C.1. Grossi - Catastrophe Modeling

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C.1. Grossi - Catastrophe Modeling
2015-09-16 19:47:43
Gross Kunreuther Catastrophe Modeling

Grossi & Kunreuther - Catastrophe Modeling: A New Approach to Managing Risk
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  1. Users of cat model for risk management
    • insurers and reinsurers: evaluate their own exposure to catastrophe losses
    • reinsurance brokers: assess risk for their clients to send to reinsurers
    • capital markets: more accurately price cat bonds
    • government: regulators and emergency management agencies
  2. 2 main risk management strategies
    • risk reduction: non-renewing policies, limiting coverage, changing rates or deductibles
    • risk transfer: insurer purchasing reinsurance, or issuing catastrophe bonds
  3. Why we can't use regular statistical tools
    • insufficient historical claim data for catastrophes
    • limited data is often inappropriate due to changing factors (building codes, costs of repairs)
  4. 4 basic components (modules) of a catastrophe model
    • hazard: e.g. EQ hazard is defined by its epicentre location and moment magnitude
    • inventory (exposure): portfolio of properties at risk (location, limits and deductibles, ...)
    • vulnerability: susceptibility to damage of the structures at risk (quantify hazard physical impact)
    • loss: calculate direct (cost to repair and/or replace) and indirect (business interruption, relocation)
  5. Hazard Module Components
    • location of potential future events: for EQ this would be regions around faults
    • frequency: most critical and uncertain aspect of the model's hazard module
    • severity: model the physical parameters that describe the hazard at its source
  6. Inventory Module
    • data includes number of properties and their value by LOB, coverage, occupancy, construction type
    • inventory data should also reflect regional differences in construction practices and building codes
  7. Vulnerability Module
    • engineering judgment: based on expert opinion; simple, but not easy to update and arbitrary
    • building response analysis: based on advanced engineering techniques; more accurate, but based on specific buildings so can't be applied to an entire portfolio
    • class-based building response analysis: divide risks based on building characteristics; identify the typical building and analyze it in details; evaluate building performance for each class, computing damage ratios by coverage
  8. Loss Module
    • linking event parameters directly to expected loss: not easily updated
    • instead favour model that first estimates the physical damage from an event, and then use a cost analysis to translate this into monetary loss
    • estimation of insured losses are computed by applying policy conditions to total loss estimate
  9. Exceedance Probability
    • Occurence EP: Pr(at least one loss > specified amount) in a given time period
    • Aggregate EP: Pr(Σ losses > specified amount) in a given time period
    • Conditional EP: Pr(single event amount > specified amount) given that the event occurs
  10. Solving for OEP
    • Ei = disaster event with occurrence probability pi and loss Li
    • sort the events in decreasing order by size (E1 = largest, E2 = second largest, etc.)
    • E[Li] = pi*Li so Average Annual Loss = AAL = Σ pi*Li
    • OEP(Li) = P(L>Li) = 1 - P(L ≤ Li) = 1 - ∏(1 - pj)
    • Note that P(L = 0) = P(no event occur) + P($0 event occur)
    • OEP graph has Loss in X axis, OEP in Y
  11. Conditions for insurability of a risk
    • ability to identify and quantify, or at least partially estimate, the chances of a loss occurring and the extent of losses likely to be incurred
    • ability to set premium for each potential customer or class of customers
  12. Considerations in setting rates for catastrophe events
    • appears to not be impacted by adverse selection or moral hazard
    • uncertainty of losses: wide variation in loss distributions
    • state regulation, competition
    • highly correlated losses: involves spatially correlated losses or the simultaneous occurrence of many losses from a single event.
