Vehicle Symbol Development

© 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


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


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


Significant Variation in Pricing by Vehicle:

Background


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


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


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


Diagnostics:

Need to identify additional signal in residual that can be attributed to the vehicle dimension

Basic residual definition

∑∑

∈

∈=

VINii

VINii

VIN Expected

ActualResidual


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



Vehicle Estimator

Diagnostics:

Smoothing and diagnostics used to identify signal in the vehicle residualQQ Plot: P-Values vs Uniform

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P-Va

lues

P-Values Smoothing 1 (20)





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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ght

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


Base Price

Curb Weight

EngineSize

ModelYear

AirbagFeatures

Theft Deterrents

Vehicle Estimator



SmoothedResidual

Spatial CorrectionLow

$

High$

Vehicle Symbols


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


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


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


Base Price

Curb Weight

EngineSize

ModelYear

AirbagFeatures

Theft Deterrents

Vehicle Symbols



SmoothedResidual

Spatial CorrectionLow

$

High$

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Symbol Relativities


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


Source Data

ETL

Vehicle Proxy Model

Combine Components

Indications

Symbols

Component Symbol Model

Vehicle Residual Analysis

Summary


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


Summary

Technique has proven very successful based on proper hold-out sampling validation

Proven Results

US insurer

Canadian insurer

German insurance dataset

Summary


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

Documents

Vehicle Symbol Development