Property Ratemaking Exposure Rating

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Property RatemakingExposure Rating

• 16 July, 2007

London CARe Seminar
Steve White, FCAS MAAA, Guy Carpenter
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Property Exposure RatingTypes of Exposure Rating
Curves
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Property Exposure RatingHistory

• Lloyds
• Salzmann (1960 INA Homeowners data)
• Reinsurer Curves (Swiss Re, Munich Re, etc)
• Ludwig (1984-1988 Homeowners and Small Commercial
  data)
• ISOs PSOLD (Recent Commercial data)
• ISOs PSOLD (Recent Homeowners data)
• MBBEFD (Astin paper by Stephan Bernegger)

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Property Loss Curves Advantages/(Disadvantages)

• Lloyds Curves
• (Very old data)
• (Does not vary by amount of insurance or
  occupancy class)
• (Underlying data is largely unknown (marine
  losses? WWII Fires?))
• Salzmann (Personal Property)
• Based on actual Homeowners data
• Varies by Construction/Protection Class
• (Very old data from 1960)
• (Does not vary by amount of insurance)
• (Building losses only and Fire losses only)
• (Salzmann recommends NOT using them, only meant
  as an example)
• Reinsurer Curves (Swiss Re, Munich, Skandia, etc)
• Documented study (some curves) on personal
  commercial reinsurance business
• (Old data)
• (Does not vary by amount of insurance or
  occupancy class)

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Property Loss Curves Advantages/Disadvantages

• Ludwig Curves (Personal and Commercial)
• Based on actual Homeowners and Commercial data,
  (but uses Hartford homeowners and small
  commercial property book may not be good for
  large national accts)
• Varies by Construction/Protection Class for
  Homeowners and Occupancy Class for Commercial
• Includes all property coverages and perils
• (Old data 1984 - 1988)
• ISOs PSOLD
• Recent Data updated every 2 years
• Varies by amount of insurance, occupancy class,
  state, coverage, and peril
• Continuous Distribution (no need for
  Interpolation)
• (Based on ISO data only)

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Property Loss Curves Advantages/Disadvantages

• ISOs PSOLD (Homeowners)
• First Update to Homeowners Property since Ludwig
  study
• Varies by amount of insurance, policy form,
  state, and construction
• Continuous Distribution (no need for
  Interpolation)
• (Based on ISO data (US) only, New untested
  outside of ISO)
• MBBEFD
• Loss Distribution from Physics
• Found to be useful for Property Loss
  Distributions
• Continuous Distribution (no need for
  Interpolation)
• (Relatively unknown)
• In work by Bernegger, parameters for this curve
  that approximate the Swiss Re Y Curves have been
  produced

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Property Exposure RatingFirst Loss Scale
Methodology
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First Loss ScalesA Quick Review of FLSs
The FLS is also non-decreasing (non-negative 1st
derivative), similar to ILF
The FLS is also non-decreasing at a decreasing
rate (non-positive 2nd derivative) (many commonly
used FLSs fail this part of the test)
E(X), the unlimited average severity of X
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First Loss ScalesCalculations Calculating
Expected Losses
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First Loss ScalesCalculations Expected Claim
Count
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Using First Loss ScalesOther Issues/Observations

• Curves do not vary by Insured Value
• Need to match peril and type of policy
• Interpolation between points on the common first
  loss scales
• A Tabular First Loss Scale is not adequate for
  calculating expected claim counts
• Requires experience and judgment to know which
  First Loss Scale is appropriate to use

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Property Exposure RatingWorking with PSOLD
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PSOLDCalculations using the Mixed Exponential
wi varies by 2 - Coverage (BC, BCI)(B only, C
only dropped in 2004) 4 - Peril (BG1, BG2,
Special Causes, All) 22 - Occupancy Class 60
- Amount of Insurance (AOI) 2 - Net of
Deductible vs Ground Up 50 State Deductible
Distributions
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PSOLD MethodologyInterpreting a single policy
LAS in an AOI Ranges in PSOLD
Alternate
PSOLD

• Is the movement from one AOI range to the next a
  step Function or a smooth progression?
• Consider three policies, two within a single AOI
  range and the third in the next highest AOI range
  but close in value to the second policy
• Should two different policy limits within a
  single AOI range have the same LAS or should the
  difference in policy limits be reflected?
• PSOLD currently calculates the LAS at a single
  point, the upper bound of the AOI range for all
  policies in the range.

