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Property Ratemaking - an Advanced Approach Exposure Rating
Property Ratemaking - an Advanced Approach Exposure Rating
Property Exposure Rating Types of Exposure Rating Curves
Property Exposure Rating Types of Exposure Rating Curves
Property Loss Curves History
Property Loss Curves History
Property Loss Curves Advantages/(Disadvantages)
Property Loss Curves Advantages/(Disadvantages)
Property Loss Curves Advantages/Disadvantages
Property Loss Curves Advantages/Disadvantages
Property Loss Curves Advantages/Disadvantages
Property Loss Curves Advantages/Disadvantages
Property Exposure Rating First Loss Scale Methodology (“FLS”)
Property Exposure Rating First Loss Scale Methodology (“FLS”)
First Loss Scales A Quick Review of FLSs
First Loss Scales A Quick Review of FLSs
First Loss Scales Calculations - Detailed Policy Limits
First Loss Scales Calculations - Detailed Policy Limits
First Loss Scales Calculations - Detailed Policy Limits
First Loss Scales Calculations - Detailed Policy Limits
Using First Loss Scales Other Issues/Observations
Using First Loss Scales Other Issues/Observations
Property Exposure Rating Working with PSOLD
Property Exposure Rating Working with PSOLD
PSOLD Calculations
PSOLD Calculations
PSOLD Methodology Interpreting a single policy LAS in an AOI Ranges in
PSOLD Methodology Interpreting a single policy LAS in an AOI Ranges in
PSOLD Methodology PSOLD LAS Calculations over Single AOI Range (“Dtl”)
PSOLD Methodology PSOLD LAS Calculations over Single AOI Range (“Dtl”)
PSOLD Methodology Alternate LAS Calculations over a Continuous AOI
PSOLD Methodology Alternate LAS Calculations over a Continuous AOI
PSOLD Methodology Advantages of the Alternate LAS Calculations
PSOLD Methodology Advantages of the Alternate LAS Calculations
PSOLD Methodology Weighting between AOI Ranges
PSOLD Methodology Weighting between AOI Ranges
PSOLD Methodology Weighting between Occupancy Classes
PSOLD Methodology Weighting between Occupancy Classes
PSOLD Methodology Additional Exposure Percentage
PSOLD Methodology Additional Exposure Percentage
PSOLD Methodology Stacking and Participation
PSOLD Methodology Stacking and Participation
PSOLD+ Methodology New Homeowners Curves
PSOLD+ Methodology New Homeowners Curves
PSOLD Other Issues/Observations
PSOLD Other Issues/Observations
Stacking and Participation
Stacking and Participation
Stacking and Participation Participation
Stacking and Participation Participation
Stacking and Participation Stacking
Stacking and Participation Stacking
Stacking and Participation Stacking
Stacking and Participation Stacking
Stacking and Participation Stacking
Stacking and Participation Stacking
Stacking and Participation Partial Participation without Stacking
Stacking and Participation Partial Participation without Stacking
Stacking and Participation Partial Participation with Stacking
Stacking and Participation Partial Participation with Stacking
MBBEFD
MBBEFD
MBBEFD Curves
MBBEFD Curves
MBBEFD Curves
MBBEFD Curves

Презентация: «Property Ratemaking - an Advanced Approach Exposure Rating». Автор: Steve White. Файл: «Property Ratemaking - an Advanced Approach Exposure Rating.ppt». Размер zip-архива: 254 КБ.

Property Ratemaking - an Advanced Approach Exposure Rating

содержание презентации «Property Ratemaking - an Advanced Approach Exposure Rating.ppt»
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1 Property Ratemaking - an Advanced Approach Exposure Rating

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

Property Exposure Rating Types of Exposure Rating Curves

Section 1

3 Property Loss Curves History

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) ISO’s PSOLD (Recent Commercial data) ISO’s PSOLD+ (Recent Homeowners data) MBBEFD (Astin paper by Stephan Bernegger)

3

4 Property Loss Curves Advantages/(Disadvantages)

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)

4

5 Property Loss Curves Advantages/Disadvantages

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) ISO’s 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)

5

6 Property Loss Curves Advantages/Disadvantages

Property Loss Curves Advantages/Disadvantages

ISO’s 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)

6

7 Property Exposure Rating First Loss Scale Methodology (“FLS”)

Property Exposure Rating First Loss Scale Methodology (“FLS”)

Section 2

8 First Loss Scales A Quick Review of FLSs

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

8

9 First Loss Scales Calculations - Detailed Policy Limits

First Loss Scales Calculations - Detailed Policy Limits

9

10 First Loss Scales Calculations - Detailed Policy Limits

First Loss Scales Calculations - Detailed Policy Limits

10

11 Using First Loss Scales Other Issues/Observations

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

11

12 Property Exposure Rating Working with PSOLD

Property Exposure Rating Working with PSOLD

Section 3

13 PSOLD Calculations

PSOLD Calculations

wi varies by: 2 - Coverage (B+C, B+C+I)(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

13

14 PSOLD Methodology Interpreting a single policy LAS in an AOI Ranges in

PSOLD Methodology Interpreting a single policy LAS in an AOI Ranges in

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.

Alternate

PSOLD

14

15 PSOLD Methodology PSOLD LAS Calculations over Single AOI Range (“Dtl”)

PSOLD Methodology PSOLD LAS Calculations over Single AOI Range (“Dtl”)

LAS for an Mixed Exponential

For Coverages B, C and B+C PSOLD constrains the LAS Calculation

PSOLD has two Ranges of Interest

15

16 PSOLD Methodology Alternate LAS Calculations over a Continuous AOI

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

16

17 PSOLD Methodology Advantages of the Alternate LAS Calculations

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 wi’s as you move within an AOI range

17

18 PSOLD Methodology Weighting between AOI Ranges

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

18

19 PSOLD Methodology Weighting between Occupancy Classes

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

19

20 PSOLD Methodology Additional Exposure Percentage

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) Building+Contents Only – 50% Building+Contents+Business 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

20

21 PSOLD Methodology Stacking and Participation

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

21

22 PSOLD+ Methodology New Homeowners Curves

PSOLD+ Methodology New Homeowners Curves

Available Shortly Newest update of Homeowners Curves since Ludwig Curves vary by Insured Value (values don’t go as high as the commercial curves) State (excludes TX) Policy Form (Homeowners, Condo, both) Construction (Brick, Frame, both) (Does not include Protection Class)

22

23 PSOLD Other Issues/Observations

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

23

24 Stacking and Participation

Stacking and Participation

Section 4

25 Stacking and Participation Participation

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.

25

26 Stacking and Participation Stacking

Stacking and Participation Stacking

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 participation=0%, this is sometimes called ventilation)

Stacked Contracts

26

27 Stacking and Participation Stacking

Stacking and Participation Stacking

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

Reinsurance Layer

27

28 Stacking and Participation Stacking

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 company’s own underlying policies Stacking is commonly used in combination with participation in a subscription market like Lloyds

28

29 Stacking and Participation Partial Participation without Stacking

Stacking and Participation Partial Participation without Stacking

25% Share

50% Share

100% Share

29

30 Stacking and Participation Partial Participation with Stacking

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)

30

31 MBBEFD

MBBEFD

Section 5

32 MBBEFD Curves

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

32

33 MBBEFD Curves

MBBEFD Curves

The FLS(x) for the MBBEFD curve type where x is the Limit/TIV is as follows:

When b=0 or g=1 ProRata

When b=1 and g>1

When bg=1 and g>1

else (b>0 and b<>1 and bg <> 1 and g>1)

33

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