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Transcript of 2007 National Council on Compensation Insurance, Inc. 1 Catastrophe Modeling and Actuarial...
2007 National Council on Compensation Insurance, Inc. 1
Catastrophe Modeling and Actuarial Applications
Jonathan Evans, FCAS, MAAA
Actuary
Iowa Actuarial Club
February 23, 2007
Source: 2007 National Council on Compensation Insurance, Inc.
2
What Are Catastrophes ?
• Single events that produce such a large number of claims – that it is very highly improbable such an event
would actually occur (assuming risk exposures are independent)
• Usually resulting from a special type of peril: hurricane, earthquake, terrorist attack, asbestos, etc.
• More rarely, sometimes extremely large single claims are called “catastrophes”
Source: 2007 National Council on Compensation Insurance, Inc.
3
What Applications Make Actuaries Care About Catastrophes ?
• Ratemaking for policies exposed to catastrophes, such as homeowners in Florida
• Reserving for long tail catastrophic losses, such as asbestos in general liability
• Analyses of reinsurance programs• Analyses of insurer catastrophe risk, such as
catastrophic return period loss estimates
Source: 2007 National Council on Compensation Insurance, Inc.
4
Why Model Catastrophes ?
• For non-catastrophic perils (such as an automobile accident that independently affects risk exposures or only a few risk exposures simultaneously) it is easy to gather a credible volume of experience
• For catastrophic perils (such as hurricanes) even nationwide experience over many years may not be credible
Source: 2007 National Council on Compensation Insurance, Inc.
5
Catastrophic Versus Non-CatastrophicExperience
Hypothetical Example Of Characteristic Non-Catastrophic Experience Pattern
Hypothetical Example Of Characteristic Catastrophic Experience Pattern
Source: 2007 National Council on Compensation Insurance, Inc.
6
Who Builds Catastrophe Models ?
• Prior to the 1980s most models were built by insurers for underwriting purposes
• From the 1980s to present most models were built by specialized modeling firms and sold as software, that allows users to input exposure information
• Event databases and estimated frequencies are often prepared by scientists: geophysical for earthquake, atmospheric for hurricanes, social/behavioral for terrorism, etc.
• Loss functions are often determined by engineers• Actuaries are mostly end users of models; except for
reserving models for mass liability, such as asbestos/environmental, where actuaries have compiled databases and built their own models
Source: 2007 National Council on Compensation Insurance, Inc.
7
How Are Catastrophes Modeled ?
Catastrophe models generally consist of:
1. A database of individual exposures, such as homeowners policies by location and insured value
2. A database of potential catastrophic events, such as hurricanes by landfall location and wind speed
3. A loss function that uses as input the characteristics of a single exposure from #1 and a single catastrophic event from #2
4. Estimates for the frequency of each catastrophic event in #2
Source: 2007 National Council on Compensation Insurance, Inc.
8
Simplified Hypothetical Example Of A Catastrophe Model
Policy Insured Value (IV) Location (L)
A 1,000,000 100B 1,000,000 110C 500,000 130D 5,000,000 500E 7,000,000 600
Event Intensity (I) Center Location (LC)
U 10 300W 5 250X 3 260Y 2 105Z 1 550
Event Frequency Per Year (F)
U 0.001 W 0.005 X 0.010 Y 0.050 Z 0.100
2(L -LC)Loss = IV exp -
2000 I
1
3 4
2
Source: 2007 National Council on Compensation Insurance, Inc.
9
Example Of Calculating Loss
For Policy A and Event U the loss is calculated as:
2(100-300)Loss = 1,000,000 exp - 135,335
2000 10
Source: 2007 National Council on Compensation Insurance, Inc.
10
Example Model Loss Output
Policy U W X Y Z
A 135,335 105,399 14,028 993,769 0 B 164,474 140,858 23,518 993,769 0 C 117,873 118,464 29,902 427,673 0 D 676,676 9,652 339 0 1,432,524 E 77,763 33 0 0 2,005,534
Event Total 1,172,122 374,407 67,787 2,415,212 3,438,058
Frequency 0.001 0.005 0.010 0.050 0.100
Event
Source: 2007 National Council on Compensation Insurance, Inc.
11
Example Ratemaking Application
For Policy AEvent Loss Frequency Expected Loss
U 135,335 0.001 135 W 105,399 0.005 527 X 14,028 0.010 140 Y 993,769 0.050 49,688 Z 0 0.100 0
All Events 50,491
Insured Value 1,000,000
Pure Premium (per 100 value) 5.05
Pure PremiumPolicy Expected Loss (per 100 value)
A 50,491 5.05 B 50,792 5.08 C 22,393 4.48 D 143,981 2.88 E 200,631 2.87
All Policies 468,288 3.23
Source: 2007 National Council on Compensation Insurance, Inc.
12
Example Portfolio Risk Application
Frequency Return ExceedanceEvent Loss Frequency at or Above Period Probability
3,438,058 0.100 0.100 10 10%2,415,212 0.050 0.150 7 14%1,172,122 0.001 0.151 7 14%
374,407 0.005 0.156 6 14%67,787 0.010 0.166 6 15%
Source: 2007 National Council on Compensation Insurance, Inc.
13
Questions
Source: 2007 National Council on Compensation Insurance, Inc.
14
Further Reading
-Bouska, Amy, “From Disability Income to Mega-Risks: Policy-Event Based Loss Estimation”, CAS Forum, Summer 1996.
-Grossi, Patricia and Kunreuther, Howard, Catastrophe Modeling: A New Approach to Managing Risk (Huebner International Series on Risk, Insurance and Economic Security), Springer, 2005.
-Kozlowski, Ronald T. and Mathewson, Stuart B., “Measuring and Managing Catastrophic Risk”, CAS Discussion Paper Program, 1995.
-Woo, Gordon, The Mathematics of Natural Catastrophes, World Scientific Publishing Company, 1999.