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Property Ratemaking - an Advanced Approach Exposure Rating

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Title: Property Ratemaking - an Advanced Approach Exposure Rating


1
Property Ratemaking - an Advanced
Approach Exposure Rating
  • June 6-7, 2005

Steve White, FCAS MAAA, Guy Carpenter
2
Property Exposure Rating Types of Exposure Rating
Curves
Section 1
3
Property Loss Curves History
  • 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)

4
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)

5
Property Loss Curves Advantages/Disadvantages
  • Ludwig Curves (Personal and Commercial)
  • Based on actual Homeowners and Commercial data,
    (but uses Hartford small commercial property book
    may not be good for large national accts)
  • Varies by Construction/Protection Class for HO
    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)

6
Property Loss Curves Advantages/Disadvantages
  • ISOs PSOLD
  • 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 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 the US)

7
Property Exposure Rating First Loss Scale
Methodology (FLS)
Section 2
8
First Loss Scales A 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)
E(X), the unlimited average severity of X
9
First Loss Scales Calculations - Detailed Policy
Limits
10
First Loss Scales Calculations - Detailed Policy
Limits
11
Using First Loss Scales Other 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

12
Property Exposure Rating Working with PSOLD
Section 3
13
PSOLD Calculations
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
14
PSOLD Methodology Interpreting 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 minimum of the loss limit and
    1.5x(upper bound of the AOI range) for all
    policies in the range.

15
PSOLD Methodology PSOLD 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
16
PSOLD Methodology Alternate LAS Calculations over
a Continuous AOI Range (Grp)
Calculating the LAS over a continuous range adds
one more degree of complexity
Which simplifies to
17
PSOLD Methodology Advantages 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

18
PSOLD Methodology Weighting 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

19
PSOLD Methodology Weighting 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. 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
20
PSOLD Methodology Additional 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 50
  • BuildingContentsBusiness Interruption
    Unlimited
  • 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

21
PSOLD Methodology Stacking 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

22
PSOLD Methodology New Homeowners Curves
  • Available Shortly
  • 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)
  • (Does not include Protection Class)

23
PSOLD Other Issues/Observations
  • Limited Credibility for very Large Insured Values
  • TIV Scale Produced by PSOLD
  • Gross Limited Average Severities consistent
    across AOI ranges by Net of Deductible curves are
    not
  • Due to different mixture of deductibles

24
Stacking and Participation
Section 4
25
Stacking and Participation Participation
  • 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.

26
Stacking and Participation Stacking
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)

27
Stacking and Participation Stacking
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

28
Stacking and Participation Stacking
  • 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

29
Stacking and Participation Partial Participation
without Stacking
25 Share
50 Share
100 Share
30
Stacking and Participation Partial 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)
31
MBBEFD
Section 5
32
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

33
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)
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