% 11,00%


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

June 6-7, 2005



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


June 6-7, 2005



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


June 6-7, 2005


Conceivable actuarial approachesRisk 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.

June 6-7, 2005


Conceivable actuarial approachesRisk 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

22

2

ln

M

2

22

ln

S

V

2

1ln

1

2

V

eAlphaEst

Vq

11 2

1ln 2

V

eL

Vq

qL

June 6-7, 2005


Conceivable actuarial approachesBootstrapping 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 :

niinjCij

,...,1;1,...,1:

j

kikijCD

1

njj

,...,2:

June 6-7, 2005



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

ij

ijij

ijm

mCr

ˆ

ˆ

ijm

June 6-7, 2005



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

22ˆ)ˆ(ibsiiiiRSE

pn

nRRRERMSEP

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

June 6-7, 2005


Conceivable actuarial approachesImproving 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

June 6-7, 2005


Conceivable actuarial approachesMack’s model

1,

2

jijD

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

11,1,1

,...,/ jjijiiij

DDDDE

And consequently : 1ˆ...ˆˆ111, nininii

DR

June 6-7, 2005


Conceivable actuarial approachesMack’s model

For 1 ≤ j ≤ n – 2 :

jn

iij

jn

iji

j

D

D

1

11,

jn

ij

ij

ji

ijj D

DD

jn 1

2

1,2 ˆ1

1ˆ

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

1

1

1

2

2

2 1ˆ1

ˆˆˆ)ˆ(

n

ink

kn

jjk

ikk

k

ini

DDDRMSEP

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

2

j

June 6-7, 2005


In this example, we use the same data as Verrall (1990, 1991) and Mack (1993) :

Run-off triangle (accumulated figures)

Conceivable actuarial approachesExample

1 357 848 1 124 788 1 735 330 2 218 270 2 745 596 3 319 994 3 466 336 3 606 286 3 833 515 3 901 4632 352 118 1 236 139 2 170 033 3 353 322 3 799 067 4 120 063 4 647 867 4 914 039 5 339 0853 290 507 1 292 306 2 218 525 3 235 179 3 985 995 4 132 918 4 628 910 4 909 3154 310 608 1 418 858 2 195 047 3 757 447 4 029 929 4 381 982 4 588 2685 443 160 1 136 350 2 128 333 2 897 821 3 402 672 3 873 3116 396 132 1 333 217 2 180 715 2 985 752 3 691 7127 440 832 1 288 463 2 419 861 3 483 1308 359 480 1 421 128 2 864 4989 376 686 1 363 294

10 344 014

i 1iD

2iD

3iD

4iD

5iD

6iD

7iD

8iD

9iD

10iD

June 6-7, 2005


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


Cumulative distribution Density function

June 6-7, 2005



June 6-7, 2005



Errors of estimates:

UW Year

LatestChain

Ladder Reserve

Bootstrap Expected Reserve

Bootstrap Prediction

Error

Bootstrap Prediction

Error %

Mack Prediction

Error

Mack Prediction

Error %1 3 901 463 0 0 - - - -2 5 339 085 94 634 102 213 111 681 109,3% 75 535 79,8%3 4 909 315 469 511 478 701 215 602 45,0% 121 699 25,9%4 4 588 268 709 638 719 393 264 943 36,8% 133 549 18,8%5 3 873 311 984 889 994 458 306 094 30,8% 261 406 26,5%6 3 691 712 1 419 459 1 428 925 377 476 26,4% 411 010 29,0%7 3 483 130 2 177 641 2 204 586 500 640 22,7% 558 317 25,6%8 2 864 498 3 920 301 3 950 402 803 243 20,3% 875 328 22,3%9 1 363 294 4 278 972 4 319 336 1 080 170 25,0% 971 258 22,7%

10 344 014 4 625 811 4 689 217 2 073 770 44,2% 1 363 155 29,5%Total 34 358 090 18 680 856 18 887 230 3 036 167 16,1% 2 447 095 13,1%

June 6-7, 2005


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 »

http://www.iasplus.com/



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