1. Catastrophe Modelling GIRO1999

2. n What did we do? n Why did we do it? n What this workshop will cover.

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

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

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

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

7. Examples of classes affected n Property Risk XL n Direct & Facultative Excess n Workers Compensation n Personal Accident n 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? n Non-primary business n Non-property classes n Non-standard property n Contract terms n Not all territories n Expense/access

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

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

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

14. Fac excess rating - problems n there are no “market” Cat FLCs: underwriters use the non-Cat FLC n The “correct” Cat FLC to use may vary depending on the location/zone n Ludwig’s Hugo curve was single event - how do we allow for all possible events? n 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? n CAT models are not generally designed to cope with large deductibles n Lack of availability in many territories

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

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

18. Typical data n EML profile and territorial split

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

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

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

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

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

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

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

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

27. General level of seismicity

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

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

30. Kobe 1995 attenuation

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

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

33. Examples of isoseismal maps

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

37. Damage vs Intensity (NHRC)

38. Damage vs Magnitude (NHRC)

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

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

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

42. Example distribution for MM X event

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

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

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

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