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PSOLD MethodologyPSOLD LAS Calculations over
Single AOI Range (Dtl)
LAS for an Mixed Exponential
For Coverages B, C and BC PSOLD constrains the
LAS Calculation
PSOLD has two Ranges of Interest
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PSOLD MethodologyAlternate LAS Calculations over
a Continuous AOI Range (Grp)
Calculating the LAS over a continuous range adds
one more degree of complexity
Which simplifies to
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PSOLD MethodologyAdvantages of the Alternate LAS
Calculations

• Different policy limits within the same AOI range
  will get different LAS
• Smoother transition as you move from one AOI
  range to the next
• Since this impacts the unlimited average severity
  for the policy, it will change the allocation of
  losses to the layer for any exposed policy
• An additional enhancement would be to adjust the
  wis as you move within an AOI range

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PSOLD MethodologyWeighting between AOI Ranges

• If a range of Insured values spans more than one
  AOI Range. You need to combine the results of
  the Individual AOI ranges
• In PSOLD any AOI group included within the range
  will be given full weight
• An improvement would be to only Include an AOI
  range in proportion To the percentage that the
  range is Covered
• This was fixed in the 2004 ISO PSOLD Software

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PSOLD MethodologyWeighting between Occupancy
Classes
In PSOLD, when using more than one Occupancy
class on a single policy group, the relative
weight assigned to each occupancy class is based
on the occupancy counts in the underlying
industry data base. (this can be compensated for
by entering a separate limits profile for each
occupancy class) An improvement would be to
allow the user to define the weights between the
occupancy classes so that you can more accurately
reflect the individual ceding companies exposure
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PSOLD MethodologyAdditional Exposure Percentage

• PSOLD uses the following additional exposure
  percentage
• Building Only 50 (no longer produced in PSOLD
  2004)
• Contents Only 50 (no longer produced in PSOLD
  2004)
• BuildingContents Only 200 (50 2004 and
  prior)
• BuildingContentsBusiness Interruption 200
  (Unlimited 2004 and prior)
• These percentages are based on ISO claims
  experience
• You may want to select a different percentage due
  to any of the following
• Stacking of Excess Policies you do not want the
  policies to overlap
• Margin Clause contractually limits exposure
  greater than the limit
• Company Experience
• Judgment

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PSOLD MethodologyStacking and Participation

• Additional consideration when dealing with
  stacking an participation
• The selected AOI group should be based on a full
  value on the insured risk (same AOI group as if
  the risk was fully covered by a single policy
• All stacked policies should have the same AOI
  group
• When stacking, assume additional coverage is
  zero or the policies will overlap
• Support for stacked policies was added in 2006
  (but I have not worked with this feature)

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PSOLD MethodologyNew Homeowners Curves

• New in 2005
• Newest update of Homeowners Curves since Ludwig
• Curves vary by
• Insured Value (values dont go as high as the
  commercial curves)
• State (excludes TX)
• Policy Form (Homeowners, Condo, both)
• Construction (Brick, Frame, both)
• Protection Class (Protected, Unprotected, both)

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PSOLDOther Issues/Observations

• Limited Credibility for very Large Insured Values
• TIV Scale Produced by PSOLD
• Gross Limited Average Severities may not be
  consistent across AOI ranges for the Net of
  Deductible curves due to different mixture of
  deductibles
• Curves based on US Exposure in US Dollars
• If rating US business No Problem
• For non-US business Consider adjusting the
  scale of the curves using an international
  construction cost index
• If you adjust the scale of the model you must
  adjust BOTH the means of the mixed exponential
  AND the AOI ranges

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Stacking and ParticipationVentilated Layers
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Stacking and ParticipationParticipation

