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Friedland: Reserving in Reinsurance

Study Strategy

Checklist

  1. Be able to list and explain the purposes of reinsurance
  2. Be able to describe the different types of reinsurance
    • Treaty
    • Facultative
    • Proportional
    • Non-proportional
    • Finite risk
  3. Know the different types of data used by reinsurers
  4. Know how reinsurers obtain data
  5. Know how LAE is treated and be able to calculate estimated gross, net and ceded losses with LAE
  6. Know the data requirements for an appropriate reserve analysis
  7. Be able to explain the challenges that are present in reinsurers’ data
  8. Be able to calculate ultimate losses using traditional reserve methods
    • Development method
    • Expected loss method
    • Bornhuetter-Ferguson method
  9. Be able to calculate gross, net and ceded losses (including IBNR) for different types of reinsurance
    • Quota share
    • Surplus share
    • Excess per risk
    • Excess per occurrence (and catastrophe)
    • Aggregate excess of loss
  10. Be able to calculate gross, net and ceded losses when multiple reinsurance contracts are in use
  11. Be able to calculate ultimate catastrophe losses using the catastrophe adjustment

My Notes

Terminology

Term Definition
A
Reinsured (ceding company) (cedent) insurer that cedes its business (here, typically the primary insurer)
Reinsurer insurer that accepts all/part of insurance liabilities of the cecent)
B
Subject policies (underlying policies) ceded insurance policies
Assumed business business accepted by reinsurer from cedent
C
Retrocession (agreement) transfer of risk: reinsurer → reinsurer (reinsurance for reinsurers)
Retrocedent ceding reinsurer in retrocession
Retrocessionaire the assuming reinsurer \(\uparrow\)
D
Attachment point where reinsurance begins to apply
Working layer dollar range; expect predictable losses with high frequency; cedent retains losses within this layer and reinsure losses in excess of this layer
E
Bordereau (plural: bordereaux) data reports: cedent → reinsurer (incl. premiums and/or losses affected)
Counterparty default risk what if reinsurer is unable to meet their liabilities?
Subscription policy contract where multiple reinsurers share the risk (when AOI > what any individual insurer is willing to accept) (or to diversify default risk)
Commutation cancellation
→ Cedents: to exit LOBs, manage reserves, avoid credit risk
→ Reinsurers: to terminate relationship with cedent, protect itself from their solvency
F
Gross Loss → Cedent: sum of direct + assumed1 business
→ Reinsurer: assumed business
Ceded losses → Cedent: business transferred through reinsurance
→ Reinsurer: business transferred through retrocession
Net losses (retention) \(=\text{Gross Losses}-\text{Ceded Losses}\)
Business-covered clause which describes the risks/policies covered by the contract
→ Losses-occurring during: loss occurring during contract period, regardless of when subject policy was issued
→ Risk-attaching: subject policies with inception date during contract period, regardless of loss date.

Purposes of Reinsurance

Purpose Detail
Promote Stability cedents retain smaller, more predictable losses & ceded unusual and infrequent ones
helps limit losses from a single large events/many mid-sized events
prevents insolvency.
Increase Capacity allows insurer to take more risk than they are comfortable (as they can cede part or all of that risk)
facilitate competition. Small insurers can write more business and compete with large insurers with already great capacity to accept risk
Protect against Catastrophes (PRIMARY FUNCTION) Protect against a single large event/multiple smaller events
Protect against casualty losses (terrorist attack/vehicle accident)
Manage capital and solvency margin Less retained risk \(\implies\) less capital required (frees capital for other use)
Ceding helps lower solvency margin2 allow writing of more business
Reinsurer pays cedent: ceded commissions to cover a portion of the cost of writing new business.
Access technical expertise Reinsurers provide technical expertise (U/W, marketing, claims, loss prevention, pricing → help manage risk)
Helpful for small insurers or seekers of new LOBs or regions
Facilitate withdrawal from a LOB, region etc If insurer wishes to exit LOB, cede all of the risk to reinsurer and be free from it
Arbitrage Purchasing reinsurance could cost less than profits gained by that purchase.

