C.2. Clark - Reinsurance Pricing

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C.2. Clark - Reinsurance Pricing
2015-09-28 18:07:48
Clark Basics Reinsurance Pricing

Clark - Basics of Reinsurance Pricing
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  1. Difference between insurance and reinsurance pricing
    • a reinsurance program is generally tailored more closely to the buyer
    • there is no such thing as the average reinsured or average reinsurance price
    • pricing paradox: if you can precisely price a contract, the ceding company will not want to buy it
  2. 2 main methods by which Reinsurance can be applied
    • facultative: designed and purchased separately for each individual risk
    • treaty: single contract allowing the reinsurer to cover many risks (price aggregate)
  3. Bases for Reinsurance policies
    • risk attaching: all policies that begin or renew during the contract period are covered, regardless of when their losses occur or are reported (policy year / written premium)
    • losses occurring: covers all claims that occur during the contract period, regardless of when the policies were incepted or when the losses are reported (accident year / earned premium)
  4. 2 Methods to price Reinsurance
    • experience rating: use adjusted historical experience to calculate premium (burn cost = unadjusted ratio of past ceded losses to premium
    • exposure rating: use the current risk profile and estimated loss distributions to calculate premium; often used in combination with experience rating for non-proportional reinsurance
  5. Proportional treaty
    • agreement where the reinsurer assumes a given percent of losses and premium
    • quota share: reinsurer receives X% of premium + ceding commission and pays X% of losses
    • surplus share: reinsurer assumes x * retained line, translated to a % of losses; this type of treaty allows the reinsured to limit its exposure on any one risk. This is not XS insurance, as we only use the line to calculate the % of risk, which is what's being reinsured on a ground-up basis
    • fixed and variable quota share: underlying business is XoL, but reinsurer takes a % only
  6. Pricing analysis for proportional treaties
    • compile historical experience on treaty (premium & as-if losses for 5+ years)
    • exclude catastrophe (EQ, hurricane) and shock losses (large settlement on a single policy)
    • adjust experience to ultimate level and project to future period
    • select the expected non-cat LR (using historical data, industry average, ceding company gross LR)
    • load for catastrophes (e.g. spread large losses or use engineering models)
    • estimate combined ratio given ceding commission, reinsurer's GE and overhead, brokerage fees
    • estimate technical ratio = ELR + Commission
  7. Inflation vs Policy limits
    • concern is that insureds tend to purchase higher limits over time, so capping losses at historical policy limits and using those to predict future losses may understate the future loss potential
    • an alternative is to trend limits and losses, assuming policy limits increase with inflation
    • disadvantage of alternative is that historical premium should then be adjusted to reflect higher limit, and that can be difficult to quantify
  8. Special features of proportional treaties
    • sliding scale commission: sliding % of premium paid by the reinsurer to the ceding company
    • carryforward provision: allows that if the past LR have been above the minimum commission requirement, the excess loss amount may be included in the current year's losses
    • profit commission: substracts the actual loss ratio, ceding commission and a margin for expenses from the treaty premium and returns a % of this as additional commission
    • loss corridors: ceding company will reassume a portion of the losses if LR > threshold
  9. Property per risk XS treaties
    • provides a limit of coverage in excess of retention, attached to a single location
    • treaty premium is set as a % of GNEPI or GNWPI (Gross Net Earned/Written Premium Income), which is the premium net of any other reinsurance inuring to the benefit of the per risk treaty, but gross of the per risk treaty being priced
  10. Property per risk XS treaties - Exposure rating
    • advantage is that the current risk profile is modeled, not was was written years earlier
    • assumes that the exposure curve applies regardless of the size of the insured value
    • let R = retention, L = limit, IV = insured value
    • Exposure curve = P(p) = ∫0 to p*IV [1 - F(x)]dx / E[X] = E[X; p * IV] / E[X]
    • Portion of expected loss on risk in treaty layer = exposure factor = P((R+L)/IV) - P(R/IV)
    • Note that the table of exposure factor will likely go over 100% as limits profile often don't include business interruption coverage (commercial) or living expenses (homeowner)
  11. Exposure rating and deductible changes
    • when deductible increases / decreases, subject premium decreases / increases but E[L] may not change significantly so the old exposure rate would be too low / high
    • when deductible decreases, losses below the original deductible may be unknown making it challenging to derive a new exposure curve
  12. Free cover
    • experience rating in which no losses trend into the highest portion of the layer being priced
    • should use experience rating as a basis for the lower portion and then use relativities in the exposure rating to project the higher layer (where there are no losses)
  13. Credibility
    • first measure is # of expected claims (or $ losses based on exposures) during the historical period
    • second measure is year-to-year variation in projected loss cost
    • have to balance with the credibility of the complement itself → subjective exercise
  14. Inuring Reinsurance
    • occurs when an excess treaty covers losses after a surplus share treaty is applied
    • in experience rating we should restate the historical loss experience net of inuring reinsurance
    • exposure rating can be applied directly to a risk profile adjusted for reinsurance
  15. Casualty per occurrence XS treaties
    • working layer: low layer attachment which is expected to be penetrated (multiple claims per year)
