cas annual meeting new orleans, la new orleans, la november 10, 2003 jonathan hayes, acas, maaa...
DESCRIPTION
Florida Hurricane Amounts in Millions USDTRANSCRIPT
CAS Annual MeetingCAS Annual Meeting New Orleans, LANew Orleans, LA
November 10, 2003November 10, 2003Jonathan Hayes, ACAS, MAAAJonathan Hayes, ACAS, MAAA
UNCERTAINTY AROUND UNCERTAINTY AROUND MODELED LOSS ESTIMATESMODELED LOSS ESTIMATES
AgendaAgenda ModelsModels
Model ResultsModel Results Confidence BandsConfidence Bands
DataData Issues with DataIssues with Data Issues with InputsIssues with Inputs Model OutputsModel Outputs
Company ApproachesCompany Approaches Role of JudgmentRole of Judgment ConclusionsConclusions
Florida HurricaneFlorida Hurricane
Amounts in Millions USD
Return Period A B C 20 249 217 233 50 593 467 545 100 1,056 757 820 250 1,924 1,148 1,197
Annual Average 58.9 46.8 44.3
Mean, unitized 126 100 95 100, unitized 139 100 108 250, unitized 168 100 104
100/20 424% 349% 352%250/100 182% 152% 146%
Model
Florida HurricaneFlorida Hurricane
Event Loss A B C
250 95.0% 95.4% 95.2%500 97.2% 98.4% 97.6%750 98.3% 99.0% 98.7%
1000 98.9% 99.4% 99.3%
Non-Exceedance Probability (Approx)
Amounts in Millions USD
Modeled Event LossModeled Event LossSample Portfolio, Total EventSample Portfolio, Total Event
Modeled Event LossModeled Event LossBy State DistributionBy State Distribution
Modeled Event LossModeled Event LossBy County Distribution, State SBy County Distribution, State S
AgendaAgenda ModelsModels
Model ResultsModel Results Confidence BandsConfidence Bands
DataData Issues with DataIssues with Data Issues with InputsIssues with Inputs Model OutputsModel Outputs
Company ApproachesCompany Approaches Role of JudgmentRole of Judgment ConclusionsConclusions
Types Of UncertaintyTypes Of Uncertainty(In Frequency & Severity)(In Frequency & Severity)
Uncertainty (not randomness)Uncertainty (not randomness) Sampling ErrorSampling Error
100 years for hurricane100 years for hurricane Specification ErrorSpecification Error
FCHLPM sample dataset (1996) 1 in 100 OEP of 31m, 38m, FCHLPM sample dataset (1996) 1 in 100 OEP of 31m, 38m, 40m & 57m w/ 4 models40m & 57m w/ 4 models
Non-sampling ErrorNon-sampling Error El Nino Southern OscillationEl Nino Southern Oscillation
Knowledge UncertaintyKnowledge Uncertainty Time dependence, cascading, aseismic shift, Time dependence, cascading, aseismic shift,
poisson/negative binomialpoisson/negative binomial Approximation ErrorApproximation Error
Res Re cat bond: 90% confidence interval, process risk Res Re cat bond: 90% confidence interval, process risk only, of +/- 20%, per modeling firmonly, of +/- 20%, per modeling firm
Source: Major, Op. Cit..
Frequency-Severity UncertaintyFrequency-Severity UncertaintyFrequency Uncertainty (Miller)Frequency Uncertainty (Miller)
Frequency UncertaintyFrequency Uncertainty Historical set: 96 years, 207 hurricanesHistorical set: 96 years, 207 hurricanes Sample mean is 2.16Sample mean is 2.16 What is range for true mean?What is range for true mean?
Bootstrap methodBootstrap method New 96-yr sample sets: Each sample set New 96-yr sample sets: Each sample set
is 96 draws, with replacement, from is 96 draws, with replacement, from originaloriginal
Review ResultsReview Results
Frequency BootstrappingFrequency Bootstrapping Run 500 resamplings and graph relative Run 500 resamplings and graph relative
to theoretical t-distributionto theoretical t-distribution
Source: Miller, Op. Cit.
