Catastrophe Assessment: Actuarial SOPs and Model Validation CAS Seminar on Catastrophe Issues New Orleans – October 22, 1998 Session 12 Panel: Douglas J. Collins Karen F. Terry Patrick B. Woods

Model Validation and Uncertainty Session 12 Panel: Presentation by Douglas J. Collins

3 Outline of presentation Catastrophe model validation and uncertainty How catastrophe models work Hurricane model validation types of validation validation data Model uncertainty

4 Science 1. Model Physical Event n Select a peril n Assess likelihood at location n Assess intensity, given location 1. Model Physical Event n Select a peril n Assess likelihood at location n Assess intensity, given location Engineering 2. Predict Damage n Values (building, contents, loss of use) n Vulnerability functions  building type  construction 2. Predict Damage n Values (building, contents, loss of use) n Vulnerability functions  building type  construction Insurance 3. Model Insured Claims n Limits relative to values n Deductibles n Ancillary exposures n Reinsurance 3. Model Insured Claims n Limits relative to values n Deductibles n Ancillary exposures n Reinsurance How catastrophe models work General logic

5 Meteorology 1. Model Storm Path and Intensity n Landfall probabilities n Minimum central pressure n Path properties n Windfield n Land friction effects 1. Model Storm Path and Intensity n Landfall probabilities n Minimum central pressure n Path properties n Windfield n Land friction effects Engineering 2. Predict Damage n Values (building, contents, loss of use) n Vulnerability functions  building type  construction 2. Predict Damage n Values (building, contents, loss of use) n Vulnerability functions  building type  construction Insurance 3. Model Insured Claims n Limits relative to values n Deductibles n Ancillary exposures n Reinsurance 3. Model Insured Claims n Limits relative to values n Deductibles n Ancillary exposures n Reinsurance How catastrophe models work Hurricane modeling

6 How catastrophe models work Hurricane windfield map

7 How catastrophe models work Historical event information

8 How catastrophe models work Models can create a robust set of events

9 How catastrophe models work Homeowners loss costs

10 Component validation probabilistic parameters (e.g., landfall probability) wind speeds vulnerability functions Micro validation compare modeled versus actual company losses  individual claim detail  various levels of aggregation Macro validation compare modeled versus actual industry losses by event compare probabilistic and historical size-of-loss distributions and loss costs Hurricane model validation Types of validation

11 Probabilistic parameters landfall probability minimum central pressure radius Wind validation – comparisons with anemometer readings National Hurricane Center reports 100-year winds Vulnerability function validation compare damage ratios by zip/coverage and wind speed with insurer claim data input from engineers Validation of model changes component changes logical software testing procedures Hurricane model validation Component validation

12 Hurricane model validation Component validation – landfall probability

13 Hurricane model validation Component validation – landfall probability

14 Aggregated company data by lob, coverage by county, zip by construction type, quality Individual claim detail  distributions of damage ratios  deductible effects  local land friction and land use effects Hurricane model validation Micro validation – modeled versus actual losses

15 Compare modeled versus actual industry losses by event requires estimate of industry exposures requires historical loss dataset tests for overall bias, consistency Compare probabilistic and historical loss distributions and loss costs size-of-loss distributions by state  actual and modeled historical versus probabilistic  return periods from 10 years to 100 years loss costs by state and county Hurricane model validation Macro validation

16 Hurricane model validation Constructing a macro validation dataset Data sources NWS total economic impact PCS insured losses Insurers and reinsurers special studies (AIRAC, Andrew) Methodology select best estimate of industry loss allocate to state and county trending  inflation (implicit price deflator)  current inventory of properties and values (real net stock of FRTW, housing units)  current insurance system (PCS versus NWS)

17 Hurricane model validation Comparison of PCS estimated and actual insured losses

18 Hurricane model validation Comparison of PCS estimated and actual insured losses

19 How catastrophe models work Macro validation dataset

20 How catastrophe models work Macro validation dataset

21 How catastrophe models work Macro validation dataset

22 Model uncertainty Why do different hurricane models produce different results? There is considerable uncertainty in estimating probabilities of rare events meteorological records ( years) paleo proxy studies (500-5,000 years) Hurricanes are complex systems the effect of landfall is not fully understood each storm has unique characteristics  microbursts, tornados, rainfall  demand surge There is considerable uncertainty in estimating damage at a given location Uncertainty depends on use of model PMLs versus loss costs

23 Model uncertainty How credible are the models? Average hurricane loss costs by county vary significantly between modelers in some counties in Florida this should not be surprising Models are continually being improved due to: growth in modeler resources growth in information opening the black boxes greater computer power There is no better alternative robust handling of nearly all possible scenarios historical insurance experience alone is insufficient use of multiple models is growing