    • liquidity of assets: need cash to pay cat losses, so losing on investment income
  13. Role of catastrophe modeling in an insurance company’s financial management
    • capital allocation: influences calculation of cost of capital, marginal risk, VaR, incremental risk
    • ERM: risk of ruin, asset/liability management, solvency/sustainability, return on capital
  14. Relevant actuarial principles re: catastrophe modeling
    • Principle 1: a rate is an estimate of the expected value of future costs
    • Principle 2: a rate provides for all costs associated with the transfer of risk
    • Principle 3: a rate provides for the costs associated with an individual risk transfer
    • Principle 4: a rate is reasonable and not excessive, adequate, not unfairly discriminatory if it is an actuarially sound estimate of expected value of all future costs associated w/ individual risk transfer
  15. Simple Rate Making Model
    • Premium = AAL + Risk Load + Expense Load,
    • AAL = ∑piLi and we can use σ(EP curve) as risk load
    • σ = √ [ ∑(Li2pi) - AAL2 ]
    • determining whether to provide coverage P(Loss > nz + A) < p1
  16. Differentiating Risk
    • structure attributes: features of insured risk related to the physical performance of a building in an extreme event; e.g. construction, building code, year built, occupancy
    • location attributes: reflect the degree to which structure are subject to damages from hazards as a function of where they are built (e.g. flood plain, earthquake faults)
  17. Regulation vs Catastrophe Modeling
    • regulators have not been supportive of having model-generated information introduced
    • difficult to evaluate the models since they require subject matter experts
    • modeling firms are not willing to share proprietary information 
    • despite models being scientifically rational, it’s also a black box that can be used to inflate prices
    • still, regulators formed commissions made up of technical experts to certify model reasonableness
  18. California Earthquake Authority (CEA)
    • after 1996 Northridge EQ caused $b in losses, California legislature created CEA to avoid insurers leaving the market
    • constraints on CEA ratemaking: actuarially sound & scientific info must be consistent with available geophysical data and current knowledge of scientific community
  19. CEA challenges
    • recurrence rates: frequency used was twice as high as historical
    • time dependent probabilities: EQs are not time independent, except they used Poisson
    • damage estimates: damage curves used were based on just 1 event
    • underinsurance factor: modeled losses are expressed as % of TIV
    • demand surge: it's hard to quantify
    • policy sublimits: claims data wasn't detailed enough
    • rating plan deviation: grouped high and low risk for affordability reasons (potential adverse sln)
    • retrofit discount: 5+% discount to policyholder retrofitting their homes (not based on data)
  20. Open Issues for Using Cat Models to Determine Rates
    • regulatory acceptance: regulators don't have the technical expertise to assess models
    • public acceptance: acceptance is low, mostly because it results in higher rates
    • actuarial acceptance: need to get familiar with models, since it's outside of usual expertise
    • model-to-model variance: can be significant, should use one or more sub-models
  21. Actuarial Standards Board requirement re: cat models
    • determine appropriate reliance on experts
    • have a basic understanding of the model
    • evaluate whether the model is appropriate for the intended application
    • determine that appropriate validation has occurred
    • determine the appropriate use of the model
  22. Types of Uncertainty
    • aleatory: inherent randomness of natural hazard events; can't be reduced by collecting more data
    • epistemic: uncertainty due to lack of information or knowledge of the hazard (can be reduced)
  23. Sources of Uncertainty
    • limited scientific knowledge
    • lack of historical data, including specific gaps on GIS data, market values
    • cross disciplinary nature, as it's based on many assumptions from engineers, actuaries, seismology experts
    • laboratory testing of structural material has been limited to certain types of materials only
  24. Representing and Quantifying Uncertainty
    • logic trees: assign alternative parameter values for each model component, and compute the resulting weighted average result (can use credibility as weights); tractable and useful as a communication tool, but weights are often based on expert opinion (and thus biased)
    • simulation techniques: most widely used quantitative approach as it can be modelled as an extremely complex process; simulate each parameter value, then compute many sample runs
    • blended approach: used to create exceedance probability curve; instead of manually selecting the tree branches, use the simulation
  25. Catastrophe Modeling - Bottom-up approach
    • provides the most robust means to quantify portfolio risk
    • losses are first calculated at the location level based on 3 thresholds: exposure, limit, deductible
    • next all location losses are aggregated by policy, and then by portfolio
    • could also aggregate by zip code to limit exposure in high risk zones
  26. Special issues regarding Portfolio Risk
    • data quality: can reduce or increase degree of epistemic uncertainty depending on accuracy of data for construction type, building age, soil data, etc.
    • uncertainty modeling: can't only rely on μ and σ, we need the entire loss distribution
    • impact of correlation: diversification vs high concentration
  27. Considerations when adding a policy to a portfolio
    • magnitude of the risk
    • correlation with existing portfolio
    • highest price the risk is willing to pay
  28. 2 critical questions for Portfolio Managers re: cat risk
    • what is the average annual loss?
    • what is the likelihood that the insurer will go insolvent?