introduction to experience rating casualty actuarial society reinsurance pricing seminar dave clark,...

Introduction to Experience RatingCasualty Actuarial SocietyReinsurance Pricing Seminar

Dave Clark, Actuary and VPMunich Reinsurance America, Inc.

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Introduction to Experience Rating

Agenda:

Basic Experience Rating Methodology

Diagnostics: telling the story

Credibility weighting with exposure rate

Examples

Problems & Challenges (time permitting)

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Introduction to Experience RatingBasic Experience Rating Methodology

Steps in Experience Rating:

1. Assemble Data

2. Adjust Subject Premium to Future Level

3. Trend and Layer Losses

4. Apply Loss Development

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(1) Assemble Data

First Rule: Apples-to-Apples collection of

historical subject premium and loss data

Trended OnLevel Subject Premium

Trended Ultimate Layer LossesExperience Rate =

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(1) Assemble Data

Second Rule: Get all the detail on historical losses

1. Include all historical losses that would trend into the layer (rule of thumb: get all losses > half of your attachment point)

2. Split out ALAE for each loss

3. Include historical policy limits (and SIR if applicable)

4. Confirm that losses are assembled by occurrence, not by claimant

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(2) Adjust Subject Premium to Future Level

Filed [manual] rate changes

“Price-level” changes

Schedule-Rating, company tiers, etc

Also include “soft” changes such as terms & conditions, changes in

underwriting standards, etc

Exposure Trend

(for inflation-sensitive exposure bases)

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Goal is to adjust historical premium to a level “as if” it has been written

during the future period.

The split between “rate” and “price” is not always obvious (e.g., where are

LCMs or package factors included?): get a full description from the ceding

company.

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Primary Loss Ratios

0%10%

20%30%40%50%

60%70%80%

90%100%

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Accident Year

Ult

imat

e L

oss

Rat

io

Trend and Onlevel

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Note to actuaries coming from a primary rate-filing background:

In a rate filing, you typically adjust premium to the current rate level.

In reinsurance pricing, you want to adjust premium to the average rate

level in the future period.

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Obvious observation:

If the ceding company’s effective rates drop by -10% for the prospective

period, but we assume that rates are “flat,” then our experience rating

will be understated by 10%.

Recommended Reading:

Trent Vaughn’s Commercial Lines Price Monitoring; CAS Forum Fall 2004

Handouts from Chris Nyce and Brian Hughes at the 2007 CAS Ratemaking Seminar (www.casact.org)

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Change in Net Written Premium (Detrended by GDP)Industrywide, All Lines

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

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Nonproportional Casualty Reinsurance (Schedule P)Industrywide

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

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(3) Trend & Layer Losses

Purpose is to bring the historical value up to the average level in the

future period

Typically we apply trend and then cap the trended loss at the historical

policy limit

Hidden assumption: All losses trend at the same percent (trend does not

vary by size of loss)

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(3) Trend Losses: Depends on Treaty Basis:

Experience Period (AY)

Risks Attaching

Treaty

Experience Period (AY)

Losses Occurring

Treaty

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(3) Trend Losses – Leveraged Effect

1,000,000

1,200,000

trend

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(3) Trend Losses - Impact on Excess Layer

Layer: 500,000 excess of 500,000

Untrended Trended Trend %Total # of Claims 100 100

Pareto B 125,000 135,000Pareto Q 1.55 1.55Overall Severity 227,273 245,455 8.0%

Layer Counts 8.3 9.1 9.9%Layer Severity 313,899 315,687 0.6%Layer Loss Cost 2,590,513 2,864,008 10.6%

All numbers are for illustration only, and not for use in pricing.

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(4) Develop Losses to Ultimate

Factors depend on Layer of Reinsurance being priced

We apply LDFs to trended layer losses so that all years are on

the same basis.

Development is an aggregate loss concept

Includes new claims (“true IBNR”), development on known

claims, reopening of closed claims, etc

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Cumulative Reporting Pattern

0.0%10.0%20.0%30.0%40.0%50.0%60.0%70.0%80.0%90.0%

100.0%

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240

% R

epo

rted

as

of

Eva

luat

ion

Ag

e

Primary 400 xs 100 1M xs 1M


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Problem:

Most recent periods are very green and may have zero losses reported to

date. Should they be included? Alternatively, if there are losses, then they

are hit with huge LDF.

Possible Solutions: B-F or “Cape Cod” Methods

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LDF Method:

Ultimate = Reported × LDF

Bornhuetter-Ferguson (B-F) Method:

Ultimate = Reported + Prem×ELR×(1-1/ LDF)

But what ELR do we use?

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“Cape Cod” method is a special case of the B-F method.

The ELR is selected to be equal to the final value of the all-year average loss

ratio.

Subject PremiumELR

Ultimate Loss==

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“Cape Cod” ELR turns out to be calculated simply as follows:

Premium/LDFELR

Reported Loss==

Where Premium/LDF is the “exposed premium” corresponding to the

loss that we would expect to have been reported to date.

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Key Formulas in “Cape Cod” Method:

Subject Premium / LDFSubject Premium

Reported Loss × LDF Reported Loss==

Cumulative % of Loss Reported = 1 / LDF

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Introduction to Experience RatingDiagnostics: Telling the Story

Does the Experience-Rating make sense?

