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Catastrophe ModellingCatastrophe Modelling
GIROGIRO
1999 1999
Catastrophe ModellingCatastrophe Modelling
What did we do?What did we do? Why did we do it?Why did we do it? What this workshop will cover.What this workshop will cover.
What did we do?What did we do?
Discussed QUANTIFICATION of Discussed QUANTIFICATION of Catastrophe impactsCatastrophe impacts
From a practical point of viewFrom a practical point of view Questions rather than answersQuestions rather than answers Limitations of CAT modelsLimitations of CAT models London Market rather than domesticLondon Market rather than domestic Not aimed at Aggregate Cat XLNot aimed at Aggregate Cat XL
Why did we do it?Why did we do it?
Most members of WP had little Most members of WP had little Catastrophe experienceCatastrophe experience
Aimed at those with little Aimed at those with little experience - see issues faced by experience - see issues faced by other actuariesother actuaries
Areas for further actuarial inputAreas for further actuarial input Stimulate discussion rather than Stimulate discussion rather than
provide answersprovide answers
This workshopThis workshop
Aimed at entry-level to this subjectAimed at entry-level to this subject EarthquakeEarthquake Reinsurer’s perspectiveReinsurer’s perspective DIY model - components and DIY model - components and
problemsproblems Is understanding models a Is understanding models a
mandatory issue in the US?mandatory issue in the US?
QuantificationQuantification
Pricing: expectation, effect of Pricing: expectation, effect of reinsurance, ROE, ..reinsurance, ROE, ..
Exposure: PML aggregate, zonation, ..Exposure: PML aggregate, zonation, .. Reinsurance: vertical, horizontal, cost, Reinsurance: vertical, horizontal, cost,
allocation of cost to underwriters,..allocation of cost to underwriters,.. Capital: amount required, allocation, Capital: amount required, allocation,
DFA, ..DFA, .. Reserving: especially soon after eventReserving: especially soon after event
Examples of classes Examples of classes affectedaffected
Property Risk XLProperty Risk XL Direct & Facultative ExcessDirect & Facultative Excess Workers CompensationWorkers Compensation Personal AccidentPersonal Accident MarineMarine
1995/6 California PML 1995/6 California PML returns returns
PML Gross to Net PML Gross to Net San Francisco Residential Commercial TOTAL
Gross PML 3,393 8,336 11,729
Risk XL 4,120 4,120
Aggregate XL 2,088
Net PML 5,521
Overview of CAT modelOverview 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
Why aren’t CAT models Why aren’t CAT models the complete answer?the complete answer?
Non-primary businessNon-primary business Non-property classesNon-property classes Non-standard propertyNon-standard property Contract termsContract terms Not all territoriesNot all territories Expense/accessExpense/access
Example 1:Example 1: Facultative Excess Pricing Facultative Excess Pricing
Per occurrence coveragePer occurrence coverage
Warehouse Office Building
Factory
Fac Excess rating: non-CatFac Excess rating: non-Cat
Get the EML for each buildingGet the EML for each building for each of the 3 buildings determine a for each of the 3 buildings determine a
suitable rate to be applied to the EMLsuitable rate to be applied to the EML Apply suitable First Loss curve (FLC) to Apply suitable First Loss curve (FLC) to
allocate base premium to excess layer.allocate base premium to excess layer. Sum of rates for each.Sum of rates for each. Adjust for contagion, etc..Adjust for contagion, etc..
Fac excess rating : CatFac excess rating : Cat
Get TSI for eachGet TSI for each apply Cat rate on TSI to eachapply Cat rate on TSI to each sum TSI and sum Cat premiumssum TSI and sum Cat premiums use Cat FLC to allocate Cat use Cat FLC to allocate Cat
premiums to the excess layerpremiums to the excess layer
Fac excess rating - Fac excess rating - problemsproblems
there are no “market” Cat FLCs: there are no “market” Cat FLCs: underwriters use the non-Cat FLCunderwriters use the non-Cat FLC
The “correct” Cat FLC to use may vary The “correct” Cat FLC to use may vary depending on the location/zone depending on the location/zone
Ludwig’s Hugo curve was single event - Ludwig’s Hugo curve was single event - how do we allow for all possible events?how do we allow for all possible events?
The “correct” Cat FLC may also vary by The “correct” Cat FLC may also vary by other factors such as occupancy, age,.. other factors such as occupancy, age,..
Why can’t a CAT model be Why can’t a CAT model be used to solve this used to solve this
problem?problem?
CAT models are not generally CAT models are not generally designed to cope with large designed to cope with large deductiblesdeductibles
Lack of availability in many Lack of availability in many territoriesterritories
Example 2:Example 2:PML aggregate of Risk XLPML aggregate of Risk XL
Want to assess the PML exposure to Want to assess the PML exposure to various Cat.svarious Cat.s
Say three layers in program:Say three layers in program: 5M xs 5M xs 10M, 5 R/Is, 20M event 5M xs 5M xs 10M, 5 R/Is, 20M event
limitlimit 10M xs 10M, 2 R/Is, 20M event limit10M xs 10M, 2 R/Is, 20M event limit 30M xs 20M, 1 R/I, 30M event limit30M xs 20M, 1 R/I, 30M event limit
Why is this important?Why is this important?