    • exposed excess: excess layer which attaches below policy limits (not penetrated each year)
    • clash covers: high layer attachment excess (would typically need multiple policies to trigger)
  16. Situations where clash cover is exposed
    • extra contractual obligations and excess of policy limits loss
    • losses involving 2+ coverages / policies
    • ALAE covered outside of policy limits
    • WC loss above attachment (WC has no limit)
  17. Data Quality Issues in RAA report
    • reporting lag from event occurrence to the establishment of a reinsurer's case varies by company
    • mix of attachment points is not cleanly broken out
    • RAA requests data exclusive of Asbestos and Environmental claims (insurer compliance issue)
    • WC members may not handle the tabular discount on large claims in a consistent manner
  18. Casualty per Occurrence XS Treaties - Exposure Rating
    • E[x; L] = E[min(x,L)] = ∫0 to L x f(x) dx + ∫L to ∞ L f(x) dx
    • ILFL, U = E[x; U] / E[x; L] and ELFL = (E[x] - E[x; L]) / E[x]
    • Exposure Factor = [E[x; min(PL,AP + Lim)] - E[x; min(PL, AP)]] / E[x; PL]
    • if treaty includes ALAE in proportion to losses, replace AP ( + Lim) with AP ( + Lim) / (1+ e)
  19. Issues with Exposure Rating for Casualty per Occurrence XS Treaties
    • assumes that ALAE varies directly with capped indemnity, but ALAE is not a constant precent of loss (e.g. $0 losses still incur expenses); in general ALAE as a % tends to decrease as loss increases
    • it assigns an exposure factor of zero for high layers
  20. Including Umbrella policies
    • if umbrella policy is above primary policies, consider UL + XS as a single policy with a higher limit
    • problems arise when the umbrella policies are above primary policies from other carriers
    • Trended Loss = (Loss + Underlying Limit) * (Trend Factor) - Underlying Limit, which still leaves out losses from underlying policy which could pierce the layer after the trend is applied
    • Exp Factor = [E[x;min(UL+PL,UL+AP+Lim)] - E[x;min(UL+PL,UL+AP)]] / (E[x;UL+PL] - E[x;UL])
    • if there's a drop down coverage with probability ϕ, multiply numerator / denominator term by (1 - ϕ), and then repeat terms with UL = 0 multiplied by ϕ
  21. Swing Plans
    • actual losses to the layer are loaded for expenses and result is charged back to the ceding company, subject to a maximum and minimum constraints
    • Retro Premium = Actual Layer Losses * ELR
    • if plan isn’t balanced, actual ELR may be different than the Retro Premium adjustment factor
    • in this case we can adjust the loading, maximum or minimum rates to produce an acceptable LR
    • we also must be mindful of the provisional rate being well below the swing plan premium rate
  22. Aggregate distribution models options
    • empirical distribution
    • single distribution model
    • recursive calculation of aggregate distribution
  23. Empirical Distribution
    • easy to calculate, and should be used at least as a check
    • experience does not take into account all possible outcomes
    • if the volume or mix of business has been changing, volatility of future may ≠ from current
    • if using BF of Cape Cod for LDF, historical may present artificially smooth sequence of LR
  24. Single Distribution
    • assumes that the aggregate follows a known CDF (e.g. lognormal);
    • easy to use, even with limited data
    • no allowance for the loss free scenario (e.g. lognormal isn’t defined for y = 0
    • no easy way to reflect the impact of changing per occurrence limits on aggregate losses
  25. Recursive Calculation of Aggregate Distribution
    • fit an actual distribution to frequency (e.g. Poisson, Negative Binomial), and use a discrete distribution for severity with equal increments
    • simple to work with, and provides an accurate handling of lower frequency scenarios
    • for higher expected frequencies, calculation is inconvenient as it involves more scenarios
    • only a single severity distribution can be used in the analysis
  26. Disadvantages of more complex collective risk models
    • complexity of calculation can lead to black box mentality (should use more than 1 model)
    • most models assume that occurrences are independent, and so are frequency and severity
    • some models use numerical methods with a large error term for low frequency scenarios
    • aggregate distribution reflects the process variance but not the full parameter variance
  27. Traditional Property Catastrophe Covers
    • occurrence (EQ, hurricane) may often affect multiple risks and multiple policies
    • typically covers the ceding company’s retained exposure net of all other reinsurance
    • contracts will usually provide a limited number of reinstatements pro-rata as to amount/time
    • payback period: amount of time it would take for the premium to cover the full limit
  28. 4 Components of Typical Catastrophe Models
    • event sets: simulate the covered hazard based on simulated frequency and intensity
    • calculation of local event intensity for each property within a portfolio
    • estimation of damage for each property within a portfolio impacted by a given event
    • insured loss estimates based on policies written by the ceding company
  29. Information Required for Catastrophe Models
    • measure of exposure: insured values, construction types, occupancies, attachment points
    • geographical information: convert addresses into actual coordinates (or aggregate by zip code)
    • terms of the insurance policies: including deductibles, coinsurance provisions
    • details of inuring reinsurance: occurrence caps, loss corridors, etc.
  30. 2 Common Characteristics of Finite Risk Covers
    • multiple year features: e.g. 3 year contract cancellable after 1st or 2nd year if premium > losses
    • loss sensitive features: profit commissions and additional premium formulas
  31. Conditions for Reinsurance Contract
    • the reinsurer assumes significant insurance risk under the reinsured portions of the underlying insurance agreements
    • it is reasonably possible that the reinsurer may realize a significant loss from the transaction