Three sources of internal systemic risk (choices)
- Specification error (model error)
- Parameter selection error (choosing the wrong parameters or omitting important ones)
- Data error
Internal systemic risk is uncertainty in liabilities due to the internal valuation process and the fact that valuation models are an imperfect representation of the insurance process
Correlation effects
Independent risk - uncorrelated with other sources within & between valuation classes
Internal systemic risk - uncorrelated with independent & external systemic risk but correlated between classes or between OSCs and PLs
External systemic risk - in general, uncorrelated
Risk Margin Calculation
Calc Independent Risk: phi^2 = sum of (phi * w)^2
Calc Internal Systemic Risk
- get claims CoV from scorecard; set up matrix of CoVrow * weightrow * correlation * CoVcol * weightcol
- phi^2 = sum of matrix
Calc External Systemic Risk phi^2 = sumsq(event risk CoV)
Consolidated CoV = sqrt(sum of phi^2)
RMnormal = z * CoV
produces higher RM at lower probabilities of adequacy
RMlognormal = exp(z * sigma - 0.5sigma^2) - 1
sigma^2 = ln(1 + CoV^2)
produces higher RM at higher probabilities of adequacy as long as consolidated CoV is not too high
Internal Benchmarking - Independent Risk CoVs
Check CoVs across two dimensions:
1. Portfolio size - larger portfolios should have lower CoVs due to lower volatility from random effects
2. Length of claim run-off - longer tailed lines should have higher CoVs due to more time for random effects to have an impact
Internal Benchmarking - Internal & External CoVs
Internal systemic CoVs - if template models are used for similar valuation classes, you can expect similar CoVs
If similar valuation methodology is used on short- and long-tailed lines, then expect higher CoV on long tailed lines
External Systemic Risk CoVs - long-tailed portfolios should have higher CoVs than short-tailed portfolios in most cases
External Systemic Risk
Risks that are shared across claim groups or valuation classes and that are external to the valuation process (e.g. a hurricane impacting Home and Commercial Property is event risk)
Quantitative modeling can analyze past episodes of external systemic risk, but can’t adequately capture potential future external systemic risks to the extent they’re different than the past.
Independent Risk (and CoV calc)
phi^2(ind) = sum of (phi * w)^2
risk due to randomness in the insurance process and includes parameter risk and process risk.
Stochastic modeling techniques such as the Mack method, Bootstrapping, or Bayesian techniques are appropriate to assess independent risk.