Frequency Uncertainty StatsFrequency Uncertainty Stats
Standard error (SE) of the mean:Standard error (SE) of the mean:
0.159 historical SE 0.159 historical SE 0.150 theoretical SE, assuming 0.150 theoretical SE, assuming
Poisson, i.e., (lambda/n)^0.5Poisson, i.e., (lambda/n)^0.5
Hurricane Freq. UncertaintyHurricane Freq. UncertaintyBack of the EnvelopeBack of the Envelope
Frequency Uncertainty OnlyFrequency Uncertainty Only 96 Years, 207 Events, 3100 coast miles96 Years, 207 Events, 3100 coast miles 200 mile hurricane damage diameter200 mile hurricane damage diameter 0.139 is avg annl # storms to site0.139 is avg annl # storms to site SE = 0.038, SE = 0.038, assuming Poisson frequencyassuming Poisson frequency
90% CI is loss +/- 45%90% CI is loss +/- 45% i.e., (1.645 * 0.038) / 0.139i.e., (1.645 * 0.038) / 0.139
Frequency-Severity UncertaintyFrequency-Severity UncertaintySeverity Uncertainty (Miller)Severity Uncertainty (Miller)
Parametric bootstrapParametric bootstrap Cat model severity for some portfolio Cat model severity for some portfolio Fit cat model severity to parametric modelFit cat model severity to parametric model Perform X draws of Y severities, where X Perform X draws of Y severities, where X
is number of frequency resamplings and Y is number of frequency resamplings and Y is number of historical hurricanes in setis number of historical hurricanes in set
Parameterize the new sampled severitiesParameterize the new sampled severities Compound with frequency uncertaintyCompound with frequency uncertainty Review confidence bandsReview confidence bands
OEP Confidence BandsOEP Confidence Bands
Source: Miller, Op. Cit.
Model 1 in 50 1 in 100 1 in 250
A 127 139 168B 100 100 100C 117 104 108
FL HURRICANE EXAMPLE, REVISITED
OEP Confidence BandsOEP Confidence Bands At 80-1,000 year return, range fixes to 50% to At 80-1,000 year return, range fixes to 50% to
250% of best estimate OEP250% of best estimate OEP Confidence band grow exponentially at Confidence band grow exponentially at
frequent OEP points because expected loss frequent OEP points because expected loss goes to zerogoes to zero
NotesNotes Assumed stationary climateAssumed stationary climate Severity parameterization may introduce errorSeverity parameterization may introduce error Modelers’ “secondary uncertainty” may overlap Modelers’ “secondary uncertainty” may overlap
here, thus reducing rangehere, thus reducing range Modelers’ severity distributions based on more Modelers’ severity distributions based on more
than just historical data setthan just historical data set
AgendaAgenda ModelsModels
Model ResultsModel Results Confidence BandsConfidence Bands
DataData Issues with DataIssues with Data Issues with InputsIssues with Inputs Model OutputsModel Outputs
Company ApproachesCompany Approaches Role of JudgmentRole of Judgment ConclusionsConclusions
Data Collection/InputsData Collection/Inputs Is this all the subject data?Is this all the subject data?
