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©2011 AIR WORLDWIDE 1
Utilizing Cat Models to Analyze
Catastrophe Risk Pooling
Programs
Stuart Miller, PhD
December 1, 2011
©2011 AIR WORLDWIDE 2
Agenda
• About AIR
• Recap: Cat Modeling 101
• Modeling Insurance Pools – Conceptual Approach
• Model Output and Analytics
• Conclusions
©2011 AIR WORLDWIDE 3
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
©2011 AIR WORLDWIDE 4
Cat Modeling 101
Exposure
Information
Intensity
Calculation
Damage
Estimation
Policy
Conditions
Loss
Calculation
Limit
Deductible
Event Generation
©2011 AIR WORLDWIDE 5
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
©2011 AIR WORLDWIDE 6
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
©2011 AIR WORLDWIDE 7
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
©2011 AIR WORLDWIDE 8
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
©2011 AIR WORLDWIDE 9
Distribution of Hurricane Risk
©2011 AIR WORLDWIDE 10
Distribution of Earthquake Risk
©2011 AIR WORLDWIDE 11
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%
©2011 AIR WORLDWIDE 12
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
©2011 AIR WORLDWIDE 13
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%
©2011 AIR WORLDWIDE 14
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
©2011 AIR WORLDWIDE 15
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
©2011 AIR WORLDWIDE 16
Contact Information
Stuart Miller, PhD
Manager – Global Markets
+1 617 267 6645