Graphical Display

Comparisons

Prior years’ Experience Rating

Exposure Rating

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Simple test of actual versus expected:

Actual versus Expected Analysis

Accident Evaluated Evaluated Expected Expected ActualYear 06/30/2006 LDF 06/30/2007 LDF Link Ratio Dvlpmnt Dvlpmnt

1998 571,093 1.103 599,683 1.077 1.024 13,787 28,5901999 492,265 1.141 559,165 1.103 1.034 16,959 66,9002000 319,707 1.195 219,653 1.141 1.047 15,131 -100,0542001 1,762,534 1.277 1,831,330 1.195 1.069 120,944 68,7962002 250,563 1.407 285,397 1.277 1.102 25,508 34,8342003 577,569 1.633 969,391 1.407 1.161 92,772 391,8222004 362,216 2.087 854,699 1.633 1.278 100,702 492,4832005 333,336 3.376 712,321 2.087 1.618 205,879 378,9852006 110,169 14.169 408,968 3.376 4.197 352,220 298,799

Total 4,779,452 6,440,607 943,902 1,661,155


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Some questions to ask when reconciling with prior rating or exposure

rating:

Is the experience rating distorted by large losses?

Is the ELR used in exposure rating consistent with the ceding

company’s experience? Is the ALAE the same?

How has the business changed? Is the experience even relevant?

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Introduction to Experience RatingCredibility

Credibility:

Experience Rating = Projection of losses based only on what took place for

this specific account

Exposure Rating = A Priori estimate of losses based on information other

than the specific account’s experience in the layer

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Credibility:

Separating claim counts is useful for comparing experience and exposure ratings, and also for gauging credibility.

A good credibility standard is: the number of claims that we would have expected to observe in the historical periods.

Z =n

n + k

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Credibility: Other Considerations

Stability of Experience: How much would experience rate change

if we remove the largest claim or add an additional full limit loss?

Are pricing factors (LDFs, rate changes, etc) from the account or

are they default values?

Do the characteristics of the ceding company match the business in

the exposure rating curves?

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Introduction to Experience Rating

EXAMPLES

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Introduction to Experience RatingChallenges

We will look at two challenges that require some variation on the

experience-rating:

(1) Changing Mix of Business or Policy Limits Distribution

(2) Inclusion of Excess or Umbrella Policies

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(1) Changing Mix of Business

Wherever possible, we want the experience rating performed on homogeneous experience. That is, each historical period writes the same business as will be in the future period.

A changing mix by line of business means that separate experience ratings are needed by line.

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(1) Changing Policy Limits Distribution

Suppose we are pricing a 500,000 excess of 500,000 layer, but the ceding

company has only recently begun writing high limit policies.

How can the historical experience be used?

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(a) Trend past historical policy limits.

(b) Price lower “fully exposed” layer and then use exposure-rating model

relativities.

(c) Adjust each historical period to the future period’s level of exposure.

(d) Use curve-fitting model to historical losses.

Com

plex

S

impl

e

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(a) Trend past historical policy limits.

Advantage:

Very simple

Disadvantage:

Only works if the reason that policy limits have changed is that they have drifted up with inflation.

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(b) Experience rate “fully exposed layer”

Advantage:

Relatively simple

Disadvantages:

Subject premium still needs to be adjusted to the average policy limit profile of future period.

Does not make use of the loss experience in the layer that we are actually pricing.

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(c) Adjust years based on exposure rating each historical period

Advantage:

This is the most accurate method.

Disadvantage(s):

Requires full policy limit profile for each historical period

Difficulty in explaining adjustment factors

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Exposure Rate250,000 500,000

Policy Limit Distribution excess of excess ofAY 500,000 1,000,000 5,000,000 250,000 500,000

1998 75.00% 20.00% 5.00% 14.71% 3.09%1999 75.00% 20.00% 5.00% 14.71% 3.09%2000 75.00% 20.00% 5.00% 14.71% 3.09%2001 75.00% 20.00% 5.00% 14.71% 3.09%2002 75.00% 20.00% 5.00% 14.71% 3.09%2003 50.00% 20.00% 30.00% 14.24% 6.18%2004 25.00% 20.00% 55.00% 13.77% 9.27%2005 10.00% 20.00% 70.00% 13.49% 11.13%2006 10.00% 20.00% 70.00% 13.49% 11.13%2007 10.00% 20.00% 70.00% 13.49% 11.13%2008 10.00% 20.00% 70.00% 13.49% 11.13%


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(c) Adjust years based on exposure rating each historical period

The exposure rates from this table are used to “layer” the subject premium to

find the portion of premium corresponding to the losses in the layer; the

layered premium becomes the new “adjusted subject premium.”

Note: this is a variation on the exposure adjustment described by Mata & Verheyen in their Spring 2005 CAS

Forum article.

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(d) Fit curve to historical data

Advantage:

Makes use of all the loss information

Disadvantage(s):

Does not properly include development

Significant increase in complexity

Temptation to extrapolate beyond data

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(2) Inclusion of Excess Policies

Challenges:

Proper handling of “supported” and “unsupported” excess policies

Proper application of inflation trend

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Primary Policy

1M Limit

Excess

Policy

1M xs 1M2M Exposed

Excess Policy

1M xs 1M1M Exposed

“Supported” Excess “Unsupported” Excess

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“supported” and “unsupported” excess policies

(a) Combine primary and excess portions of large losses

This is the right answer, but requires the ability to match loss records

from the two types of policies

(b) Price excess layer on a “responds ground-up” basis

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Proper application of inflation trend

(a) Add SIR to loss amount before trending

(b) Use a higher trend percent to reflect “leverage”

Thank you very much for your attention.

Dave Clark, Actuary and VPMunich Reinsurance America, Inc.

© Copyright 2007 Munich Reinsurance America, Inc. All rights reserved. The Munich Re America name is a mark owned by Munich Reinsurance America, Inc.

The material in this presentation is provided for your information only, and is not permitted to be further distributed without the express written permission of Munich Reinsurance America. This material is not intended to be legal, underwriting, financial, or any other type of professional advice. Examples given are for illustrative purposes only.

introduction to experience rating casualty actuarial society reinsurance pricing seminar dave clark,...

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