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Estimating the Parameter Risk of a Loss Ratio Distribution

Estimating the Parameter Risk of a Loss Ratio Distribution. Chuck Van Kampen, FCAS American Agricultural Ins. Co. CaRe Seminar Philadelphia, Pa June 2, 2003. Motivation For Study . Price Stop Loss Reinsurance Contracts DFA Analysis. Base Case Data. Pricing Question. Assume that:

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Estimating the Parameter Risk of a Loss Ratio Distribution

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  1. Estimating the Parameter Risk of a Loss Ratio Distribution Chuck Van Kampen, FCAS American Agricultural Ins. Co. CaRe Seminar Philadelphia, Pa June 2, 2003

  2. Motivation For Study • Price Stop Loss Reinsurance Contracts • DFA Analysis

  3. Base Case Data

  4. Pricing Question • Assume that: • The LogNormal Distribution is the correct model distribution • That the parameters are known with absolute certainty • How well does ten years of data predict future experience?

  5. Bootstrap with Simulations • Use Parameters to simulate 10,000 ten-year blocks of loss ratios • How many simulated ten-year blocks have a mean, standard deviation and skewness close to the actual data?

  6. What is Close? • Ranges around actual data: • Mean 63.52% to 64.77% • Std Dev .0662 to .0762 • Skewness .29 to .71

  7. How Well Does Ten Years Predict Future Experience? • 117 out of 10,000 simulations (1.17%) have the mean, standard deviation and skewness close to the actual data • Conclude it is unlikely that the actual ten-year block of data will provide parameters that are close to the true underlying distribution

  8. Alternative Pricing • Don’t Use Best Fit parameters • Instead determine: • What sets of parameters could have produced the actual data • And the relative probability or each of these parameter sets

  9. Determining Viable Parameter Sets • Use a macro to step through parameter ranges • Create 10,000 ten-year blocks for each parameter set • Count ten-year blocks that have mean, std dev and skew close to actual data for each parameter set

  10. Sample of Parameter Sets

  11. Parameter Set Relative Probabilities – Side View

  12. Parameter Set Relative Probabilities – Top View

  13. Comparison of Parameter Set and Fitted Expected Loss

  14. Sensitivity Testing • Increase the mean • Increase the standard deviation • Increase the skew • Fewer years of data

  15. Load by ELOL for Excess Layers

  16. Loads For Primary Loss Ratios

  17. Comments on Determining Viable Parameter Sets • Step size through the parameter set ranges • Size of parameter set ranges • What is close to the actual data • Criteria used

  18. Considerations • Simulation is used, not exact • Cat exposures should be removed • Requires a fair amount of judgment • Exposures not present in data are not taken into account • Process Risk still present and not accounted for in this methodology

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