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Catastrophe Modelling

Catastrophe Modelling. GIRO 1999. Catastrophe Modelling. What did we do? Why did we do it? What this workshop will cover. What did we do?. Discussed QUANTIFICATION of Catastrophe impacts From a practical point of view Questions rather than answers Limitations of CAT models

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Catastrophe Modelling

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  1. Catastrophe Modelling GIRO 1999

  2. Catastrophe Modelling • What did we do? • Why did we do it? • What this workshop will cover.

  3. What did we do? • Discussed QUANTIFICATION of Catastrophe impacts • From a practical point of view • Questions rather than answers • Limitations of CAT models • London Market rather than domestic • Not aimed at Aggregate Cat XL

  4. Why did we do it? • Most members of WP had little Catastrophe experience • Aimed at those with little experience - see issues faced by other actuaries • Areas for further actuarial input • Stimulate discussion rather than provide answers

  5. This workshop • Aimed at entry-level to this subject • Earthquake • Reinsurer’s perspective • DIY model - components and problems • Is understanding models a mandatory issue in the US?

  6. Quantification • Pricing: expectation, effect of reinsurance, ROE, .. • Exposure: PML aggregate, zonation, .. • Reinsurance: vertical, horizontal, cost, allocation of cost to underwriters,.. • Capital: amount required, allocation, DFA, .. • Reserving: especially soon after event

  7. Examples of classes affected • Property Risk XL • Direct & Facultative Excess • Workers Compensation • Personal Accident • Marine

  8. 1995/6 California PML returns PML Gross to Net

  9. Overview of CAT model Event : Generates a stochastic set of events quantified in terms of objective measures. e.g. windspeeds Damage : Converts physical measures into damage as % of total value. Insurance : Converts damage to property into amount recoverable from the insurance

  10. Why aren’t CAT models the complete answer? • Non-primary business • Non-property classes • Non-standard property • Contract terms • Not all territories • Expense/access

  11. Example 1: Facultative Excess Pricing • Per occurrence coverage Office Building Warehouse Factory

  12. Fac Excess rating: non-Cat • Get the EML for each building • for each of the 3 buildings determine a suitable rate to be applied to the EML • Apply suitable First Loss curve (FLC) to allocate base premium to excess layer. • Sum of rates for each. • Adjust for contagion, etc..

  13. Fac excess rating : Cat • Get TSI for each • apply Cat rate on TSI to each • sum TSI and sum Cat premiums • use Cat FLC to allocate Cat premiums to the excess layer

  14. Fac excess rating - problems • there are no “market” Cat FLCs: underwriters use the non-Cat FLC • The “correct” Cat FLC to use may vary depending on the location/zone • Ludwig’s Hugo curve was single event - how do we allow for all possible events? • The “correct” Cat FLC may also vary by other factors such as occupancy, age,..

  15. Why can’t a CAT model be used to solve this problem? • CAT models are not generally designed to cope with large deductibles • Lack of availability in many territories

  16. Example 2:PML aggregate of Risk XL • Want to assess the PML exposure to various Cat.s • Say three layers in program: • 5M xs 5M xs 10M, 5 R/Is, 20M event limit • 10M xs 10M, 2 R/Is, 20M event limit • 30M xs 20M, 1 R/I, 30M event limit

  17. Why is this important? • Need to make sure that buy enough vertical and horizontal reinsurance • If too high then you’ll be wasting money buying too much reinsurance at too much cost • Make sure that underwriters are writing within their authority

  18. Typical data • EML profile and territorial split

  19. Problems • Territorial by premium% • Territories are large • How to allow for aggregate deductibles, event limits, reinstatements. • Want TSI profile not EML profile • Per occurrence coverage • Coverage erosion by attrition,other Cats • XL on XL

  20. How could PML be calculated? • Estimate a TSI risk profile by suitable Cat zones. • Apply a suitable PML Severity distribution to determine the expected PML loss to each layer • Allow for event limits to each Cat zone • Make allowance for attrition, second event, aggregate deductibles etc.

