1© CMPA Provision for Adverse Deviations : Using a probabilistic stochastic approach André...

1© CMPA www.cmpa-acpm.ca

Provision for Adverse Deviations :

Using a probabilistic stochastic approach

André L’Espérance

Canadian Institute of Actuaries18 September 2009

© CMPA www.cmpa-acpm.ca 2

Contents

• CMPA Background information Organization Actuarial liabilities Characteristics

• The valuation process

• Calculation of PfAD components

• Comments

• PfAD – CIA Standard of Practice


CMPA Background information - Organization

• Mutual Defense Association – Not for Profit organization• Monoline : medical malpractice• No insurance policy or contract • Annual membership• Services to membership

Occurrence-based protection with no limit on costs for compensation, legal and expert costs

Education and Risk Management Assistance

• “Quasi insurer” according to CIA Standards of Practice


• Cost components Damages (awards and settlements) Legal fees and disbursements Expert fees Administrative / operational expenses

• Only claim liabilities – annual valuation at year-end for financial reporting purposes

• Estimates of expected unpaid claims not yet available for individual cases

• Deterministic and probabilistic approaches using historical dollar payments data on a regional basis

CMPA Background information – Actuarial liabilities


• Exempt from regulation

• Tax exempt

• No reinsurance

• Excess assets returned over time to membership in the form of credits against annual fees

Background information - Characteristics


• Deterministic approach

Adjustment of historical data

Paid loss development techniques

• Probabilistic approach

Fitting of distributions to unadjusted historical data cells => estimation models reproducing historical data

Projected values from selected future trends applied to estimation models

Distribution of potential estimates from simulations based on distribution’s mean and S.D.

The Valuation Process


• Criteria applied for selection of estimation models for each cost component and for all cost components combined

• Best estimates validated through frequency-severity models and runoff exhibits

• Multiple scenarios applied to each estimation model Future trends Selected Estimates = Weighting of Scenarios’

Estimates

• PfAD calculated from margins based on volatility of estimation models and on structure of assets portfolio

• Actuarial provision = Selected estimates + PfAD

The Valuation Process


Calculation of PfAD components

• Margin for Claim Development (MfCD)

Considerations described in current and prior CIA Standards of Practice

Additional information : Volatility in mean / selected estimates can be used to determine the margin needed achieve given confidence level

Subject to CIA’s low and high margin limits

• No Reinsurance

• Margin for Interest Rate (MfIR)

Considerations described in CIA Standards of Practice Subject to CIA’s low and high margin limits

• PfAD = MfCD + MfIR


Calculation of PfAD components => MfCD

• Typically skewed, long tail distributions

• Volatility of each estimation model measured using the information from the standard deviation of its distribution and from the simulated values at each confidence level

• Standard deviation and simulated values calculated

for each cost component for an all cost components combined estimation model to

recognize the correlation between each case’s cost components



• MfCD can be calculated from the measures of volatility for each cost component and for all cost components combined recognizing that such measure

Includes normal fluctuations around mean Excludes ‘model risk’



• Potential MfCD = Standard Deviation (S.D.) of estimation model’s distribution

represents the S.D. of the ‘population’

includes most potential outcomes

• Potential MfCD = Simulated value at a given confidence level - Mean estimate

Issue : simulated values include a wide range of potential outcomes but unlikely all potential outcomes covered by the S.D. of the ‘population’

Issue : selection of confidence level



• A VaR approach is used to provide statistical support for the selected confidence level

i.e. The confidence level at which the expected gain from a more than sufficient MfCD is approximately equal to the expected loss from an inadequate MfCD

• Empirical testing indicates an 85% confidence level

Slightly below the required level for the damages cost component

Some conservatism for other cost components



• Selected MfCD = one S.D. of the All Cost Components model subject to

minimum = S.D. of the DAMAGES cost component

maximum = sum of S.D. of each cost component

within range defined by CIA Standards of Practice

• Takes into account the correlation between the cost components of a case

• Takes into account the higher volatility of the damages cost component


Calculation of PfAD components => MfIR

• Recognizes the characteristics and structure of the assets portfolio Fixed income (bonds) instruments Equity (stocks) Private assets and alternate arrangements (infrastructure,…)

• Selected margin = 200 basis points

• MfIR = provision discounted @ expected long-term earned rate minus 2%

- provision discounted @ expected long-term earned rate

• Calculated for each cost component


• Volatility

Varies among the estimation models of the cost components

Materially higher for the damages cost component than any other cost component => beyond the maximum allowed by CIA Standards of Practice

Difficult to justify a single percentage confidence level as a standard of practice for MFCD

Range of confidence level would be more appropriate

Comments


PfAD - CIA Standard of Practice

• Definition of ‘adverse deviations’ should be revisited

• Differences between Deterministic/traditional and Probabilistic methodologies may support separate treatment of the margin for claims development based on each methodology and resulting values should be comparable.

• For the calculation of the margin for claims development, guidance about a range rather than a single confidence level would likely more appropriately recognize the uncertainty inherent in the calculated expected costs


QUESTIONS

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