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4 components of catastrophe models
- hazard: produces the parameters of the catastrophe
- inventory: pf info (location, construction type, age, ...)
- vulnerability: susceptibility of the properties to damage
- loss: generates $ loss (direct & indirect)
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Parties interested by catastrophe models
- insurer & reinsurer
- reinsurer broker (assess client risk)
- capital mkt (cat-related products)
- regulators
- emergency mgt agencies (coordinate emergency response)
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Exceedance Probability (EP) curve
- indicates probability that a specific loss level will be surpassed during a given period
- insurers can use it to decide how much risk to transfer
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EP formulas
- assume only 1 loss can occur annually
- EP(Li) = p(L≥Li) = 1 - p(L≤Li) = 1 - Π(1-pi)Average Annual Loss = AAL = ΣpiLi
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Probable Maximum Loss (PML)
Loss associated with a given low probability level
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Segmenting EP curve
- general case: 3 parties involved = insd (ded), insr (lim), reinsr
- each has its own EP curve allocated
- each can decide how to price, how much covg needed, ...
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2 criterias for an insr to provide covg
- ability to identify & quantify event prob & loss severity
- ability to set premiums for each potential customer
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Factors to consider when determining premium
- balance btwn profitability & demand
- state regulation
- competition
- uncertainty of losses
- loss correlation
- adverse selection
- moral hazard
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Determining whether to provide coverage
- insr wants prob of insolvency to be less than p1
- assume each prop has prem Z, surplus A
- if p(loss > n * Z + A) < p1 we can keep growing
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Regular statistical tools vs cat modeling
- often inappropriate
- insufficient claim data
- limited avail data usually inappropriate due to changing factors
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Hazard model main parameters
- location
- frequency
- severity
- historic data can only be used for initial prob dist
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Inventory model
- most of the data comes from governmt
- data includes # prop & value by LOB / Occupancy / Covg / Construction Type
- insr may incorporate more risk-specific info
- identify missing & erroneous data, test for reasonability
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Vulnerability model
- estimate damage to properties
- engineering judgment: (+) simpler (-) arbitrary (-) hard to update
- building response analyses based on advanced engineering techniques (+) more accurate (-) inappropriate for assessment of entire pf (tailored towards specific buildg)
- tweak prev method: split pf into classes; identify typical buildg; evaluate buildg performance (damage fctn) (damage ratio = repair cost / replacement)
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Loss model
- link parameters of the event directly into $ (opinion based) (+) more straightforward (-) hard to update
- determine physical damage from event & use engineering to convert to $
- finally derive insd loss considering limits / ded / coins / ...
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2 types of cat model uncertainty
- Aleatory: inherent randomness associated w natural hazard events. Usually reflected in prob dist
- Epistemic: due to lack of info / knowledge of hazard
- not necessary to distinguish, make sure not ignored or double counted
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Sources of epistemic uncertainty
- limited scientific knowledge
- limited historic data
- cross-disciplinary nature of cat (seism, meteo, engineer)
- lack of data to create GIS database
- limited laboratory testing on certain types of materials
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2 methods to incorporate uncertainty
- logic tree: displays param or math relationship along w weights (+) tractability & usefulness to communicate risk
- simulation techniques: can be used for more complex scenarios or to derive prob dist (+) more accurate
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Insurance vs catastrophic losses
- losses from hazards are highly correlated
- insr need to maintain sufficient liquid assets → reflect opportunity cost in P
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4 principles that determine whether a rate is actuarially sound, reasonable and not unfairly discriminatory
- a rate needs to be an estimate of the expected value of future costs
- a rate provides for all costs associated with the transfer of risk
- a rate provides for the cost associated w indiv risk transfer
- a rate is reasonable & not excessive, adequate, or not unfairly discriminatory if it is an actuarially sound estimate of the exp value of all future costs associated w individual risk transfer
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Simple ratemaking model
- P = AAL + Risk load + Expense Load
- risk load depends on the uncertainty on AAL
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2 most important cat model factors to diff btwn risks
- structure attribute of a pf (inventory cpnts) determine physical performance of building
- location attribute (proximity / succeptibility to hazard)
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Regulation & cat modeling
- can use cat modeling to help educate regulators
- regulators historically not supportive since (1) requires expertise and (2) modeling firms want to protect proprietary info
- (+) provides scientifically rational approach
- (-) can be used to justify rate increase
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Case study: California EQ Authority (CEA)
- formed after insr concerned w EQ threatened to leave mkt
- 2 rate constraints: actuarially sound, scientific info consistent w avail geophysical data & current knowledge
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Major issues w CEA model
- EQ recurrence rates: more than twice historical record
- uncertainty around time dependant probabilities
- damage curve based mainly on Northridge EQ
- model loss = % of bldg value → understated if val < replacmt
- diff to determine degree of demand surge
- model can't account for CEA policy features
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Open issues on cat model
- regulatory acceptance: no technical expertise
- public acceptance: low because results in higher rates
- actuarial acceptance: lie outside of actuary's usual experise but ASB requires reliance on experts; basic understanding; determine appropriate use of model
- model to model variance: often significant btwn models
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Pf composition
- Residential: simple structure. Covers bldg, ctnt, living exp. Insr has detailed data
- Commercial: may have several loc w high replacemt cost, need for highly detailed data
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Factors to consider when deciding whether to add account to pf
- magnitude of the risk
- correlation w existing pf
- highest price the risk is willing to pay
- cat model = transparent method of evaluating impact of new risk
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Cat modeling: bottom-up approach
- calculate loss for insd & insr at the location lvl
- aggregate all locations losses by policy
- aggregate all losses
- all steps based on current pf
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2 critical questions when facing cat risk
- what is AAL
- what's the likelihood that the insr would go insolvent → need a good model for right EP tail
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Special issues regarding pf risk
- data quality: need to ensure it's accurate to reduce epistemic uncertainty
- uncertainty modeling: losses should not be allocated to parties based solely on exp value
- impact of correlation: impacts amt of diversification
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