All/coastal statesAll/coastal states Inland Marine, Builders Risk, APD, Dwelling FireInland Marine, Builders Risk, APD, Dwelling Fire Manual policiesManual policies
General level of detailGeneral level of detail County/zip/streetCounty/zip/street Aggregated dataAggregated data
Is this all the needed policy detail?Is this all the needed policy detail? Building location/billing locationBuilding location/billing location Multi-location policies/bulk dataMulti-location policies/bulk data Statistical Record vs. policy systemsStatistical Record vs. policy systems Coding of endorsementsCoding of endorsements
Sublimits, wind exclusions, IMSublimits, wind exclusions, IM Replacement cost vs. limitReplacement cost vs. limit
More Data IssuesMore Data Issues
Deductible issuesDeductible issues Inuring/facultative reinsuranceInuring/facultative reinsurance Extrapolations & defaultsExtrapolations & defaults Blanket policiesBlanket policies HPRHPR Excess policiesExcess policies
Model OutputModel Output Data Imported/Not ImportedData Imported/Not Imported Geocoded/Not GeocodedGeocoded/Not Geocoded VersionVersion Perils RunPerils Run
Demand SurgeDemand Surge Storm SurgeStorm Surge Fire FollowingFire Following
DefaultsDefaults Construction MappingsConstruction Mappings Secondary CharacteristicsSecondary Characteristics
Secondary UncertaintySecondary Uncertainty DeductiblesDeductibles
AgendaAgenda ModelsModels
Model ResultsModel Results Confidence BandsConfidence Bands
DataData Issues with DataIssues with Data Issues with InputsIssues with Inputs Model OutputsModel Outputs
Company ApproachesCompany Approaches Role of JudgmentRole of Judgment ConclusionsConclusions
Company ApproachesCompany ApproachesAvailable ChoicesAvailable Choices
Output From:Output From: 2-5 Vendor Models2-5 Vendor Models
Detailed & Aggregate ModelsDetailed & Aggregate Models ECRA FactorsECRA Factors Experience, ParameterizedExperience, Parameterized
Select (weighted) AverageSelect (weighted) Average
Company ApproachesCompany ApproachesLoss CostsLoss Costs
Arithmetic averageArithmetic average Subject to changeSubject to change Significant u/w flexibilitySignificant u/w flexibility
Weighted averageWeighted average Weights by region, peril, class et al.Weights by region, peril, class et al. Weights determined by:Weights determined by:
Model reviewModel review Consultation with modeling firmsConsultation with modeling firms Historical event analysisHistorical event analysis JudgmentJudgment
Weight changes require formal sign-offWeight changes require formal sign-off
ConclusionsConclusions Cat Model Distributions VaryCat Model Distributions Vary
More than one point estimate usefulMore than one point estimate useful Point estimates may not be Point estimates may not be significantlysignificantly different different Uncertainty not insignificant but not insurmountableUncertainty not insignificant but not insurmountable What about uncertainty before cat models?What about uncertainty before cat models?
Data Inputs MatterData Inputs Matter Not mechanical processNot mechanical process Creating model inputs requires many decisionsCreating model inputs requires many decisions User knowledge and expertise criticalUser knowledge and expertise critical
Loss Cost Selection Methodology MattersLoss Cost Selection Methodology Matters # Models used more influential than weights used# Models used more influential than weights used
Judgment UnavoidableJudgment Unavoidable Actuaries already well-versed in its useActuaries already well-versed in its use
ReferencesReferences Bove, Mark C. et al.., “Effect of El Nino on US Landfalling Bove, Mark C. et al.., “Effect of El Nino on US Landfalling
Hurricanes, Revisited,”Hurricanes, Revisited,” Bulletin of the American Meteorological Bulletin of the American Meteorological SocietySociety, June 1998., June 1998.
Efron, Bradley and Robert Tibshirani, Efron, Bradley and Robert Tibshirani, An Introduction to the An Introduction to the BootstrapBootstrap, New York: Chapman & Hall, 1993., New York: Chapman & Hall, 1993.
Major, John A., “Uncertainty in Catastrophe Models,” Major, John A., “Uncertainty in Catastrophe Models,” Financing Financing Risk and ReinsuranceRisk and Reinsurance, International Risk Management Institute, , International Risk Management Institute, Feb/Mar 1999.Feb/Mar 1999.
Miller, David, “Uncertainty in Hurricane Risk Modeling and Miller, David, “Uncertainty in Hurricane Risk Modeling and Implications for Securitization,” Implications for Securitization,” CAS Forum,CAS Forum, Spring 1999. Spring 1999.
Moore, James F., “Tail Estimation and Catastrophe Security Moore, James F., “Tail Estimation and Catastrophe Security Pricing: Cat We Tell What Target We Hit If We Are Shooting in the Pricing: Cat We Tell What Target We Hit If We Are Shooting in the Dark”, Dark”, Wharton Financial Institutions CenterWharton Financial Institutions Center, 99-14., 99-14.