Predictive Modeling and By-Peril Analysis for Homeowners Insurance

Transcription

1 Predictive Modeling and By-Peril Analysis for Homeowners Insurance Contents Case for by-peril modeling By-peril model building Data Peril grouping Variables Interactions By-peril territories Model validation Conclusion Case for by-peril modeling Modeling options All peril losses combined Regional players Limited number of states with fairly constant peril mix True by-peril modeling Separate by-peril Average the true by-peril estimates Increased aggregated into Practical to do if legacy systems can only implement one accuracy single rate set of rates True by-peril rating Conceptually makes sense Certain variables are predictive for certain perils (e.g. fire protective devices are predictive for the fire peril) Responsive to state peril mix differences and changes in those

2 Case for by-peril modeling Root mean error (smaller is better) True by-peril Aggregate byperil rate (M) Aggregate byperil rate (M) Significant difference in predictive e accuracy All peril losses combined 4 By-peril model building: data staging Data options Years used Balance volume with recency to reflect an appropriate mix of business Data used Internal data used for non-catastrophes Simulated data for catastrophes Data split Modeling/testing/validation Modeling/validation Out of time data split Out of sample data split 5 By-peril model building: peril grouping Grouping or peril separation Theft Disappearance/theft on premises Disappearance/theft off premises Liability Liability/Medical payments Fire Human-made fire Environmental fire Water Weather water Non-weather water Grouping or breaking of perils -- considerations Availability of detailed/accurate peril codes from claims Is the correct cause of loss captured? Wind or hail damage to the roof? Are there additional peril code break-outs available? Grouping or breaking Use judgment, intuition, similarity Electrical l fire Grease fire from kitchen Fire from candles Fire from cigarette smoking Children playing with matches Fireplace fire Fire caused by electrical appliance Other Aircraft Vehicles 6

3 By-peril model building: data staging Practical considerations Indications for appropriate rate level Systems cost trade off cost benefit analysis of by-peril implementation Time constraints / speed to market / will dictate some of the options Impact on other departments: claims, systems, pricing/actuarial, financial i reporting 7 By-peril model building: variable selection House characteristics Amount of insurance Number of stories Number of rooms Square footage Age of electrical Age of home Age of plumbing Age of roof Roof material Construction type Protective devices Occupant characteristics Age Gender Marital status Insurance score Occupation/retired Number of occupants Prior claim activity Other personal lines Full payment/installments Billing lapse Good payer Location and / or External variables Weather Temperature Precipitation Elevation Slope Geography Commercial business Protection class Demographics Density Which variables are predictive for which peril? Financial variables 8 By-peril model building: variable selection Univariate analysis Amount of Insurance (bucketed).%.8 9.%.6 8.%.4 7.%. 6.% 5.%.8 4.%.6.%.4.%..%.% Exposure Indicated + SE SE Predictability by peril Shape: continuous or categorical Splines Transformations Equal buckets Amount of Insurance (bucketed) Continuous Fits Reduced number of parameters Allows for extrapolations outside of range Avoids out-of-model smoothing Complex patterns fitted with piecewise splines % 9.% 8.% 7.% 6.% 5.% 4.%.%.%.%.% Exposure Indicated Cubic Fit 9

4 By-peril model building: variable selection Univariate analysis Age of Home Indicated + SE SE Age of Home Indicated + SE SE Piecewise Continuous Fit Model building: consistency over time Urban Rural trend over time Exposure Year Rural Urban Looking for a stable trend over time Data quality Correlation with other variables Variable selection: occupant characteristics Considerations Options Age Gender Marital status Insurance score Occupation/retired Number of occupants Other personal lines Full payment/installments Billing lapse Good payer Named insured Policy level Presence of Number of Maximum/minimum age Composition 4

5 Variable selection: occupant characteristics Considerations Vendor data House characteristics Insurance scoring Prior claim activity Weather Demographics Elevation External data links Cost How often is the data updated by the vendor? How often does the data have to be updated? Regulatory support and environment Variable selection: predictiveness by peril Variable\Peril Fire Liability Theft Water Wind Other By-Peril Territory Insurance Score Age of Home Protection class Construction material Amount of Insurance Other lines Full Pay Square Feet Number of Rooms Claim Free Retired Flag Good Payer Prior Claims Secondary Residence Fire Protective Device Theft Protective Device Number of Occupants By-peril territory, Insurance Score, Amount of Insurance, Full Pay, Age of Home, and Claims History are consistently powerful across all perils Territory shows larger spread in weather perils Insurance Score is predictive in weather perils 4 Variable selection: identifying interactions Looking for situations where the effect of variable x differs depending on variable y Granularity can be a problem so grouping is often needed before testing for interactions.5 Factor.5 low mid high low high mid y x 5 5

6 Variable selection: modeling interactions Move from categorical*categorical interaction to categorical*continuous interaction small household large household young old household household Age of Oldest Occupant / occupants + occupants 6 Variable selection: modeling interactions Age of Occupant %.%.% 8.% 6.% 4.%.% / Occupants + Occupants Exposure % Age of Occupant %.%.% 8.% 6.% 4.%.% / Occupants + Occupants Exposure % 7 By-peril territories Practical considerations Territories are a collection of units (5 digit postal code, digit postal code, counties, puma, etc) Data at the unit level by-peril is noisy due to limited information in one area Territories are correlated with other rating variables (e.g. amount of insurance, age of home) Modeling solutions Use territories developed by third parties using industry data Use residual risk based on initial models that include house information, occupant information, and external weather, demographics, geographical data Use residual risk based on internal data only 8 6

7 By-peril territories Unsmoothed residual risk 9 By-peril territories: smoothing Distance based Nearby units play a bigger role Farther units play a smaller role Each unit of distance adds the same amount of risk independent of location More appropriate for weather related Adjacency based Surrounding units play a bigger role Outer rings of units play a smaller role Clustering smoothed residuals Maximize variance between clusters Minimize variance within clusters By-peril territories: how much smoothing? 7

8 By-peril territories: how much smoothing? By-peril territories: how much smoothing? Model validation A couple of options Out of sample validation Traditional splitting of modeling and validation of the entire dataset may not work Out of sample validation might fail if the observations are not independent (weather related perils) The losses coming from the same event would be found both in the modeling and in the validation dataset Out of time validation Could solve the independence issue if one year is kept aside for validation 4 8

9 Conclusion Homeowners predictive modeling could be as sophisticated and innovative as auto modeling By-peril modeling is an important way of achieving increased sophistication and accuracy Contact Cristina I. Gheorghe Principal Predictive Modeler Allstate Insurance Company 5 9