Types of Reinsurance

Disclaimer

These are just generalizations. Reinsurance policies are tailor-made to the requirements of the reinsurer and the cedent.

  • Treaty vs Facultative → what can be ceded & what the reinsurer is required to accept.
  • Proportional vs Non-proportional → What portion/part of losses are retained and what is ceded.
    • Proportional
      • Quota Share
      • Surplus Share
    • Non-proportional
      • Excess per risk
      • Excess per occurrence & catastrophe
      • Annual aggregate excess of loss
      • Clash
  • Finite Risk Reinsurance
    • Loss Portfolio transfers
    • Adverse development cover

Treaty

Synopsis

Cede all! Accept all! (Reinsurers don't conduct own underwriting)

  • Cedent cedes ALL business (LOB specified in contract)
  • Reinsurer agrees to accept all business in contract, including unwritten policies that are expected to be written in the contracts' course
  • KEY: Reinsurer is willing to accept whatever risks cedent is willing to write. (doesn't conduct own underwriting)
  • One/multiple reinsurers
  • One/multiple years

Facultative

Synopsis

Cede some (requires certificate). Reinsurer has option! (can conduct own underwriting)

  • Reinsurer and cedent have the option to accept/reject individual risks/groups
  • Certificate of reinsurance is used to record coverage (proof)
  • Mostly for high-value and hazardous commercial risks
  • PURPOSE: Improve capacity of cedent
  • Reinsurer can conduct own underwriting to mitigate risk of adverse selection.

Hybrid (Treaty, Facultative)

  • To provide capacity and stabilization
  • E.g.
    1. Facultative auto reinsurance → limited rights with reinsurer to decline individual risks
    2. Facultative obligatory treaties → primary insurer has option to cede (i.e. submit), which must be accepted by reinsurers
    3. Facultative semi-obligatory treaties → Same as (2) but option only for a DEFINED CLASS
    4. Non-obligatory agreements → cedent (reinsurer) may choose not to cede (assume) every risk

Proportional

a.k.a

  • Pro rata reinsurance
  • Participating reinsurance
  • Premiums and losses are shared based on ceding percentage
  • Reinsurer pays ceding commission → cover expenses for writing/servicing policies
  • Protection from high frequency & high severity claims, catastrophes
  • Increases capacity, allow writing larger risks
  • Help manage capital & solvency margins
  • Improves net leverage ratios \(=\dfrac{\text{WP}}{\text{surplus}}\)
  • Insurer's solvency is more dependent on reinsurer's solvency (as Surplus aid to surplus ratio \(=\dfrac{\text{reinsurance}}{\text{surplus}}\) increases)
Quota Share
  • Both parties agree on a cession percentage (\% of both premium and losses shared)
    • Possible to vary cession \% based on risk characteristics
    • State assumptions if not clear whether its ceded or retained \%

Observation

Quota share reinsurance doesn't impact Loss Ratio

Surplus Share

Synopsis

Reinsurer pays this proportion: \(\dfrac{\text{PL}-\text{RL}}{PL}\) of losses, which varies with the policy limit.

  • Variable cession \% → depending on size of underlying risk
  • Cedent determines max policy limit (willing to fully retain) → the line
  • Reinsurer will cover anything above the line up to a multiple of the line.
    • The multiple is determined by the policy limit. See demo
\[ \text{Prop Ceded} = \dfrac{\text{Policy Limit}-\text{Retained Line}}{\text{Policy Limit}} \]

Demo

Var E.g. 1 E.g. 2 E.g. 3
Policy Limit 5M 10M 15M
Retained Line 5M 5M 5M
Prop ceded \(\dfrac{5-5}{10} = 50\%\) \(\dfrac{10-5}{10} = 50\%\) \(\dfrac{15-5}{10}=66.7\%\)
Gross Loss 3M 3M 3M
Ceded loss 3M \(\times\) 0% = 0M 3M \(\times\) 50% = 1.5M 3M \(\times\) 66.7% = 2M
Retained Loss 3M 1.5M 1M
  • Policy limit is at or below the line \(\implies\) reinsurer doesn't cover anything

