vehicle symbol development
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© 2008 EMB. All rights reserved.
Vehicle Symbol DevelopmentSerhat GuvenSenior Consultant
September 2009
Vehicle Symbol Analysis
© 2008 EMB. All rights reserved. Slide 2
OUTLINEBackgroundVehicle Estimator
Initial EstimatorDiagnosticsVehicle Spatial Correction
Vehicle SymbolsVehicle RelativitiesSummary
PURPOSE: To discuss techniques for creating proprietary symbols within the context of multivariate review, including proper tools and diagnostics
Background
© 2008 EMB. All rights reserved. Slide 3
Response Variable
Systematic Component
Random Component
= +
Signal:Function of the rating
factors/predictors
Noise:Reflects stochastic
process
Overall Mean“Best”Model
1 parameter for each
observation
Model Complexity
(Number of Parameters)
Basics of Predictive Modeling:
Background
© 2008 EMB. All rights reserved. Slide 4
Vehicle Symbol/Relativity Analysis:
Vehicle is a major risk driver and accounts for much rate variation
Two elements:
Symbols
Relativities
Historically, focus on relativities and not symbols
Symbols on limited data, anecdotal evidence, competitors, bureaus, and judgment
Liability symbols relatively recent phenomenon
Regular reviews of relativities with “tweaking” symbols
Background
© 2008 EMB. All rights reserved. Slide 5
Significant Variation in Pricing by Vehicle:
Background
© 2008 EMB. All rights reserved. Slide 6
Issues with Symbol Analysis:
High-dimensionality
Vehicle symbol requires a large number of small units as building blocks
Companies have limited data, so many building blocks have little or no claims experience
High correlation
Symbols tends to be highly correlated with other rating variables (e.g., age, credit, tier, etc)
Multivariate framework required to handle highly correlated variables
Background
© 2008 EMB. All rights reserved. Slide 7
Vehicle Symbol/Relativity Analysis
Vehicle symbol analysis is a multi-stage process.
Initial Estimator
Vehicle Symbols
Vehicle Risk Estimator
Symbol Relativities
Standardized fitted value from multivariate model
By coverage or cause of loss.
Frequency and severity determined separately
Spatial corrections
Component estimators combined
Overall estimators clustered to form symbols
Relativities calculated for each symbol
Initial Estimator:
Component models built using vehicle characteristics
© 2008 EMB. All rights reserved. Slide 8
Base Price
Curb Weight
EngineSize
ModelYear
AirbagFeatures
Theft Deterrents
Vehicle Estimator
Modeled Vehicle Signal
Vehicle Component Relativities
Vehicle characteristics are used as proxies for VIN
Use diagnostics from statistical routine to assess performance
Issues with raw residual
VINs are very small building blocks with limited data
Unordered categorical data creates interpretation problems
Use ‘spatial smoothing’ concepts to investigate signals
Vehicle Estimator
© 2008 EMB. All rights reserved. Slide 9
Diagnostics:
Need to identify additional signal in residual that can be attributed to the vehicle dimension
Basic residual definition
∑∑
∈
∈=
VINii
VINii
VIN Expected
ActualResidual
© 2008 EMB. All rights reserved. Slide 10
Vehicle Estimator
Similar issue for boundary analysis solved via smoothing of results
Distance-based smoothing
Adjacency-based smoothingDistance Adjacency
Smoothing techniques can be applied to vehicle residuals to identify signal
Diagnostics:
High number of dimensions (e.g. make/model)
May by only a few observations for any one dimension
“Neighbor” Vehicles
Once the “neighbors” are determined, the same techniques used for territorial analysis can be applied
Instead of using latitude/longitude to build adjacency relationships, use vehicle dimensions
© 2008 EMB. All rights reserved. Slide 11
© 2008 EMB. All rights reserved. Slide 12
Vehicle Estimator
Diagnostics:
Smoothing and diagnostics used to identify signal in the vehicle residualQQ Plot: P-Values vs Uniform
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Uniform
P-Va
lues
P-Values Smoothing 1 (20)
P-Values Smoothing 2 (40)
P-Values Smoothing 3 (60)
P-Values Smoothing 4 (80)
P-Values Smoothing 5 (100)
P-Values Time Period Selector Node 1
Uniform Line
QQ plot on smoothed residual indicates potential signal
If no signal, then all estimated cdfs would be above uniform cdf
Smoothing 4 (80)
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Smoothing 4 (80) Band
Nod
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Consistency tests further support signal identification
Both time and data consistency tests should be performed
Vehicle Spatial Correction:
Residual signal used to adjust scores from multivariate model
© 2008 EMB. All rights reserved. Slide 13
Base Price
Curb Weight
EngineSize
ModelYear
AirbagFeatures
Theft Deterrents
Vehicle Estimator
Modeled Vehicle Signal
Vehicle Component Relativities
SmoothedResidual
Spatial CorrectionLow
$
High$
Vehicle Symbols
© 2008 EMB. All rights reserved. Slide 14
Clustering Basics
Clustering used to produce groupings that are predictive of the future:
Minimize within-group heterogeneity.
