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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