Non-proportional

a.k.a

  • Excess of Loss (XOL) reinsurance

Synopsis

Reinsurer pays anything above \(\text{Limit}\)

  • Premium non-proportional to coverage
  • Ceded loss depends on size of loss
  • Covers all/part above a specified limit
  • PRO: Provide stability, improve capacity, protects from catastrophes, helps manage capital
  • Provides expense & surplus relief
Excess per risk

Synopsis

Reinsurer pays anything between \((\text{Attachment},\text{Attachment + Limit})\)

  • All/part over a specified attachment point for each risk (typically for property/casualty lines)
    • Risk = a building or group of buildings under the same policy
  • PRO:
    • Increase capacity.3
    • May have ceding commissions (less than that for #Proportional)
  • Demo
    • Attachment point → 4M
    • Limit → 3M
    • Value of house → 5M
    • Reinsurer covers 4M to (4+3)M → \((4,7)\)
    • For policies
      1. Loss = 2M → nothing is ceded
      2. Loss = 5M → \(5-4\) = 1M ceded
      3. Loss = 8M, → 8 > 7 \(\implies\) 3M ceded (at limit)
  • It is different from #Surplus Share (SS) since SS uses policy limits to determine a proportion, which is applied to all losses, no matter how large or small.
Excess per occurrence & catastrophe #doubt

Synopsis

Like #Excess per risk but for total estimated event ultimate (instead of individual claims)

  • Very similar to #Excess per risk (Same "attachment point" rules) but…
    • They apply to all losses from a single event OR series of catastrophic events
    • Rather than a single policy
  • Catastrophe reinsurance allow for reinstatement → reset the policy limit if its depleted, subjected to a reinstatement premium.
    • Automatic / one or more times or available upon request
Annual aggregate XOL

a.k.a

  • Aggregate stop-loss reinsurance
  • Aggregate reinsurance

Synopsis

Aggregate reinsurance protects net results (other reinsurance coverages apply first, and aggregate reinsurance applies to the net).

  • Prevents losses during a given period from exceeding a given threshold.
    • threshold = \% of premiums or fixed amount.
  • If the losses (in accumulation) is a very large sum (say 25M, after ceding the via the excess per risk), which the cedent may not be prepared to pay
  • In such a case, it can opt for an aggregate policy with an attachment point (say 10M). This would lead to them retaining only 10M and 15M would be ceded.
  • PRO: The best way to protect capital!
  • BUT: Unavailable / very expensive → Need careful cost benefit analysis

Another way to express % coverage

Reinsurance covering 30% loss ratio in excess of their retention of 100% loss ratio → If Subject Premium = 100M, coverage layer = (100, 100+30) in losses.

Clash

Synopsis

  • Similar to Excess per occurrence but exclusively covers casualty losses
  • This coverage attaches above all other policy limits
  • Clash event
    • Loss must arise out of multiple policies held by one insured or similar policies held by multiple insureds
    • Damages must be traceable to and direct consequence of a specific event
    • Event must take place during specific time frame
  • If event qualifies as a clash event \(\implies\) calculation would be identical to calculations for excess per occurrence coverage

Finite Risk Reinsurance

  • Incorporates TVM (accounts for investment income over contract period)
  • Multi-year contracts, spreading risk over time
  • Often associated with run-off products (to cover volatility from past activities)
  • Reasons why a company may choose a run-off option:
    1. Corporate restructuring
    2. Mergers and acquisitions
    3. Exiting an LOB
    4. Regulatory, accounting or tax changes
Loss portfolio Transfers
  • Assumes future loss payments for policies written in prior years
  • TVM is considered so premiums \(\lt\) ultimate expected payments
  • Main risk: timing
    • Earlier settlement \(\implies\) less investment income \(\implies\) less profit
  • See this #later
  • When an insurer writes a policy, they must set aside Loss Reserves. These are estimates of the total amount they will eventually pay for claims from that policy year.
    • Before Ceding: The insurer lists these reserves as a liability on their balance sheet. They also hold a corresponding amount of cash or bonds as assets to back those liabilities.
    • After Ceding: The insurer pays a premium to the reinsurer. In exchange, the reinsurer takes over the liability. The primary insurer removes the "gross reserves" from their books (or offsets them with a "reinsurance recoverable" asset), effectively shifting the risk of those claims to the reinsurer.
  • Commonly used for long-tailed lines.
Adverse Development Cover
  • If ceding reserves exceed a certain threshold.
  • No transfer of reserves → ceding company maintains claims management
  • Used in mergers and acquisitions
  • See this #later

