Liabilities, Technical Provisions, Sufficiency Analysis and Security Margins Use of Statistical Models on the Supervisory Process of Non-Life Claims Provisions

Liabilities, Technical Provisions,

Sufficiency Analysis and Security Margins

Use of Statistical Models

on the Supervisory Process of

Non-Life Claims Provisions

Instituto de Seguros de Portugal

27/04/2006

ASSAL XVII Annual MeetingASSAL XVII Annual Meeting

Agenda

Non-Life Technical Provisions

ISP Supervisory Process Ratio Analysis Statistical Approaches Examples

Solvency II – expected future developments Best Estimate Risk Margin



Claims Provisions

Coverage of outstanding liabilities arising from past claims, reported and unreported, including claims management expenses

Premium Provisions

Coverage of liabilities arising from future claims, for policies in-force at the valuation date




0%

25%

50%

75%

100%

Accident &Health

Fire & Otherdamages

Motor Maritime andTransports

Aircraft Goods in Transit General Liability Miscellaneous TOTAL

Portuguese Market 2004

Other

Math. Prov.

Claims Prov.

Prem. Prov.


Ideally, technical provisions should correspond to the amount of discounted liabilities arising from insurance contracts

However, value of liabilities is unknown today and it can only be estimated A single point estimate is not enough Increasingly, liabilities are estimated using assumptions

of probability distributions for risk factors and stochastic properties

Due to estimation uncertainty, security margins are needed to ensure that technical provisions are sufficient enough to ensure the run-off of liabilities or their transferability at a high confidence level


ISP Supervisory Process

• ISP pays particular attention to the responsible actuary’s critical analysis of the technical provisions’ estimates

• Several ratios are computed and analysed

• ISP runs various statistical methods (deterministic and stochastic) to estimate the expected value and variability of non-life claims provisions

• A detailed technical and practical manual is available to ISP supervision staff as a guidance for the analysis of claims provisioning (off-site and on-site analysis)


ISP Supervisory ProcessRatio Analysis

• Ratios and indicators considered on ISP analysis of non-life claims provisions:

Growth on Premiums Average Premium Loss Ratio Average Cost of New Claims Average Claims Provision Claims Frequency Development of Claims Payments “Speed” of Process closure Re-openings Claims Expenses Provisioning, including IBNR Readjustments

• Ratios are calculated individually and compared on a static and evolutionary perspective with peer group and market benchmarks


ISP Supervisory ProcessStatistical Approaches

• The statistical methods’ objective is to project the expected future claims experience, using assumptions based on past data analysis complemented with expert opinion

• The analysis should consist of:

Analysis of results (particularly the estimation error), taking into account the theoretical assumptions underlying each model

Analysis of relevant graphs and hypothesis tests to assess each models’ fitness



• Format of a Run-off triangle representing accident year x development year• Run-off triangles may refer to:

Number of claims Claims paid (common approach) Claims incurred, i.e. Claims paid + Claims provision

• Aim is to estimate the lower unknown triangle (shaded):


0 1 2 3 4 5 6 7 8 > 81997 45.591 17.534 5.430 4.700 3.486 2.821 3.590 2.728 2.003 1.3581998 48.639 20.062 5.460 3.988 3.655 4.556 2.390 2.7401999 50.007 28.797 7.722 6.474 5.269 4.859 4.0742000 53.871 30.759 7.750 5.121 4.205 5.7252001 55.158 29.658 8.802 5.297 5.1892002 49.106 30.203 7.369 7.2502003 51.372 28.112 7.5012004 53.832 27.4922005 50.825 (m.u.: thousand euros)

Acc

iden

t yea

r

Development year


• Deterministic methods

Projection of past claims experience assuming fixed development factors

Provides point estimates of the expected future claims amounts Various actuarial techniques are available

• Stochastic models

Random nature of variables is considered Generally speaking, the future claims amounts are assumed to

follow a specified probability distribution Allows for the measurement of the estimates variability,

essential for the construction of confidence intervals for the estimates

Various actuarial models are available


Statistical ApproachesStatistical Methods available at ISP

• ISP has in-house built programs that allow for the automatic testing of the following statistical methods:

• Some of the methods consider: Possibility for inflation correction Variant approaches based on different assumptions Advanced refinements to include reparameterization and

expert opinion


Deterministic Stochastic

Grossing Up Thomas Mack Model

Link Ratio Generalised Linear Models:

Chain-Ladder Over-dispersed Poisson

Taylor Gamma

Loss Ratio Inverse Gaussian

Bornhuetter-Ferguson Loglinear Model (Kremer)

Stress TestingBootstrap simulation

(VaR and Tail VaR

calculations)

Statistical ApproachesExample

• Results from running the programs for the previous run-off triangle:


Provision held

Best Estimate

Estim. Error

Estim. Error (%)

BE Sufficiency

BE Sufficiency

(%)

Suffic. Probab. Normal

Suffic. Probab.

Lognormal

DETERMINISTIC

Grossing Up - Average 198.594 183.294 15.300 8%

Link Ratio - Average 198.594 183.760 14.834 8%

Grossing Up - Weighted 198.594 183.294 15.300 8%

Link Ratio - Weighted 198.594 183.760 14.834 8%

Chain Ladder - no inflation 198.594 184.319 14.275 8%

Chain Ladder - w / inflation 198.594 184.624 13.970 8%

STOCHASTIC

Mack's Model 198.594 184.319 8.644 5% 14.275 8% 95% 95%

ODP 198.594 184.319 13.121 7% 14.275 8% 86% 86%

ODP - Bootstrap 198.594 184.319 13.751 7% 14.275 8% 85% 85%

Gamma 198.594 188.328 12.367 7% 10.266 5% 80% 80%

Gamma - Bootstrap 198.594 188.328 12.415 7% 10.266 5% 80% 80%

Inv. Gauss. 198.594 189.225 28.180 15% 9.368 5% 63% 66%

Inv. Gauss. - Bootstrap 198.594 189.225 28.699 15% 9.368 5% 63% 65%

Loglinear 198.594 191.399 12.850 7% 7.195 4% 71% 72%

Loglinear - Bootstrap 198.594 191.399 12.917 7% 7.195 4% 71% 72%

m.u.: thousand euros

Statistical ApproachesExample (cont.)

• Simulated empirical distribution of the total claims provision using Bootstrap ODP stochastic model:


0

50

100

150

200

250

300

350

137.597

140.458

143.319

146.180

149.041

151.902

154.763

157.624

160.485

163.346

166.207

169.069

171.930

174.791

177.652

180.513

183.374

186.235

189.096

191.957

194.818

197.679

200.541

203.402

206.263

209.124

211.985

214.846

217.707

220.568

223.429

226.290

229.151

232.013


• Goodness-of-fit tests for the Analytic ODP stochastic model:


Test: Significance of model parametersParâm. Estim. EP % W X^2(1) Decisão P-value

M 10,62361766 0,048932988 0,46% 47134,76939 3,841455338 Par. Não Nulo 0,00%A1998 0,063261536 0,063706426 100,70% 0,98608188 3,841455338 Par. Nulo 32,07%A1999 0,253050203 0,061666529 24,37% 16,83892524 3,841455338 Par. Não Nulo 0,00%A2000 0,291874246 0,061832402 21,18% 22,28226398 3,841455338 Par. Não Nulo 0,00%A2001 0,309298151 0,062455212 20,19% 24,52546637 3,841455338 Par. Não Nulo 0,00%A2002 0,254721372 0,064085587 25,16% 15,79828854 3,841455338 Par. Não Nulo 0,01%A2003 0,241283213 0,065434972 27,12% 13,59672679 3,841455338 Par. Não Nulo 0,02%A2004 0,262774653 0,066738007 25,40% 15,50316883 3,841455338 Par. Não Nulo 0,01%A2005 0,212529774 0,077018058 36,24% 7,614728641 3,841455338 Par. Não Nulo 0,58%

