Generalised Linear Modelling for improved ratema · PDF file advanced ratemaking ... general...

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Transcript of Generalised Linear Modelling for improved ratema · PDF file advanced ratemaking ... general...

  • Pricing Advantage David Kirk 2008

    Generalised Linear Modelling for improved ratemaking

  • How to achieve Pricing Advantage

  • Competition & Market Dynamics

    Sharper ratemaking can provide a competitive advantage for increased market share and higher margins

  • Rating uncovers hidden risk characteristics

  • So that we can group risks and price effectively

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    Claim Frequency

  • -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

    Current Premium Subsidies

    Why we need to rate more accurately

    Subsidised Subsidising

    Unprofitable Risk being undercut

  • Modelling the potential benefits Policyholder behaviour and market dynamic model

    Needs plenty of assumptions  Price sensitivity

     Information accessibility

     Loyalty

    And estimates Distribution of policyholders by risk

    Competitive response

     Pricing accuracy

    “all models are wrong… but some are useful.”

  • Price Sensitivity Price sensitivity  If Price Sensitivity is 100%, policyholders always choose cheapest

    alternative

     If Price Sensitivity is 0%, policyholders ignore price in their decision

    Can be estimated Market Research and Surveys

    Analysis of offer accept and decline statistics

    Affects speed of change in market share and equilibrium level

  • Information Accessibility  Information accessibility  If Information Accessibility is 0%, then Price Sensitivity is irrelevant

     If Information Accessibility is less than 100%, then the effect of Price Sensitivity is dampened

    Can be estimated Market Research and Surveys

    Can be changed through advertising

    Affects speed of change in market share and equilibrium level

  • Loyalty Customer Loyalty  If Loyalty is 100%, no existing clients ever change insurer

     If Loyalty is 0%, then at renewal the current insurer has no advantage

    Can be estimated Market Research and Surveys

    Analysis of offer accept and decline statistics

    Affects speed of change in market share but not the eventual equilibrium level

  • Competitive Response No competitive response assumed for following projections Not realistic

    Overstates the results

    Difficult to quantitatively assess competitive response  Prefer to model knowing it’s incorrect

    Rather than model something which we don’t understand

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    Years in projection

    Projected Market Share

    Some actual results

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    Years in projection

    Projected Profitability (assuming no competitive

    reaction)

    Some actual results

  • Seeing the light

    A South African insurer started in 1998 now has over 10% market share, higher than average profitability using advanced ratemaking

    Top 20 US insurers all using multivariate techniques

    Even more prevalent in UK

  • What makes good rates?

    A good ratemaking process will generate rates that achieve specific objectives

  • Choosing Rating Objectives Accuracy

    Ease and cost of administration

    Flexibility of approach

    Statistical efficiency of estimates

    Consistency over time

    Objectivity and freedom from manipulation

    Transparency

    Consistent with other corporate objectives

  • Correlation, causation and predictive value Correlation does not imply causation A vehicle accident or restaurant fire last year does not cause the

    accident or fire this year

    A prior accident or fire claim is a useful predictor of future claims

    Correlation can have predictive value even if there is no causation Rating factors versus risk factors

    Understanding the cause is preferable, but not required in order to use the factor

  • Introduction to statistical ratemaking

    Scientific ratemaking doesn’t have to be complex

  • Univariate Analysis Consider one rating factor at a time Age

    Gender

    Vehicle Make

     Property type

    Simple analysis can be performed in a spreadsheet

    Can be performed on  Loss Ratios

     Pure Premiums

  • Loss Ratio Analysis Consider differences in Loss Ratios between different rating

    factors or groups

    Data requirements  Premium and claim amounts for each policy

     Premiums for prior periods must be re-rated to be consistent with current rating standards

    May require re-underwriting if underwriting approach has changed

    Rating factors associated with each policy

    New rates are an adjustment to old rates

  • Loss Ratio Analysis example

  • Pure Premium Analysis The Pure Premium is the absolute premium rate applied to the

    exposure

    Frequency & Severity estimated separately

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  • Pure Premium Analysis

  • Pure Premium example

  • Pure Premium Analysis Based on exposures rather than premiums

    Doesn’t require re-rating of past premiums to current on-level premiums

    Analysis isn’t affected by special or negotiated rates

    Can be used for a new line without an existing basis

    Requires a coherent exposure measure Unique or idiosyncratic risks not well suited

  • Advanced Scientific Ratemaking Ratemaking

    Multivariate, robust, accurate, flexible, understood and competitive ratemaking using GLM

  • Revisiting correlation, causation and predictive value Correlation does not imply causation

    Correlation can have predictive value even if there is no causation

    Correlation is a measure of linear relationships Not all relationships of interest are linear

    Correlation doesn’t guarantee low variance of prediction

    Correlation neither sufficient nor necessary to be predictive

  • Univariate analysis is flawed

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    Comparison of GLM and Univariate Rates

    GLM Univariate

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    Multiple Regression

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  • Theoretical and practical problems

    Multiple Regression assumes normal distribution of residuals Common actual distributions for frequency is Poisson and for severity

    is Gamma

    Multiple Regression can lead to frequencies and severity estimates less than 0

    Can still be useful Widely understood technique

    Can even do analysis in a spreadsheet

    Problems with Multiple Regression

  • GLM: Some evidence GLM is used widely and successfully in insurance around the

    world

    Part of ultra-competitive UK non-life industry for many years

    Growing quickly in the US since 1990s introduction As pricing restrictions are reduced, competition has increased

     Top 20 insurers all use GLM now

    Casualty Actuarial Society heavily involved

    Expensive software available, and in demand

  • GLM: Basic concepts GLM is still a form of linear modelling

    Generalised to allow for different distributions And technically, we need iterative estimation techniques

     But practically this has little effect given current computing power

    And making use of transformations of the dependent variable

  • GLM: The Link Function

    g is known as the Link Function and links the expected value of the dependent variable to a linear combination of risk factors or exposure measures

    Ca