Utilizing Cat Models to Analyze Catastrophe Risk Pooling...

©2011 AIR WORLDWIDE 1

Utilizing Cat Models to Analyze

Catastrophe Risk Pooling

Programs

Stuart Miller, PhD

December 1, 2011


Agenda

• About AIR

• Recap: Cat Modeling 101

• Modeling Insurance Pools – Conceptual Approach

• Model Output and Analytics

• Conclusions


About AIR

• AIR Worldwide was founded in 1987 as the first

catastrophe modeling company

• Develops models which help over 400 clients, including

insurers, reinsurers, governments and investors manage

their catastrophe risk

• Experience in Mexico:

– Mexico Earthquake model released in 2000

– Mexico Tropical Cyclone model released in 2008

– Risk Analysis for CAT-Mex catastrophe bond in 2006

– Risk Analysis for MultiCat catastrophe bond in 2009

– Consulting projects with SHCP & Agroasemex


Cat Modeling 101

Exposure

Information

Intensity

Calculation

Damage

Estimation

Policy

Conditions

Loss

Calculation

Limit

Deductible

Event Generation


Modeling Insurance Pools – Conceptual Approach

• Catastrophe models, traditionally used by the private

sector, can also be applied to analyze the impact of risk

pooling arrangements

• Models and their output allow users to test the impact of

different risk pooling arrangements before making a

decision and purchasing coverage in the market

• This process can be broken down into three distinct

components:

– (1) collection of exposure data

– (2) analyze exposure in model

– (3) integrate results into risk pooling decisions


Modeling Process

• Exposure Data:

– Exposure data refers to the value, location, usage and construction

type of assets

– Mexico has an existing database of public sector assets

– AIR has a database of private sector assets

• Analyze Exposure in Model

– Once formatted, exposure can be analyzed in catastrophe models

to generate a risk profile which includes key statistics used in the

marketplace

• Integrate Results into Pooling Decisions

– Evaluate pooled risk profile and risk transfer decisions


Model Outputs

Statistic Definition

Average Annual Loss (AAL) The average loss the layer can expect to incur in any

given year; “pure premium”

Attachment Probability The annual probability that the attachment point

(deductible) will be met

Expected Loss The AAL as a percentage of the layer size

Exhaustion Probability The annual probability that the exhaustion point (limit)

will be met

Standard Deviation A measure of uncertainty around the AAL


Mexico as a Candidate for Pooling

• Mexico’s risk profile allows for a large amount of

diversification

• Tropical Cyclone

– Atlantic and Pacific Basins which have a negative correlation with

respect to storm activity

– Inland versus coastal regions

– Northern/Southern regions versus central regions

• Earthquake

– Different zones of seismic activity

– Geographically diversified


Distribution of Hurricane Risk


Distribution of Earthquake Risk


Modeling Different A Hypothetical Portfolio

• Cat models can quantify the gains of pooling

• Benefits start as early as the 10 year RP and increase

AAL 10 20 50 100 250 500 1,000

Lo

ss (

$)

Return Period

Non-Pooled

Pooled

-52%

-49%

-44%

-35%

-22%

-9% -1%

-53%


Member Contributions to the Pool’s Profile

• Models can also be applied to analyze the contribution of

each member to the pool’s risk profile

• This information can be used to arrive at a mutually

agreeable split for premium and payout


Modeling Risk Transfer

• Once the pool has been formed models can be used to

analyze the impact of different risk transfer options as the

pool seeks coverage in the marketplace

• Cat models can incorporate financial terms to simulate

how coverage will perform (e.g. sample Cat XOL layer)

Attach

Exhaust Exhaust Probability 1.27%

Attachment Probability: 4.39%


Forming an Optimal Portfolio

• Using the result of cat model analyses sophisticated

optimization algorithms can be used to determine the most

efficient portfolio composition

• Mathematics can be applied to identify the optimal

structure with regards to desired risk metrics

• This data gives pool managers information as to how they

can best form the pool to meet the stated objectives

• Optimization analyses can also be used to determine the

selection of risk retention and transfer levels


Conclusions

• Mexico’s cat risk profile presents opportunities for

diversification through pooling

• Catastrophe models can be used to generate the risk

profile of different risk pooling arrangements

• Model output provides the user with a range of data that

can be used in evaluating the composition of risk pools

• Cat models also allow the user to test different risk

retention and transfer structures to assess

• Advanced analytics (portfolio optimization) can be used to

provide additional information to stakeholders


Contact Information

Stuart Miller, PhD

Manager – Global Markets

[email protected]

+1 617 267 6645

mailto:[email protected]



Utilizing Cat Models to Analyze Catastrophe Risk Pooling...

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