1. Use of Statistical Models on the Supervisory Process of
ASSAL XVII Annual Meeting
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

2. ASSAL 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

3. ASSAL XVII Annual Meeting Non-Life Technical Provisions
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

4. ASSAL XVII Annual Meeting Non-Life Technical Provisions

5. ASSAL XVII Annual Meeting Non-Life Technical Provisions
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

6. ASSAL XVII Annual Meeting 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)

7. ASSAL XVII Annual Meeting ISP Supervisory Process
Ratio 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
1- Growth on Premiums = Written Premiums (n) / Written Premiums (n-1)
2- Average Premium = Earned Premiums / Average nr. of insured cars
Average nr. of insured cars = [ nr. of insured cars (n) + nr. of insured cars (n-1) ] / 2
3- Loss Ratio = Incurred Claims / Earned Premiums
4- Average Cost of New Claims = Incurred Claims (estimated on accident year) / Nr. Claims (incurred and reported at accident year)
5- Average Claims Provision = Claims Provision / Nr. of Claims outstanding
6- Claims Frequency = Nr. Claims incurred / Average nr. of insured cars
7- Development of Claims Payments = Paid amounts / Incurred Claims
8- “Speed” of Process closure = Nr. of claims incurred and closed at year / Nr. of claims incurred at year
9- Re-openings = Nr. of claims reopened at year / Nr. of claims closed at year
10- Claims Expenses = Claims Management Costs / Net Paid Amounts
11.1- Claims Provision / Earned Premiums
11.2- Claims Provision / Incurred Claims
11.3- Claims Provision / Paid Claims
11.4- Incurred Claims / Earned Premiums
12. Readjustments = Provision (n) + Paid Claims (n) – Provision (n-1)

8. ASSAL XVII Annual Meeting
ISP Supervisory Process
Statistical 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

9. ASSAL XVII Annual Meeting
ISP Supervisory Process
Statistical Approaches
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):

10. ASSAL XVII Annual Meeting
ISP Supervisory Process
Statistical Approaches
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

11. ASSAL XVII Annual Meeting
Statistical Approaches
Statistical 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

12. ASSAL XVII Annual Meeting Statistical Approaches
Example
Results from running the programs for the previous run-off triangle:

13. ASSAL XVII Annual Meeting Statistical Approaches
Example (cont.)
Simulated empirical distribution of the total claims provision using Bootstrap ODP stochastic model:

14. ASSAL XVII Annual Meeting Statistical Approaches
Example (cont.)
Goodness-of-fit tests for the Analytic ODP stochastic model:

15. ASSAL XVII Annual Meeting Statistical Approaches
Example (cont.)

16. ASSAL XVII Annual Meeting 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

17. ASSAL XVII Annual Meeting Solvency II: Technical Provisions
Can be decomposed on 2 components:
Best Estimate
Corresponds to the expected value of liabilities, i.e. the average of the corresponding probability distribution
Risk or Security Margin
An additional cushion that takes into account the volatility and uncertainty of liabilities
Aimed at ensuring that provisions are enough to run-off or transfer liabilities with a high level of confidence
Best Estimate
Risk Margin

18. ASSAL XVII Annual Meeting 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

19. ASSAL XVII Annual Meeting 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

20. ASSAL XVII Annual Meeting Solvency II: Risk Margin
2 main approaches are on discussion:
Percentile approach
Underlying philosophy is to ensure that provisions are enough to run-off the liabilities with an x% probability confidence level
Risk margin corresponds to the difference between a specified x% quantile of the loss probability distribution and the best estimate
Implicitly, Value-at-Risk is the risk measure used. Variant approaches can consider other risk measures, such as TailVaR.

21. ASSAL XVII Annual Meeting

22. ASSAL XVII Annual Meeting Motor – estimated BE+RM Claims Provision

23. ASSAL XVII Annual Meeting Motor – estimated BE+RM Premium Provision

24. ASSAL XVII Annual Meeting Solvency II: Risk Margin
Cost-of-Capital
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
Risk margin corresponds to Market Value Margin, based on the cost of future regulatory capital required for on-going business
MVM corresponds to the amount that a rational investor would demand in excess of the best estimate to take over the liabilities
Technical provisions correspond to the fair value of liabilities, i.e. are, conceptually, fully market consistent

25. ASSAL XVII Annual Meeting
Source: CRO Forum