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Deviation of actual from expected experience may result from
- Error of estimation
- Unexpected change in experience
- Statistical fluctuation
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MfAD - Defn
Difference btw the assumption for a calculation and corresponding BE assumption
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PfAD - Defn
Difference btw result of a calculation and corresponding result using BE assumptions
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MfAD may be expressed as
- Difference btw assumption for valuation and BE assumption (investment return)
- Multiplier to liabilities without PfAD (claim dev't)
- Addition to liabilities without PfAD, determined thru scenario testing
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Desirable risk margin characteristics
- Higher when
- Less is known about current estimate
- Risks with low frequency / high severity (than high frequency / low severity)
- Contracts that persist over a longer time
- Risks with a wide probability distribution
- Should decrease as emerging experience reduces uncertainty
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A risk margin methodology should
- Consistent for lifetime of contract
- Use assumptions consistent with those for current estimates
- Determined based on sound insurance pricing practices
- Vary by product based on risk differences
- Easy to calculate
- Consistent btw periods and varies from period to period only for real changes in risk
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Situations appropriate to select larger MfAD and examples
- Situations
- Significant degree of uncertainty in assumptions used
- Event assumed farther in the future
- Potential consequence more severe
- Occurrence more subject to stat fluctuation
- Examples
- Reinsurer financial distress
- Hyperinflation
- New LOB / lack of data to use
- Change in tort system affecting future claims
- Recession - high investment return risk
- Company experience volatile
- High uncertainty on the future development for Asbestos
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Categories of MfAD
- Claims development (2.5%-20%): % of claim liabilities excl PfAD
- Recovery from reinsurance ceded: (0%-15%) % of reinsurance recovery excl PfAD
- Investment return rates (25bp-200bp): deduction from expected investment return
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Claims development MfAD considerations
- Insurer’s operations
- claims handling (stable and consistent; sig changes)
- adequacy of staffing
- UW guideline (specific; lack of)
- Data on which the estimate is based
- data volume (high; sig YoY changes)
- stability of loss experience
- homogeneity in data grouping
- LOB
- environment (stable; changes)
- tail (short; long)
- latent claims (low potential; high)
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Situations that support claims dev't MfAD outside the range
- higher:
- significant changes from tort reform
- new LOB / lack of data to use for reserving
- recession and effect on LT lines
- lower:
- LOB in runoff (100% ceded to a reinsurer)
- Insurer has stop loss coverage that is reserved at stop loss limit
- LOB where all payments are certain
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Recovery from Reinsurance Ceded MfAD considerations
- Ceded LR
- Reinsurers in runoff
- Unregistered reinsurance
- Reinsurers in weak financial condition
- Unregistered reinsurance
- Claim disputes with reinsurers
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Risks that MfAD for investment return rates addresses
- Mismatch risk btw payment of claims and availability of liquid assets
- Error in estimating the payment pattern of future claims
- Asset risk incl:
- credit/default risk
- liquidity risk
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MfAD for investment return rates considerations
- Matching of assets and liabilities
- Quality of assets
- Asset default risk
- Eco conditions
- Investment expenses
- Concentration by type of investments
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When may MfAD change
when some of the considerations in determination of MfAD change
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2 formula-based / quantitative approaches for deriving MfAD for investment return (subject to min/max)
- Weighted Formula
- Explicit Quantification – Three Margins
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Weighted Formula
MfAD = iPM – iAM = iPM – min (iPM, iRFM x (1- k)) - iPM = interest rate for discounting based on matching of assets to claim liabilities before MfAD
- iAM = interest rate for discounting after MfAD
- iRFM = interest rate of risk-free bonds with reasonable match to payout of claim liabilities (at least duration)
- k = factor to adj for possible shortening of claim liabilities duration due to misestimated payment pattern and shift in yield curve
- market spread btw risk-free bonds and other investments removed for discounting purposes
- k directly related to size of MfAD
- Advantage: easily adaptable to principles-based approach of IFRS
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Explicit Quantification - 3 Margins
- Sum of:
- Asset/liability mismatch risk margin
- Timing risk margin
- Credit risk margin
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Asset/Liability Mismatch Risk Margin
- A/L Mismatch Risk Margin
- = coverage ratio
- × (A duration – L duration)/L duration
- × interest rate movement in run-off period
- Coverage ratio = (premium liability + claims liability) / (investments + installment premiums)
- Interest rate movement in run-off period = base year bond yield * 1 stdev of change in investment yield
- Where the bond is a risk-free bond with a similar duration to that of L
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Timing Risk Margin
- If duration of liabilities D is shortened by x%, then margin =
- method #1: discount rate (d) * x%
- method #2: (1+d)^((1-x%)*D) = (1+d adjusted for timing risk)^D
- margin = d - d adjusted for timing risk
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Credit Risk Margin
- Difference btw yield on high quality (e.g. corp) bonds and risk free gov bond with similar duration
- Rationale: higher than risk free implies credit risk (dif = credit risk spread)
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MfAD Stochastic techniques - Why prescription around assumptions / ranges for broad use is impractical
- Time-consuming review of industry experience
- Need to cover large # of assumptions
- Difficult to anticipate all company circumstances
- Ranges need regular update to reflect emerging experience
- Undermine integrity of AA
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Types of products suitable for stochastic modelling and examples
- Examples:
- Stop loss reinsurance
- CAT insurance
- Credit, warranty, and mortgage insurance
- LT LOB (prof liability)
- Skewed cost distributions due to:
- low frequency / high severity
- extend for many years
- LT
- correlation between lines, e.g. dependent on eco forces
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Stop Loss Reinsurance - Why stochastic
- to limit losses for an agg # of risks over a specified period
- evaluated by simulation and skewness of the cost distribution will increase as threshold increases
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CAT risks - Why stochastic
Evaluated by simulation of effects of CAT to provide a representation of the severity
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Credit, warranty, and mortgage guarantee insurance - Why stochastic
- Extend for many years -> significant premium liabilities at financial reporting date.
- Results highly dependent on eco forces (inflation, interest rates), with significant correlation btw classes -> subject to losses driven by high frequency related to eco
- Stochastic modeling of premium liabilities and MfAD more appropriate than deterministic
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LT LOB - Why stochastic
- Distribution of unpaid volatile and subject to external forces (eco and social inflation, judicial changes)
- Stochastic analyses of LDFs / frequency / severity may be beneficial when estimating claim and premium liabilities.
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Quantile approaches for the determination of MfAD based on stochastic techniques
- Multiples of the standard deviation
- Percentile or confidence levels (VaR)
- CTE / TVaR
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Multiples of Standard Deviation - Advantages
Simplicity and practicality
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Percentile or Confidence Levels - defn
Extra amount added to expected value so probability of actual outcome < amount of liability (including risk margin) over selected time period = target level of confidence
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CTE
- Conditional expected value based on downside risk
- Avg of outcomes that exceed (Qth percentile)
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2 aspects of insurance liabilities be considered to measure risk margin
- Time: rate of risk being released over time (i.e., settlement pattern)
- Shape: distribution of possible outcomes around mean, at reporting date, over a specified time horizon
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Practical Issues and Partial Solutions of Quantile Approaches
- How to select Confidence Level: no theory
- Dif Confidence Levels for dif Products: difficult to achieve consistency.
- During claim runoff, distribution wider and more skewed (fewer claims and larger) -> need dif confidence intervals by year.
- Insufficient info on extreme events. possible solution: Weighted avgs of extreme scenarios; Judgment on operational issues
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