  21. Why can’t a CAT model be used to solve this problem? • CAT models do not use exposure data in the form of a risk profile • Need to allow for underlying deductibles • CAT models work in the aggregate, not at the per risk level

  22. Explicit Modelling • Better understanding of CAT models if we try to build one ourselves • Ability to vary the assumptions to test the sensitivity • Able to slice the predicted experience in more useful ways • Useful for non-standard risks

  23. A simple earthquake model • Event module • Return Periods • Richter, Mercalli, PGA • Attenuation • Damage module • Insurance module

  24. Magnitude, Intensity, PGA • Magnitude : Richter, single number for an event, eg RM 7.3 • Intensity: Mercalli, different values for an event, eg MM VIII • PGA: Peak Ground Acceleration: measure of seismic shaking at a site • How are these related? • Duration and frequencies also important - Arias Intensity

  25. Return Periods • Guttenberg-Richter: a.10-bM • See Matthewson’s CAS paper for details • For PML need to estimate magnitude for given return period eg 200 years • Lack of historical data? • Add 1 to RM scale means 32X energy released, 10X shaking intensity • Location: specific or zone?

  26. Return periods - problems • Lack of historical data • extrapolation from G-R function • Historical data may need to be converted from MM to RM • Conversion of RM to epicentral PGA

  27. General level of seismicity

  28. Attenuation • Shows how the intensity decreases with distance from rupture • Usual form : • Ln(PGA) = a +b.Ln(R +C(M)) • R = hypocentral distance • R approx =-1, though wide variation by underlying geology • Also local soil conditions important

  29. Attenuation-problems • Depends on rupture depth - which is difficult to obtain • Seismologists understand attenuation from deep ruptures better than shallow • Affected by factors such as mountain ranges, rivers

  30. Kobe 1995 attenuation

  31. Isoseismals • Use the attenuation function to obtain PGA at distance from rupture • Use table to convert from PGA to MM • Could miss this step if damage function based on PGA • Not circular due to length of rupture

  32. Isoseismals - problems • PGA continuous, MM discrete • PGA doesn’t include duration of shaking, but MM does implicitly, so not exact correlation • PGA not well correlated to damage

  33. Examples of isoseismal maps

  34. Damage function • Used to convert MM at location into repair cost as % of total value • Engineers’ measures of damage not directly useful as don’t show repair cost as % of value • Vary by a range of factors such as age, height, construction, occupancy,… • Vary for Buildings, contents, BI • ATC-13 is the source report

  35. Damage vs Intensity (NHRC)

  36. Damage vs Magnitude (NHRC)

  37. Damage - problems • ATC-13 or similar may not be appropriate for all territories • Conversion from ATC-13 categories to other classification systems • Not available for unusual risks • Not available for other classes • FFQ, inundation, liquifaction, landslide,.. • Business interruption

  38. Damage - problems • Do the damage % refer to amounts above a notional insurance deductible? • Demand surge inflation? Eg cost of bricks, carpenters, etc.. • MM is a discrete scale, but damage is continuous • Fraud, loss adjustment, ...

  39. Variation of Damage • Similar, adjacent properties will not suffer same % damage • Pounding, design, construction, occupancy, time of day, day of week, preparedness, FFQ, …. • Some authors suggest lognormal

  40. Example distribution for MM X event

  41. FGU loss cost • Convert the isoseismal map into an “isodamage” map • Estimate the exposure in each of the band of the isoseismal. • Multiply to get the amount of damage • Per-risk, by risk profile band, or in aggregate, depending on use

  42. FGU loss cost - problems • Where is the epicentre? • Where is the exposure relative to the epicentre? • How do you allow for those exposures which suffer no damage?

  43. PML estimation using model • Work out/estimate location of exposure in a zone. • Assume that PML event occurs at greatest concentration of exposure? • Estimate MM at given PML return period

  44. Summary • CAT models don’t yet provide all the answers • Useful to know roughly how they work • Useful to understand the limitations of their components • We can make simple models ourselves • Useful to be able to calibrate in-house against external models

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