Need to make sure that buy Need to make sure that buy enough vertical and horizontal enough vertical and horizontal reinsurancereinsurance
If too high then you’ll be wasting If too high then you’ll be wasting money buying too much money buying too much reinsurance at too much costreinsurance at too much cost
Make sure that underwriters are Make sure that underwriters are writing within their authoritywriting within their authority
Min Max Number Premium Rate1,000 2,000 5,632 25,344 0.30%2,000 3,000 3,012 20,331 0.27%3,000 5,000 1,526 14,833 0.24%5,000 10,000 754 12,367 0.22%
10,000 15,000 542 13,335 0.20%15,000 20,000 301 9,331 0.18%20,000 25,000 126 4,520 0.16%25,000 30,000 79 3,117 0.14%30,000 35,000 21 881 0.13%35,000 40,000 12 523 0.12%40,000 45,000 9 400 0.10%45,000 50,000 6 268 0.09%
Typical dataTypical data
EML profile and territorial splitEML profile and territorial split
UK
Europe
Africa
Middle East
Asia
Australasia
ProblemsProblems Territorial by premium%Territorial by premium% Territories are largeTerritories are large How to allow for aggregate deductibles, How to allow for aggregate deductibles,
event limits, reinstatements.event limits, reinstatements. Want TSI profile not EML profileWant TSI profile not EML profile Per occurrence coveragePer occurrence coverage Coverage erosion by attrition,other CatsCoverage erosion by attrition,other Cats XL on XLXL on XL
How could PML be How could PML be calculated?calculated?
Estimate a TSI risk profile by Estimate a TSI risk profile by suitable Cat zones.suitable Cat zones.
Apply a suitable PML Severity Apply a suitable PML Severity distribution to determine the distribution to determine the expected PML loss to each layerexpected PML loss to each layer
Allow for event limits to each Cat Allow for event limits to each Cat zonezone
Make allowance for attrition, second Make allowance for attrition, second event, aggregate deductibles etc.event, aggregate deductibles etc.
Why can’t a CAT model be Why can’t a CAT model be used to solve this used to solve this
problem?problem?
CAT models do not use exposure CAT models do not use exposure data in the form of a risk profiledata in the form of a risk profile
Need to allow for underlying Need to allow for underlying deductiblesdeductibles
CAT models work in the aggregate, CAT models work in the aggregate, not at the per risk level not at the per risk level
Explicit ModellingExplicit Modelling
Better understanding of CAT Better understanding of CAT models if we try to build one models if we try to build one ourselvesourselves
Ability to vary the assumptions to Ability to vary the assumptions to test the sensitivitytest the sensitivity
Able to slice the predicted Able to slice the predicted experience in more useful waysexperience in more useful ways
Useful for non-standard risksUseful for non-standard risks
A simple earthquake A simple earthquake modelmodel
Event moduleEvent module Return PeriodsReturn Periods Richter, Mercalli, PGARichter, Mercalli, PGA AttenuationAttenuation Damage moduleDamage module Insurance moduleInsurance module
Magnitude, Intensity, PGAMagnitude, Intensity, PGA
Magnitude : Richter, single number for Magnitude : Richter, single number for an event, eg RM 7.3an event, eg RM 7.3
Intensity: Mercalli, different values for Intensity: Mercalli, different values for an event, eg MM VIIIan event, eg MM VIII
PGA: Peak Ground Acceleration: PGA: Peak Ground Acceleration: measure of seismic shaking at a sitemeasure of seismic shaking at a site
How are these related?How are these related? Duration and frequencies also important Duration and frequencies also important
- Arias Intensity- Arias Intensity
Return PeriodsReturn Periods
Guttenberg-Richter: a.10Guttenberg-Richter: a.10-bM-bM
See Matthewson’s CAS paper for detailsSee Matthewson’s CAS paper for details For PML need to estimate magnitude For PML need to estimate magnitude
for given return period eg 200 yearsfor given return period eg 200 years Lack of historical data?Lack of historical data? Add 1 to RM scale means 32X energy Add 1 to RM scale means 32X energy
released, 10X shaking intensityreleased, 10X shaking intensity Location: specific or zone?Location: specific or zone?