• Participation allows you to correctly model the
  situation where a contract only covers a
  proportional share of the underlying loss.
• It is most common in a subscription type market
  like Lloyds, but it is also useful for modeling
  some facultative business.
• Example
• Assume the following
• Write 25 participation on a 1M Contract.
• You reinsure a 200K xs 200K layer
• In order to get a loss that will expose the
  Reinsurance Cover
• You must have a loss to the primary contract
  greater than 800K (200K / 25)
• The largest loss you can have exposing the layer
  is 250K (25 of 1M) or 50K to the layer
• Actually, you would take 25 of losses ceded to
  an 800K xs 800K reinsurance layer. But since the
  primary policy is 1M, it is effectively 25 of
  200k xs 800k.

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Stacking and ParticipationStacking
Stacked Contracts

• Stacking is where an insurer issues multiple
  excess contracts covering the same underlying
  risk
• Assume someone writes a series of policies
  covering the same risk, 100K x 100K (Yellow),
  300K x 200K (Blue), 500K x 500K (Red) and 1M x 1M
  (Green)
• If all are written at the same level of
  participation then effectively it is the same as
  a single 1.9M xs 100K (Purple) policy with the
  given participation
• In practice, not all contracts are at the same
  participation and not all contract are written
  (can be thought of as participation0, this is
  sometimes called ventilation)

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Stacking and ParticipationStacking
Reinsurance Layer

• Now Assume there is a 500K x 500K reinsurance
  contract covering these contracts
• If the contracts are assumed to be independent,
  then you would only cover the 500K x 500K layer
  on the 1M x 1M policy. No other policy would
  expose.
• If the contracts are assumed to be stacked, then
  you would cover the 500K x 500K layer on the 1.9M
  x 100K policy.
• There can be significantly greater exposure to
  the Reinsurance Contract under the stacked
  assumption

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Stacking and ParticipationStacking

• Stacking is Generally thought of as an
  International Issue, but
• Stacking can be used in the Facultative Markets
• Stacking can be used to model Umbrella written
  over a companys own underlying policies
• Stacking is commonly used in combination with
  participation in a subscription market like Lloyds

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Stacking and ParticipationPartial Participation
without Stacking
25 Share
50 Share
100 Share
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Stacking and ParticipationPartial Participation
with Stacking

• Assume someone writes a series of policies
  covering the same risk, 100K x 100K (Yellow),
  300K x 200K (Blue), 500K x 500K (Red) and 1M x 1M
  (Green).
• Your participation on each is 100K xs 100K
  (100), 300K xs 200K (100), 500K xs 500K (50),
  1M xs 1M (25)
• These policies are stacked
• You reinsure a 500K xs 500K layer
• In order to get a loss that will expose the
  Reinsurance Cover
• You must have a loss to the excess contracts
  greater than 600K (100K / 100 300K / 100
  100K / 50)
• The largest loss you can have exposing the layer
  is 900K (100K 100 300K 100 500K 50
  1M 25) or 400K to the layer

25 Share (250k)
50 Share (150k)
50 Share (100k)
100 Share (300k)
100 Share (100k)
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MBBEFD CurveMaxwell-Boltzmann, Bose-Einstein,
Fermi-Dirac
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MBBEFD Curves

• Contains the Maxwell-Boltzmann, Bose-Einstein,
  Fermi-Dirac distributions.
• Curves used in Physics but found to be useful for
  Property Severity curves
• 1999 ASTIN Paper by Stephan Bernegger of Swiss Re
• Two parameter distribution. In Paper a single
  parameter version is presented where both
  parameters are defined as function of a new
  parameter c. Many of the Swiss Re Y scales are
  reasonably approximated using values for c.
• Fits many of the common first loss scales
  reasonably well

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MBBEFD Curves
The FLS(x) for the MBBEFD curve type where x is
the Limit/TIV is as follows
When b0 or g1 ProRata
When b1 and ggt1
When bg1 and ggt1

else (bgt0 and bltgt1 and bg ltgt 1 and ggt1)