Risk-Based Capital Case Study for General Insurance

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Risk-Based Capital Case Studyfor General
Insurance

• Glenn Meyers
• Insurance Services Office, Inc.
• CAS Spring Meeting
• May 18, 2004

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General Insurance Case Study

• Proposal for Standardized Approach
• Illustrative Internal Model

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Desirable Properties of a Standard Formula

• Simplicity The formula fits on a spreadsheet.
  This may allow for some complexity in the
  formulas, as long as the objective of the
  formulas is clear.
• Input Availability The inputs needed for the
  formula are either readily available, or can be
  reasonably estimated with the help of the
  appointed actuary.
• Conservative When there is uncertainty in the
  values of the parameters, the parameters should
  be chosen to yield a conservative estimate of the
  required capital

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A Proposal for a Standard Formula

• The formula is sensitive to
• The volume of business in each line of business
• The overall volatility of each line of insurance
• The reinsurance provisions and
• The correlation, or dependency structure, between
  each line of business.

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Correlation Generated byMultiple Line Parameter
Uncertainty

• A model where losses tend to move together
• Select b from a distribution with Eb 1 and
  Varb b.
• For each line h, multiply each loss by b.

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Correlation Generated by Multiple Line Parameter
UncertaintyA simple, but nontrivial example
Eb 1 and Varb b
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Low Volatility b 0.01 r 0.50
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Low Volatility b 0.03 r 0.75
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High Volatility b 0.01 r 0.25
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High Volatility b 0.03 r 0.45
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Dependency Analyses are Directed Toward Goal of
Evaluating Insurer Capital Costs

• If bad things happen at the same time, your need
  more capital.

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Volatility Determines Capital NeedsLow Volatility
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Volatility Determines Capital NeedsHigh
Volatility
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Correlation and Capital b 0.00

• Low correlation implies lower capital

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Correlation and Capital b 0.03

• High correlation implies higher capital

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Features of the Formula

• Input for insurance losses
• Expected losses for current business
• Loss Reserves (at expected values of payout)
• Parameters - Specified by regulator (??)
• Claim severity distribution by line of business
• Claim count distribution
• Dependency model parameters (see next slide)
• Calculates first two moments of aggregate loss
  distribution. Using lognormal approximation
• Capital TVaR99 Expected Loss

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Dependency Model Parameters

• Common shock model
• Uncertainty in trend affects all lines
  simultaneously
• Magnitude of shock varies by line of business
• Catastrophes treated separately
• Capital TVaR99 Expected Loss Cat PML
• Calculate Cat PML with a catastrophe model

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Example on Spreadsheet

• Big Insurer ABC Insurance Company
• Small Insurer XYZ Insurance Company
• ABC Volume 10 times XYZ Volume
• Otherwise they are identical
• Spreadsheet on CAS website for this session

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ABC with no Reinsurance
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ABC with Reinsurance
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XYZ with no Reinsurance
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XYZ with Reinsurance
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• Diversification effect of size ABC lt 10XYZ
• Reinsurance has proportionally greater effect on
  XYZ

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Moving Toward an Internal Model

• Recall WP recommendations
• That the Standard Model be deliberately
  conservative.
• Several modifications to the Standard Model are
  possible.
• Insurer internal models are to be subject to
  standards for risk-based capital formulas.

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Possible Improvements with Internal Model

• More realistic claim severity distributions
• Tailored to the individual insurer
• Richer dependency structure
• Parameter uncertainty in claim frequency as well
  as claim severity
• Parameter uncertainty in claim frequency applied
  across groups of lines.

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Possible Improvements with Internal Model

• Calculate aggregate loss distribution directly
  rather than by moments
• Include catastrophe model directly in aggregate
  loss calculation, rather than add PML.
• Allow for more flexible reinsurance arrangements.
• e.g. varying participation by layer

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• Diversification effect of size ABC lt 10XYZ
• Internal model is less conservative

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Requirements for Internal Models

• The insurer should have an independent internal
  risk management unit, responsible for the design
  and implementation of the risk-based capital
  model.
• The insurers Board and senior management should
  be actively involved in the risk control process,
  which should be demonstrated as a key aspect of
  business management.

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Requirements for Internal Models

• The model should be closely integrated with the
  day-to-day management processes of the insurer.
• An independent review of the model should be
  carried out on a regular basis. (Amongst other
  considerations, it should be recognised that
  evolution of the modelling capabilities is to be
  encouraged)
• Operational risks should be fully considered

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Requirements for Internal Models

• The model should be closely integrated with the
  day-to-day management processes of the insurer.
• Examples using an internal model
• Reinsurance analysis
• Allocating Capital and Underwriting Targets
• Evaluating growth strategies

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• Cat Reinsurance is the best strategy

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Note Cats are analyzed separately from other HO
and CMP
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• Prospect 2 is the best growth decision for the
  insurer

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Summary

• Simple factor-based models for capital
  requirements are available that reflect
• Volatility by line and size of insurer
• Reinsurance
• Correlation
• Working party proposal is to allow insurer to use
  internal models to justify capital
• Subject to standards