B1 -0,65074148 0,03587058 5,51% 329,1093138 3,841455338 Par. Não Nulo 0,00%B2 -1,956979381 0,063860539 3,26% 939,09028 3,841455338 Par. Não Nulo 0,00%B3 -2,218541598 0,077551497 3,50% 818,3795636 3,841455338 Par. Não Nulo 0,00%B4 -2,434593748 0,09410069 3,87% 669,3717645 3,841455338 Par. Não Nulo 0,00%B5 -2,373562924 0,10359585 4,36% 524,9486045 3,841455338 Par. Não Nulo 0,00%B6 -2,617893165 0,137099385 5,24% 364,6135692 3,841455338 Par. Não Nulo 0,00%B7 -2,74215242 0,184910402 6,74% 219,9178577 3,841455338 Par. Não Nulo 0,00%B8 -3,021378097 0,303590867 10,05% 99,04504351 3,841455338 Par. Não Nulo 0,00%B9 -3,410210981 0,367195751 10,77% 86,25160822 3,841455338 Par. Não Nulo 0,00%

Nív. Sig.: 5,00%

Test: Trends on residuals per development year

-3,0000

-2,0000

-1,0000

0,0000

1,0000

2,0000

3,0000

0 1 2 3 4 5 6 7 8 >

Test: Assumption of normality of residualsy = 1,038x - 0,007

R2 = 0,9774

-3

-2

-1

0

1

2

3

-2,5 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5



Solvency II – Expected Future Developments

Harmonisation of technical provisions across the European Union: Rules for the valuation of the Best Estimate and Risk

Margin Rules for inclusion of diversification benefits Reporting tools Supervisory techniques for sufficiency and adequacy

assessment Main objective is to embed a risk management culture

within the companies, across all functions


Solvency II: Technical Provisions

Can be decomposed on 2 components: Best Estimate

o Corresponds to the expected value of liabilities, i.e. the average of the corresponding probability distribution

Risk or Security Margino An additional cushion that takes into

account the volatility and uncertainty of liabilities

o Aimed at ensuring that provisions are enough to run-off or transfer liabilities with a high level of confidence


Best Estimate

Risk Margin

Solvency II: Best Estimate

Calculation per homogeneous risk group Based on realistic actuarial and economical assumptions,

i.e. expected values of risk factors Should incorporate all the factors with impact on the

amount, timing or probability of cash flows: Inflation Reinsurance Recoveries ...

Should be based on more than past experience: expert opinion is crucial

Allowance for future expected developments and trends Regular review of assumptions


Solvency II: Risk Margin

Main factors that can affect the volatility and uncertainty of the estimated liabilities: Statistically ‘normal’ market volatility Characteristics (riskiness) of the insurance

portfolio held by the company, including concentration

Quantity and quality of the data used for the estimation process

Estimation model and parameter errors



2 main approaches are on discussion: Percentile approach

o Underlying philosophy is to ensure that provisions are enough to run-off the liabilities with an x% probability confidence level

o Risk margin corresponds to the difference between a specified x% quantile of the loss probability distribution and the best estimate

o Implicitly, Value-at-Risk is the risk measure used. Variant approaches can consider other risk measures, such as TailVaR.



0 0,5 1 1,5 2 2,5 3

BEST ESTIMATE (AVERAGE)

VaR 75%

TVaR 75%

Motor – estimated BE+RM Claims Provision


0%

20%

40%

60%

80%

100%

12345678910111213141516171819Size of portfolio


RM

BE

Motor – estimated BE+RM Premium Provision


0%

20%

40%

60%

80%

100%

12345678910111213141516171819Size of portfolio


RM

BE


Cost-of-Capitalo Underlying philosophy is to ensure that liabilities can be

transferred to a willing, rational, diversified counterparty in an arms’ length transaction under normal business conditions

o Risk margin corresponds to Market Value Margin, based on the cost of future regulatory capital required for on-going business

o MVM corresponds to the amount that a rational investor would demand in excess of the best estimate to take over the liabilities

o Technical provisions correspond to the fair value of liabilities, i.e. are, conceptually, fully market consistent


Source: CRO Forum


Documents

Liabilities, Technical Provisions, Sufficiency Analysis and Security Margins Use of Statistical Models on the Supervisory Process of Non-Life Claims Provisions