Catastrophe Modeling in the
Caribbean
17 May 2005
The Issue

Hurricane Ivan caused an estimated $11 billion damage in the
Caribbean and USA
– Grenada (7 Sep 04)
– Cayman Islands (11-12 Sep 04)
– Gulf of Mexico / Offshore Marine (13-15 Sep 04)
– United States (16-24 Sep 04)

Third highest insured natural perils loss in history

“According to the NHC, Ivan is the sixth-strongest storm to ever hit
the Atlantic basin” (13 Sep 04)
Guy Carpenter
2
Hurricane Ivan track
Guy Carpenter
3
The Issue

Insurer insolvencies and impairment
– “Industry PMLs” provided insufficient levels of protection
– Cat models did not generally anticipate the extent of storm
surge damage in the Cayman Islands
Guy Carpenter
4
The Caribbean

26 countries

Hundreds of islands

38 million people
– Three major languages

Spanish
65%

French
22%

English
14%

Approximate land size and population of the USA between
Pennsylvania and Maine

Spread out over an area roughly equivalent to the USA east of the
Mississippi
Guy Carpenter
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Guy Carpenter
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The Caribbean

Huge natural perils exposure
– Atlantic hurricane track
– Caribbean plate

Market standard natural perils deductibles
– Typically 2% of insured values
– Can be higher

Property insurance rates vary from 0.3% to 3.0% (and higher)
– Depending on geographical location, recent loss activity,
historical activity, perceived exposure, occupancy, construction,
coverage, quality, cat modeling, and market practice
– Little or no rate regulation
Guy Carpenter
7
“PML”
Definitions



“MPL” (Maximum Possible Loss) for any given portfolio is 100% of
insured values (less deductibles)
– Absolute worst case
“MFL” (Maximum Foreseeable Loss) for any given portfolio may be
lower than 100%
– Generally associated with the extreme “tail” of a distribution
(e.g., cat model output, realistic disaster scenario)
“PML” (Probable Maximum Loss) for any given portfolio may be
lower than 100%
– Explicitly or implicitly associated with a frequency (“return
period”)
– There exist a range of PMLs for various interested parties with
various risk appetites
Guy Carpenter
8
“PML”

Could be 100% for any given location

Mathematically, limited to the range (0%, 100%)
– 0% at frequent return periods (e.g., per day, per month)
– 100% at remote return periods (e.g., per millenium, per eon)
Guy Carpenter
9
“PML”
Historical practice

Historically, based on extrapolation of extreme events from
relatively small sample event sets

Insurance and Reinsurance market rules of thumb

Regulatory requirements

Rating agency requirements
Guy Carpenter
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“PML”
Caribbean practice

Caribbean companies have historically been among the leaders in
cat risk management of necessity
– Reinsurer pricing and PMLs guide market practice
– Explicitly split rates (Fire vs Cat premium)
– CRESTA system set up in 1977 to capture exposure data by
zone
– Caribbean exposures by CRESTA zone were generally
provided on reinsurance submissions
Guy Carpenter
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“PML”
Caribbean practice

USVI

Caymans
15% - 20%

Bahamas
8% - 15%

Barbados
10% - 15%

BVI
10% - 25%

Market practice can and does vary widely from insurer to insurer
due to variances in deductibles, spread of exposure, quality of
construction, level of capitalization, and risk appetite
Guy Carpenter
25%
12
“PML”
Current practice

Exposure data capture and quality

Hazard frequency and severity
– Hurricane
– Earthquake
– Other perils

Damage functions
– Wind
– Water
– Shake
– Fire following
Guy Carpenter
13
“PML”
Current practice


Financial variables
– Coverages
– Deductibles
– Coinsurance
– Insurance to value
– Sublimits
– Hours clauses
– Loss Adjustment Expense
– Demand surge
Combination of factors produces “PML” estimates
– Cat models often provide our current best estimates of damage
for “modeled” perils and events
Guy Carpenter
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“PML”
Current practice

Cat models
– RMS
– EQE
– AIR
– Reinsurer models
– Insurer models
– Broker models
– Consultant models
Guy Carpenter
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“PML”
Current practice

Post-event, cat modelers learn from losses and adjust models

Recent Caribbean events
– Gilbert (1988)
– Hugo (1989)
– Marilyn & Luis (1995)
– Georges (1998)
– Ivan (2004)?
Guy Carpenter
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Caribbean PMLs
Scenario estimates

Caribbean “MFLs” often assume it’s possible for an island to be hit
with a SS-5 hurricane
– “Close” vs. “Direct” hit?
– Fast-moving vs. slow-moving?
– Dry vs. wet storm?
– Without storm surge or with?
Guy Carpenter
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Caribbean PMLs
Scenario estimates

Limited geographical scope (single island)
– Easier to model “small” islands (e.g., Caymans, Barbados, St
Croix)
– More difficult for “larger” islands (e.g., Puerto Rico, Hispaniola,
Cuba), as storm intensity will vary over the island
– Portfolio damage is weighted average of individual location
damage
Guy Carpenter
18
Caribbean PMLs
Probabilistic estimates

Cat models are collections of event scenarios
– Discrete approximations, with probabilities attached to each
scenario
– Not exhaustive
– Limited perils
– Calibrated using historical experience

Recalibrated as required, based on research and actual
event experience
Guy Carpenter
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Risk Management in the Caribbean


Define “PML” as the maximum loss an insurer can reasonably
expect to pay with 99% certainty
Define “PML Bust” as the occurrence of an event that produces
loss in excess of the “PML”
– “PML Bust” is unlikely, but not impossible
– “PML Bust” events will in all likelihood happen every year,
somewhere in the world
Guy Carpenter
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Risk Management in the Caribbean

First principles
– PMLs range from 0% to 100%
– PMLs are associated with return periods (frequency)
– PMLs less than 100% will always (eventually) be exceeded
Guy Carpenter
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Risk Management in the Caribbean

Many Caribbean insurance companies cede away most premium
proportionally
– Geographically concentrated portfolios and high levels of
natural perils exposure
– Security of insurance product is dependent on security of
backing reinsurance and Event Limits purchased
– Insurance company net results are largely dependent on
overrides and volume (rather than profitability of rates and risk
appetite)

Costs can still be high for those who purchase a mix of excess of
loss and proportional reinsurance
– Geographically concentrated portfolios and high levels of
natural perils exposure
Guy Carpenter
22
Risk Management in the Caribbean

Insurance is a business
– It’s impractical to hold capital and/or purchase reinsurance up
to full limits (“MPL”)

Suboptimal use of capital
– The market (e.g., insureds, regulators, ratings agencies) deems
it acceptable to provide less than perfect insurance and
reinsurance security
– Need to quantify risk appetite

Probability of default

Risk-equivalent returns
– Need to use best available tools in a cost-effective manner to
make sound business decisions

Multiple cat models, combined with first principles
Guy Carpenter
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Risk Management in the Caribbean

Most people want certainty, not “sufficiently low probabilities”
– Most insurance companies think and plan in terms of “point
estimates” rather than distributions
– Regulators want policyholders to be paid
– Cat models should be used as a guide, not a rule

Never lose sight of first principles
– Deterministic thinking pervades society

Guy Carpenter
Statistics is a relatively young science
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Guy Carpenter
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CARIBBEAN
Guy Carpenter
SEA
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