Solving the Puzzle: The Hybrid Reinsurance Pricing Method John Buchanan Platinum Reinsurance CARe Lo - PowerPoint PPT Presentation

Loading...

PPT – Solving the Puzzle: The Hybrid Reinsurance Pricing Method John Buchanan Platinum Reinsurance CARe Lo PowerPoint presentation | free to view - id: 14a993-YjdkN



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Solving the Puzzle: The Hybrid Reinsurance Pricing Method John Buchanan Platinum Reinsurance CARe Lo

Description:

1. Solving the Puzzle: The Hybrid Reinsurance Pricing Method. John Buchanan ... It may be tempting to think the next step is to refine the estimate of w ... – PowerPoint PPT presentation

Number of Views:114
Avg rating:3.0/5.0
Slides: 49
Provided by: timh66
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Solving the Puzzle: The Hybrid Reinsurance Pricing Method John Buchanan Platinum Reinsurance CARe Lo


1
Solving the Puzzle The Hybrid Reinsurance
Pricing Method John Buchanan - Platinum
Reinsurance CARe London Casualty Pricing
Approaches 16 July, 2007
CARe London-7/2007 The Hybrid Reinsurance
Pricing Method
2
Agenda
  • Typical Puzzle
  • Improvements to Traditional Methods
  • Analogy to Reserving
  • Hybrid Experience / Exposure Method
  • Overriding Assumptions
  • Testing Default Parameters
  • US and Global Benchmarks

3
Reinsurance Proposal
  • Layer 100,000 xs 100,000
  • Estimated Premium 40,000,000
  • GL Business
  • Southeast US
  • Underwriting and Claims Info

4
Traditional Methods
  • Experience
  • Relevant parameter defaults/overrides for
  • LDFs (excess layers)
  • Trends (severity, frequency, exposure)
  • Rate changes
  • LOB/HzdGrp indicators
  • Adjust for historical changes in
  • Policy limits
  • Exposure differences
  • Careful as-if
  • Exposure
  • Relevant parameters defaults/overrides for
  • ILFs (or ELFs, PropSOLD)
  • Direct loss ratios (on-level)
  • ALAE loads
  • Policy profile (LOB, HzdGrp)
  • Limit/subLOB allocations
  • Adjust for expected changes in
  • Rating year policy limits
  • Rating year exposures expected to be written

5
Whats your final answer?
  • Experience for this layer is half of the Exposure
  • Exposure 3.92 (1.57 mm)
  • Experience 1.85 (0.74 mm)
  • Trick Question…

6
Traditional Naïve Approach
  • Naïve approach
  • Estimate Exposure Rate X
  • Estimate Experience Rate Y
  • Combine as w(X)(1-w)Y
  • It may be tempting to think the next step is to
    refine the estimate of w
  • Not easy, but luckily, not the right next step

Source Stephen Philbrick Seminar on
Ratemaking March 7-9, 2007
7
Better Approach
  • Use the Experience results of the layer, and
    adjacent layers to examine the Exposure rating
    assumptions
  • Use the Exposure rating assumptions to help
    distinguish noise from signal in the Experience
    rating
  • Use claim count to emphasize signal over noise
    Exposure model can help provide expected
    frequencies

Source Stephen Philbrick Seminar on
Ratemaking March 7-9, 2007
8
Better Approach continued
  • Apply forensic actuarial techniques to bring the
    Exposure and Experience models closer together
  • Apply the Hybrid method to the adjusted Exposure
    and Experience models to arrive at the Hybrid
    answer
  • Optionally, weight the answer with the Exposure
    indication. Ideally, the indications are now much
    closer, so the exact value of the weight is less
    important.

Source Stephen Philbrick Seminar on
Ratemaking March 7-9, 2007
9
Better Approach Reserving Analogy
From paper submitted to CAS Variance John
Buchanan / Mike Angelina THE HYBRID REINSURANCE
PRICING METHOD A PRACTITIONERS GUIDE
10
Exposure Pricing (before investigation)
  • Dont look just at layer you are pricing (100 xs
    100k)
  • Look at layers below and above as well
  • Look at Exposure burns and claim counts

11
Experience Pricing (before investigation)
  • Ditto for Experience Pricing
  • Use same layers for easier comparison

12
Exposure and Experience Comparison
  • In this case study (CASRM 3/2007), there is an
    inconsistent relationship as move up the
    attachment points
  • While the low layer Experience is about half of
    Exposure, the upper layers are about equal to
    Exposure
  • Need more investigation to reconcile and help
    solve the puzzle

13
Overall Pricing Process
  • We don't really know what exposure curve applies
    to a given account (e.g. we don't know that LN
    50k and CV 400 is the true underlying
    distribution)
  • We have a hunch based on established curves (e.g.
    we postulate LN 50k and CV 300)
  • We obtain some observations from a certain number
    of claims over a certain number of years
  • in the long run the results will track with the
    true underlying distribution in 1 but these
    observations will initially be compared to the
    hypothesis given in 2
  • If we make enough correct adjustments to the
    observations and underlying exposures then we
    will start to see a non-constant pattern in the
    ratios of the observed experience results to the
    initially selected exposure results (the Hybrid
    ratios).
  • In this example, the actual Experience will end
    up being heavier for the top layers
  • If credible, this lack of constant Hybrid ratios
    creates a pressure to fatten the tail of the
    exposure distribution. Making this change to the
    exposure curve will allow us to create a better
    balance (e.g. Hybrid ratios will all be closer to
    100).