Return periods - problemsReturn periods - problems
Lack of historical dataLack of historical data extrapolation from G-R functionextrapolation from G-R function Historical data may need to be Historical data may need to be
converted from MM to RMconverted from MM to RM Conversion of RM to epicentral PGAConversion of RM to epicentral PGA
General level of seismicityGeneral level of seismicity
AttenuationAttenuation
Shows how the intensity decreases Shows how the intensity decreases with distance from rupturewith distance from rupture
Usual form : Usual form : Ln(PGA) = a +b.Ln(R +C(M))Ln(PGA) = a +b.Ln(R +C(M)) R = hypocentral distanceR = hypocentral distance R approx =-1, though wide variation R approx =-1, though wide variation
by underlying geologyby underlying geology Also local soil conditions importantAlso local soil conditions important
Attenuation-problemsAttenuation-problems
Depends on rupture depth - which Depends on rupture depth - which is difficult to obtainis difficult to obtain
Seismologists understand Seismologists understand attenuation from deep ruptures attenuation from deep ruptures better than shallowbetter than shallow
Affected by factors such as Affected by factors such as mountain ranges, riversmountain ranges, rivers
Kobe 1995 attenuationKobe 1995 attenuation
IsoseismalsIsoseismals
Use the attenuation function to obtain Use the attenuation function to obtain PGA at distance from rupturePGA at distance from rupture
Use table to convert from PGA to MMUse table to convert from PGA to MM Could miss this step if damage Could miss this step if damage
function based on PGAfunction based on PGA Not circular due to length of ruptureNot circular due to length of rupture
Isoseismals - problemsIsoseismals - problems
PGA continuous, MM discretePGA continuous, MM discrete PGA doesn’t include duration of PGA doesn’t include duration of
shaking, but MM does implicitly, so shaking, but MM does implicitly, so not exact correlationnot exact correlation
PGA not well correlated to damagePGA not well correlated to damage
Examples of isoseismal Examples of isoseismal mapsmaps
Damage functionDamage function
Used to convert MM at location into Used to convert MM at location into repair cost as % of total valuerepair cost as % of total value
Engineers’ measures of damage not Engineers’ measures of damage not directly useful as don’t show repair cost directly useful as don’t show repair cost as % of valueas % of value
Vary by a range of factors such as age, Vary by a range of factors such as age, height, construction, occupancy,…height, construction, occupancy,…
Vary for Buildings, contents, BIVary for Buildings, contents, BI ATC-13 is the source report ATC-13 is the source report
Damage vs Intensity Damage vs Intensity (NHRC)(NHRC)
Damage vs Magnitude Damage vs Magnitude (NHRC)(NHRC)
Damage - problemsDamage - problems ATC-13 or similar may not be ATC-13 or similar may not be
appropriate for all territoriesappropriate for all territories Conversion from ATC-13 categories to Conversion from ATC-13 categories to
other classification systemsother classification systems Not available for unusual risksNot available for unusual risks Not available for other classesNot available for other classes FFQ, inundation, liquifaction, landslide,..FFQ, inundation, liquifaction, landslide,.. Business interruptionBusiness interruption
Damage - problemsDamage - problems
Do the damage % refer to amounts Do the damage % refer to amounts above a notional insurance above a notional insurance deductible?deductible?
Demand surge inflation? Eg cost of Demand surge inflation? Eg cost of bricks, carpenters, etc..bricks, carpenters, etc..
MM is a discrete scale, but damage MM is a discrete scale, but damage is continuousis continuous
Fraud, loss adjustment, ...Fraud, loss adjustment, ...
Variation of Damage Variation of Damage
Similar, adjacent properties will not Similar, adjacent properties will not suffer same % damagesuffer same % damage
Pounding, design, construction, Pounding, design, construction, occupancy, time of day, day of occupancy, time of day, day of week, preparedness, FFQ, ….week, preparedness, FFQ, ….
Some authors suggest lognormalSome authors suggest lognormal
Example distribution for Example distribution for MM X eventMM X event
Assumed distribution by MM
0%
20%
40%
60%
80%
100%
0 20 40 60 80 100 120
VI
VII
VIII
IX
X
Weighted
FGU loss costFGU loss cost
Convert the isoseismal map into an Convert the isoseismal map into an “isodamage” map“isodamage” map
Estimate the exposure in each of Estimate the exposure in each of the band of the isoseismal.the band of the isoseismal.
Multiply to get the amount of Multiply to get the amount of damagedamage
Per-risk, by risk profile band, or in Per-risk, by risk profile band, or in aggregate, depending on useaggregate, depending on use
FGU loss cost - problemsFGU loss cost - problems
Where is the epicentre?Where is the epicentre? Where is the exposure relative to Where is the exposure relative to
the epicentre?the epicentre? How do you allow for those How do you allow for those
exposures which suffer no exposures which suffer no damage?damage?
PML estimation using PML estimation using modelmodel
Work out/estimate location of Work out/estimate location of exposure in a zone.exposure in a zone.
Assume that PML event occurs at Assume that PML event occurs at greatest concentration of greatest concentration of exposure?exposure?
Estimate MM at given PML return Estimate MM at given PML return periodperiod
SummarySummary
CAT models don’t yet provide all the CAT models don’t yet provide all the answersanswers
Useful to know roughly how they workUseful to know roughly how they work Useful to understand the limitations of Useful to understand the limitations of
their componentstheir components We can make simple models ourselvesWe can make simple models ourselves Useful to be able to calibrate in-house Useful to be able to calibrate in-house
against external modelsagainst external models