1. 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)
  2. Parties interested by catastrophe models
    • insurer & reinsurer
    • reinsurer broker (assess client risk)
    • capital mkt (cat-related products)
    • regulators
    • emergency mgt agencies (coordinate emergency response)
  3. 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
  4. 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
  5. Probable Maximum Loss (PML)
    Loss associated with a given low probability level
  6. 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, ...
  7. 2 criterias for an insr to provide covg
    • ability to identify & quantify event prob & loss severity
    • ability to set premiums for each potential customer
  8. Factors to consider when determining premium
    • balance btwn profitability & demand
    • state regulation
    • competition
    • uncertainty of losses
    • loss correlation
    • adverse selection
    • moral hazard
  9. 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
  10. Regular statistical tools vs cat modeling
    • often inappropriate
    • insufficient claim data
    • limited avail data usually inappropriate due to changing factors
  11. Hazard model main parameters
    • location
    • frequency
    • severity
    • historic data can only be used for initial prob dist
  12. 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
  13. 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)
  14. 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 / ...
  15. 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
  16. 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
  17. 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
  18. Insurance vs catastrophic losses
    • losses from hazards are highly correlated
    • insr need to maintain sufficient liquid assets → reflect opportunity cost in P
  19. 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
  20. Simple ratemaking model
    • P = AAL + Risk load + Expense Load
    • risk load depends on the uncertainty on AAL
    • Image Upload 1
  21. 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)
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
Card Set
Catastrophe Modeling: A New Appproach to Managing Risk