14
Overriding Assumptions of the Hybrid Method
  • In theory, with perfect modeling and sufficient
    data the results under the Experience and
    Exposure methods will be identical.
  • In practice,
  • if the model and parameter selections for both
    Experience and Exposure methods are proper and
    relevant,
  • then the results from these methods will be
    similar,
  • except for credibility and random variations.
  • Lower layer experience helps predict higher less
    credible layers.
  • Frequency is a more stable indicator than total
    burn estimates.

15
Basic Steps of The Hybrid Method
  • Step 1 Estimate Experience burns counts
  • Step 2 Estimate Exposure burns counts
  • Step 3 Calculate Experience/Exposure frequency
    ratio by attachment point
  • Step 4 Review Hybrid frequency ratio patterns
  • Adjust experience or exposure models if needed
    and re-estimate burns (!!)
  • Step 5 Similarly review excess severities and/or
    excess burns
  • Step 6 Combine Hybrid frequency/severity results
  • Step 7 Determine overall weight to give Hybrid

16
Step 4-Review Hybrid Frequency Ratios
Important Selection
6.00 expos x 80.0
17
Steps 1-7 Bringing it All Together
Step 1
Step 3
Step 5
Step 4
Step 6
Step 2
Step 7
18
Example 2 (adjusting Experience for
historically higher policy limits)
19
Example 3 (adjusting Exposure for clash
potential)
20
Benefits of Hybrid Method
  • One of main benefits is questioning Experience
    and Exposure Selections
  • To the extent credible results dont line up,
    this provides pressure to the various default
    parameters
  • For example, there would be downward pressure on
    default exposure ILF curves or loss ratios if
  • Exposure consistently higher than experience, and
  • Credible experience and experience rating factors
  • A well constructed Hybrid method can sometimes be
    given 100 weight if credible
  • Can review account by account, and aggregate
    across accounts to evaluate pressure on industry
    defaults

21
Test of Default Parameters
  • Aggregate across similar accounts to evaluate
    pressure on industry defaults
  • May want to re-rate accounts using e.g. default
    rate changes, ILFs, premium allocations, LDFs,
    trends, etc.
  • Each individual observation represents a
    cedant/attachment point exper/expos ratio
  • Review dispersion of results and overall trend
  • E.g. if weighted and/or fitted exper/expos ratios
    are well below 100 (or e.g. 90 if give some
    underwriter credit) then perhaps default L/Rs
    overall are too high (or conversely LDFs or
    trends too light)
  • If trend is up when going from e.g. 100k to 10mm
    att pt, then perhaps expos curve is predicting
    well at lower points but is underestimating upper
    points

22
Test of Default Parameters (cont.)
  • Before making overall judgments, must consider
  • UW contract selectivity (contracts seen vs.
    written),
  • Sample size ( of cedants/years),
  • Impact as-if data (either current or
    historical)
  • Survivor bias
  • Systematic bias in models
  • Lucky

23
Test of Default Rating Factors Example 1
Well below 100, pressure to reduce expos params
or increase exper params…but credible??
24
Test of Default Rating Factors Example 2
Exposure curve too light with higher attachment
points?
25
Reinsurance Market
  • Reinsurance business mix1 Europe US / Can
  • Property 46 34
  • Motor 21 8
  • Liability WC 20 35
  • Other 3 23
  • Reinsurance type2
  • Proportional 70 50
  • Non-Proportional 30 50
  • P C Reinsurance Demand3 51 b 65 b

Source Tim Aman CARe-Phila 1 Axco, 2
Estimated, 3 A M Best Co
26
Exposure Benchmarks
  • Insurance business mix Europe US / Can
  • Property 24 27
  • Motor 38 41
  • Liability 10 14
  • WC 0 11
  • AH 17 2
  • Other 11 5

Lloyds, SRe, MRe
ISO
GLD (dated)
NCCI
Consultants
  • Lots of US Exposure Curves available
  • But many sub-lines dont have standard curves and
    questionable applicability to many other lines
    DO, EO, EPLI, Umbrella, most international
    lines
  • Companies need to accumulate own difficult,
    credibility issues

Mix Source Tim Aman CARe-Phila Axco
27
Global Hurricane Activity
Used by permission from UK Met
28
Summary
  • Weighting of alternative methods should be viewed
    as the actuarial equivalent of crying uncle.
  • Do not view weighting as a positive approach to
    coming up with an answer, but a concession that
    there are things going on you havent modeled
  • Perfectly acceptable if the only remaining
    differences are noise if not, improve the model

Source Stephen Philbrick Seminar on
Ratemaking March 7-9, 2007
29
Appendices
  • More Advanced Puzzle Solving Techniques
  • Hybrid Steps
  • Credibility
  • One of the most difficult puzzle pieces

