Catastrophe Modelling

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
• Reinsurers 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 arent 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
• Ludwigs 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 cant 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 2PML 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 youll 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 cant 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 Matthewsons 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 doesnt include duration of shaking, but MM
  does implicitly, so not exact correlation
• PGA not well correlated to damage

33
Examples of isoseismal maps
34
(No Transcript)
35
(No Transcript)
36
Damage function

• Used to convert MM at location into repair cost
  as of total value
• Engineers measures of damage not directly useful
  as dont 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

37
Damage vs Intensity (NHRC)
38
Damage vs Magnitude (NHRC)
39
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

40
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, ...

41
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

42
Example distribution for MM X event
43
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

44
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?

45
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

46
Summary

• CAT models dont 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