Maximize cross-group heterogeneity.
Commonly-used clustering methods:
Quantiles
Equal Weight
Similarity Methods
- Average Linkage
- Centroid
Vehicle Symbols
© 2008 EMB. All rights reserved. Slide 15
Clustering Methodologies:
Quantiles
Create groups with an equal number of observations
Equal Weight
Create groups which have an equal amount of weight
Similarity Methods:
Rank the data set by the statistic you wish to cluster
Decide on which pair of records are the ‘most similar’
Group these records
Repeat until left with the desired number of groups
Vehicle Symbols
© 2008 EMB. All rights reserved. Slide 16
Similarity MethodsAverage Linkage
Difference between clusters is the average difference between pairs of observations, one in each clusterTends to join clusters with small variances
CentroidDifference between clusters is the difference between the mean values of the clusters squaredVINs allocated to more extreme groups
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Statistic
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Percentageof Weight
Statistic
Average Linkage Centroid
Clustering:
Vehicle estimator is clustered into new symbols
© 2008 EMB. All rights reserved. Slide 17
Base Price
Curb Weight
EngineSize
ModelYear
AirbagFeatures
Theft Deterrents
Vehicle Symbols
Modeled Vehicle Signal
Vehicle Component Relativities
SmoothedResidual
Spatial CorrectionLow
$
High$
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1 71 81 92 0
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Symbol Relativities
© 2008 EMB. All rights reserved. Slide 18
Model fit using new symbol definitions instead of vehicle proxies
Test relativities using standard tests
Lift statistics used to judge explanatory power
Consistency tests used to judge predictive power
Refine symbols/relativities as appropriate
Incorporate rule-based restrictions
Apply actuarial knowledge
Investigate “neighbors” with very different relativities
Vehicle Symbols
Symbol Relativities
Symbol Relativities
© 2008 EMB. All rights reserved. Slide 19
Source Data
ETL
Vehicle Proxy Model
Combine Components
Indications
Symbols
Component Symbol Model
Vehicle Residual Analysis
Summary
© 2008 EMB. All rights reserved. Slide 20
Vehicle Symboling Overview
Accurate estimation of underlying risk associated with the vehicle
Step 1Obtain a separate estimator by claim type and by frequency and severity for each vehicle building block. Combine estimators, as appropriate.
BIFrequency
Severity
Estimator
Estimator
PDFrequency
Severity
Estimator
Estimator
CompFrequency
Severity
Estimator
Estimator
CollFrequency
Severity
Estimator
Estimator
BI Estimator
PD Estimator
Comp Estimator
Coll Estimator
Vehicle Symbols
Symbol Relativities
Step 2Cluster vehicle building blocks to develop symbols separately by coverage(s) and component
Step 3Determine by-coverage relativities for each vehicle group
© 2008 EMB. All rights reserved. Slide 21
Summary
Technique has proven very successful based on proper hold-out sampling validation
Proven Results
US insurer
Canadian insurer
German insurance dataset
Summary
© 2008 EMB. All rights reserved. Slide 22
Vehicle groupings are a major driver of risk, thus it is critical that companies review symbols and relativities regularly.
Issues exist that create special challenges with regards to symbol analysis.
High-dimensionality
Heavily correlated
Vehicle symbols require a range of different approaches and tools (as there are different loss drivers)
Diagnostics needed to ensure best model possible
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