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