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Outline

To focus the talk and keep to the time limit, only one kind of deal will be covered: pricing a sliding scale commission. Outline. Pricing A Sliding Scale Commission What a sliding scale commission looks like Why arises in practice Pricing steps Traps for the unwary.

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Outline

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  1. To focus the talk and keep to the time limit, only one kind of deal will be covered: pricing a sliding scale commission

  2. Outline • Pricing A Sliding Scale Commission • What a sliding scale commission looks like • Why arises in practice • Pricing steps • Traps for the unwary

  3. Commission is function of loss ratio

  4. Differing Views Different views about loss ratio probabilities mean that the reinsurer and insurer will value a sliding scale commission differently, opening the door to compromise.

  5. Differing Views

  6. Note • This kind of deal is usually NOT appropriate for a low-frequency/high severity layer (such as property cat or casualty clash) • 90% of the time you have no losses==> pay max commission • So you boost the price (by virtually the entire max commission) to account for this • Pointless trading of $

  7. Some Comments about Casualty • Note that for a casualty contract, either you must • Wait for “all” the claims to settle before paying the slide (typically with interim adjustments), or • Put IBNR factors into the formula, or • Jigger the pricing to account for when you (over)pay the sliding scale commission because claims are missing

  8. A Comment About Risk Transfer • The commission is higher when losses to the reinsurer are lower. • And vice-versa. • Less risk is transferred to the reinsurer than in the equivalent flat commission deal. • To the extent your profit margin is based on risk transfer, it should be adjusted to account for this.

  9. Pricing Steps • Patrik’s 13 point program • Specific example (property quota share with sliding scale commission)

  10. Patrik’s Thirteen Step Program • 1. Gather and reconcile primary exposure, expense, and rate information segregated by major rating class groups. • 2. Calculate an exposure expected loss cost, and, if desirable, a loss cost rate. • 3. Gather and reconcile primary claims data segregated by major rating class groups.

  11. Patrik’s Thirteen Step Program • 4. Filter the major catastrophe claims out of the claims data. • 5. Trend the claims data to the rating period. • 6. Develop the claims data to settlement values. • 7. Estimate the catastrophe loss potential.

  12. Patrik’s Thirteen Step Program • 8. Adjust the historical exposures to the rating period. • 9. Estimate an experience expected loss cost, and, if desirable, a loss cost rate. • 10. Estimate a “credibility” loss cost or loss cost rate from the exposure and experience loss costs or loss cost rates.

  13. Patrik’s Thirteen Step Program • 11. Estimate the probability distribution of the aggregate reinsurance loss, if desirable, and perhaps other distributions, such as for claims payment timing. • 12. Specify commission, internal expense, and profit loads.

  14. Patrik’s Thirteen Step Program • 13. Negotiate, reconcile opinions and estimates, alter terms and finalize.

  15. Pricing: Example • Price a property quota share with a sliding scale commission

  16. Da Ponte Insurance Company • Rating Period = 2001 • 25% Quota Share on Property lines • Primary premium = $10,000,000 • Per-occurrence limit = $7,500,000

  17. The Basic Formula • RCR = PRCR - SF x {(RL/RP) - (1 - PRCR - RM)} • RCR = Reinsurance commission rate • Subject to Min RCR <= RCR <= Max RCR

  18. The Basic Formula • RCR = PRCR - SF x {(RL/RP) - (1 - PRCR - RM)} • PRCR = provisional reinsurance commission rate • SF = Slide Factor • RL = Reins. Losses RP = Reins. Prem • RM = Reinsurer’s Margin

  19. The Basic Formula • RCR = PRCR - SF x {(RL/RP) - (1 - PRCR - RM)} • PRCR = 33% • SF = 50% • Min RCR = 25% Max RCR = 35% • RM = 5%

  20. The Basic Formula • RCR = 33% - 50% x {(Loss Ratio) - (62%)} • = 64% - (50% x Loss Ratio) • Subject to min of 25% and max of 35%

  21. Commission is function of loss ratio

  22. Pricing Example • Get exposure rate (Patrik 1, 2) • Get experience rate (Patrik 3, … 9) • Get credibility compromise between experience and exposure rates (Patrik 10)

  23. Pricing Example • Get distribution of aggregate losses (= Patrik 11) • Transform into distribution of loss ratios • For each loss ratio, find the commission • Find the expected commission,etc. • Integrate the commission for each loss ratio against the probability density of that loss ratio

  24. Pricing Example • Increase the reinsurance premium until the expected net (after commission) premium is adequate to pay losses, reinsurer expenses, and profit margin.

  25. Property Example Expected Loss Ratio is 65% (including cats) Based on analysis of cedant rate level, expenses [Patrik step 2]

  26. Property Example ($ 000)

  27. Estimate Cat loss potential • Cat loss ratio with $7.5 million per-occurrence limit = 12% • From (e.g., CatMap, Eqecat, …) • TOTAL filtered experience loss ratio + cat load • = 48% + 12% = 60%

  28. Estimate “Credibility” Rate • Exposure rate = 65% • Experience rate = 60% • Credibility rate = 62%

  29. Factors in setting credibility • Accuracy of the exposure expected loss costs • How well do you know rate changes, deviations, expenses? • Accuracy of the experience expected loss costs • Accuracy of: trend, development, on-levelling • Stability of losses over time • Changes in underlying exposure over time

  30. Finding the aggregate loss distribution • Look at annual loss ratios • Use standard risk-theoretic model

  31. Look at annual loss ratios • Bad: Do as-if on unfiltered loss ratios • Cats (or lack thereof) distort • Small sample • Will not respond to changes in deal for loss ratios outside the range of experience • Do it, but don’t believe it

  32. Look at annual loss ratios • Use adjusted loss ratios to find mean and standard deviation of loss ratio distribution • Filtered: mean 48%, standard deviation 6.1% • Cats: mean 12%, standard deviation of 13.9%

  33. Use method of moments • Cats and other losses are independent • Mean = 50% (48%) + 12% • Variance = (6.1%)^2 + (13.9%)^2 • Find alpha and beta for gamma distribution by equating gamma mean and variance to sample values

  34. Standard Risk-Theoretic Model • Mean and variance of aggregate losses can be expressed in terms of mean and variance of claim count and severity distributions • Use for method of moments • Or simulate • Or use Panjer, Heckman-Meyers, etc.

  35. Aggregate Loss Distribution/Profit

  36. Traps for the unwary • Parameter risk: Error in estimating parameters, model error, etc. • Often impacts reinsurer more than insurer • What if the program doesn’t grow as projected? • Sensitivity analysis • Small changes in deal may make big difference • Cancellation provisions

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