30
Appendix - More advanced techniques for Solving
the Puzzle
  • Inspecting Experience/Exposure differences

31
Appendix - More advanced techniques for Solving
the Puzzle
  • Pressure Indicators years (or layers)

32
Basic Steps of The Hybrid Method
  • Step 1 Estimate Experience burns counts
  • Select base attachment points/layers above the
    reporting data threshold
  • Estimate total excess burns using projection
    factors
  • Estimate excess counts using frequency trends,
    claim count LDFs
  • Calculate implied severities
  • Step 2 Estimate Exposure burns counts
  • Use same attachment points/layers as Experience
  • Estimate total burns and bifurcate between
    counts, average severities
  • Step 3 Calculate Experience/Exposure frequency
    ratio by attachment point
  • Estimate overall averages using number of
    claims/variability
  • Step 4 Review frequency ratio patterns
  • Adjust experience or exposure models if needed
    and re-estimate burns (!!)
  • Select indicated experience/exposure frequency
    ratio(s)
  • Step 5 Similarly review excess severities and/or
    excess burns
  • Step 6 Combine Hybrid frequency/severity results
  • Using experience adjusted exposure frequencies
    and severities
  • Step 7 Determine overall weight to give Hybrid

33
Estimation of Hybrid Counts Preview Steps 1 to 4
  • A Select base attachment points above data
    threshold
  • Example threshold150k reins layers500x500k,
    1x1mm
  • Select 200k, 250k, 350k, 500k, 750k, 1mm
    attachment points
  • B Calculate experience counts
  • At lower attachment points, year by year patterns
    should be variable about some mean
  • For example, if upward trend, then perhaps
  • Overdeveloping or trending later years
  • C Calculate exposure counts for comparison
  • D Review experience/exposure frequency patterns
  • Should be relatively stable until credibility
    runs out
  • Double back to methods if not
  • Select frequency ratios to estimate Hybrid counts

34
Step 1a Experience Counts and Burns Sublayer
150,000 xs 350,000
35
Step 1b Review Experience Counts Year
Variability gt350,000 Attachment
Apparently random pattern around selection of
12.05
Note Claim counts are on-leveled
36
Step 1c Review Experience Counts Year
Variability gt1,000,000 Attachment
Credibility runs out indication is .36
37
Step 1-Recap Estimation of Experience Burns,
Counts and Implied Severities
To be compared to exposure counts
38
Step 2 Estimation of Exposure Burns Bifurcated
Between Counts and Severities
12.05 exper / 15.34 expos 78.6
39
Step 3 Calculate Experience/Exposure Frequency
Ratios and Base Layer Weights
12.05 exper / 15.34 expos 78.6
40
Step 4a Review Exper/Expos Frequencies Attachment
Point Pattern 200k…1mm
Expos and Exper count ratios relatively
consistent through 350k- IF experience very
credible, then perhaps pressure to reduce
exposure L/R check out spikes
41
Step 4-Recap Select Exper/Expos Frequency Ratio
For Hybrid Claim Count Estimate
Important Selection
6.00 expos x 80.0
42
Step 5 Selected Severity
Unrealistic experience severity
43
Step 6 Selected Overall Hybrid Burn
Hybrid Experience adjusted Exposure count
severity… 100 credibility to burn??
44
Classical Credibility Weighting
  • Estimate separate Experience and Exposure burns
  • Select credibility weights using combination of
  • Formulaic Approach
  • Expected of Claims / Variability
  • Exposure ROL (or burn on line)
  • Questionnaire Approach
  • Apriori Neutral vs. Experience vs. Exposure
  • Patrik/Mashitz paper
  • Judgment
  • Need to check that burn patterns make sense
  • i.e. higher layer ROL lt lower ROL
  • similar to Miccolis ILF consistency test

45
Classical Credibility Weighting
Credibility weights judgmentally selected
46
Assessing Credibility of Exposure Method
  • Assess confidence in
  • Exposure curve selected
  • Exposure profile
  • Source of hazard or sub-line information
  • Prediction of next years primary loss ratio
  • Percentage of non-modeled exposure, clash, etc.
  • Company strategy and ability to realize strategy
  • Possibly take questionnaire / scoring approach to
    mechanize (Patrik/Mashitz)

47
Assessing Credibility of Experience Method
  • Assess confidence due to
  • Overall volume of claims
  • Volume of claims within layer (lucky or unlucky?)
  • Stability of year by year experience results
  • layer to layer experience
    results
  • Source of loss development, trend factors,
    historical rate changes and deviations
  • Changes in historical profile limits
  • Appropriateness of any claims or divisions that
    may have been removed (or as-ifd)
  • Experience score compared to exposure score to
    determine credibility weight

48
Increase Credibility by Reducing Variability
  • Above figure from iconic Philbrick CAS paper
  • In this case, A represents Experience rating
    average (with indicated process noise), while B
    represents Exposure
  • Goal will be to bring A and B closer together
    thereby reducing parameter variance, with any
    remaining difference being process noise
About PowerShow.com