How Reinsurance Contracts Work Together

  • Cedent can buy more than one type of reinsurance

  • How do they work together? Define properly

  • Contract A insures to the benefit of another contract B.

    • Inuring contract (contract A) applies first. (excess per risk)
    • Contract B applies to the remaining (to the net of excess per risk)
\[ \text{retained loss} = \text{gross loss} - \text{Contract A ceded Loss} - \text{Contract B ceded Loss} \]

Types of Data

  • Paid Loss
  • Case Reserves (set by cedent)
  • ACR (set by reinsurer)
  • Reported/incurred loss (i.e. paid + case reserves)
  • Written and earned premiums

NOT AVAILABLE: Claims counts and earned exposures

How reinsures receive data

  • Through bordereaux, periodically provided by cedent
    • containing insurance premiums/losses affected by reinsurance
    • list of policies covered by reinsurance (name, addresses of insureds, amount, location of risk)
    • list of claims + amounts paid by ceding insurer
  • Issues in bordereau
    • Manner of cumulation differs by insured
    • different IT systems → different types of reports (how to absorb in a useful format? manually intensive)
    • frequency of reporting
  • Requirement to standardize dataset requirements
    • requires significant effort to update
    • many insureds haven't yet implemented
  • Smaller reinsurer, not enough internal data. Use external sources
    • Reinsurance Association of America (RAA)
    • Best's Aggregates and Averages
    • Global brokers' reports (Guy Carpenter, Aon)
    • Global reinsurers' reports (Swiss Re, Munich Re)
  • But these may be highly aggregated → not appropriate without adjustments (should be well documented)

Loss Adjustment Expenses

  • Need data regarding LAE, requires close attention as handling differs by contract.
  • ULAE is usually excluded from reinsurance coverage.
  • ALAE can be treated in 3 ways:
    1. Included with claim amount (most common)
      • Just add to get Gross Loss & ALAE
    2. Included pro rata (using \(\dfrac{\text{Excess Loss}}{\text{Total Loss}}\) ratio for gross loss)
      • The same percentage of ALAE is ceded
    3. Excluded from coverage
      • Only use gross loss amount to determine what is ceded

Data Requirements

General requirements for any dataset but focusing on how the requirements differ for reinsurers as compared to primary insurers.

  • Sufficient and reliable Data
  • Homogenous and credible Data
  • Organization of Data by experience period

Reinsurers' Data Challenges

  • Change in Operation and Environment
  • Report Lags
  • Heterogeneity of Contract Wordings
  • Multiple Currencies
  • Large Losses
  • Recoveries

Reserving Methods

  • Importance of having appropriate estimates of reserves?
    1. Internal management
      • pricing
      • UW
      • strategic planning
      • financial decision making
    2. Investors
    3. Insurance regulators
    4. Rating agencies
  • Need to calculate three metrics
    1. Gross
    2. Net
    3. Ceded losses

Two approaches to estimate the three if we have aggregated data:

  1. Project gross (w/ unpaid loss) and net (w/ unpaid loss) to ultimate. The difference is ceded.
  2. Project gross (w/ unpaid loss) and ceded (w/ unpaid loss) to ultimate. The difference is net.

Losses in higher layers (ceded losses) are less credible and thus LDFs are leveraged → Thus prefer approach (1)

  1. Any business they assume from another insurer ↩

  2. Solvency margin = \(\dfrac{\text{net premium}}{\text{surplus}}\) ↩

  3. Lowering the liability side of the balance sheet effectively increases the ratio of surplus to net written premium, allowing the insurer to write more business than its own capital base would otherwise permit ↩

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