Catastrophe Models

December 2, 2010

Richard Bill, FCAS, MAAA

R. A. Bill Consulting

Bill.consulting@frontier.com

Overview

Use of Cat Models in:

•Exposure Management

•Ratemaking

Note: will use Hurricane as example

3

Cat Models

RABill Consulting 4

Exposure Management - In old days, pins were used to identify concentration of risk

Exposure Management – Pins in Map

• Cumbersome practice was eliminated due to expense considerations

• Billions of Dollars of Exposure is on or near the coast of the US subject to severe hurricanes

• Likewise, for earthquake, the insurance industry exposure is tremendous, particularly in California and the New Madrid Area

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• How do insurance companies judge how much business to write in catastrophe prone areas such as on the coast of Florida without exposing the company to bankruptcy????

Catastrophe Ratemaking Problem• A Hurricane is an unlikely event for a particular

location on the coast

• The experience period for making rates would need to be very long to reflect the probability of a Hurricane at a particular location

• Even if past history were available, it would not reflect the increase in new construction on the coast

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• How do Insurers decide how much to charge for catastrophe prone areas????

Catastrophe Models evolved as a solution to the problem

• AIR founded the catastrophe modeling industry in 1987

• Models were not used much in the beginning

• Hurricane Hugo in 1989 and particularly Hurricane Andrew in 1992 were wakeup calls

• Many insurance companies had not realized the extent of their exposure concentrations.

Cat Model Definition

Catastrophe modeling is the process of using computer-assisted calculations to estimate the losses that could be sustained by a portfolio of properties due to a catastrophic event such as a hurricane or earthquake

Property Casualty Insurance Industry

Major Risk Factors

• Hurricanes• Earthquakes• Terrorism Losses• Insufficient Reserves• Asbestos/Pollution or similar Exposure • Poor underwriting and/or Inadequate Rates• Collectibility of Reinsurance• High Expenses• Bad Investments

TYPES OF MODELS

• Earthquake

• Fire Following EQ

• Hurricane

• Storm Surge

• Tornado/Hail

• Winter Storm

• Terrorism

Catastrophe Models

• Catastrophe events are simulated for many years (for example 10,000)

• Company submits detailed information on their book of business

• Losses are calculated based on the company’s book of business

• Losses are stated in terms of return time, i.e. 100 year event

Construction of Hurricane Model• The annual number of occurrences is generated from

the frequency distribution• Landfall Location of each Hurricane is determined• Simulation of Storm track after landfall• Hurricane severity simulation

• Wind Speed

• Size of Hurricane

• The movement of the event across the affected area is simulated, and dollar damages are calculated based on insured value, type of building, deductible, etc.

Simplified Example

Simulation of Frequency

• Assume average of 3 Hurricane Landfalls per year• Assume Poisson Distribution

Probability of X Number of Hurricanes , Avg Freq = 3 Per Year

# of Percentile # of SimulatedHurricanes Probability Accumulative F(x) Hurricanes

0 5% 5% 0 - 5% 01 15% 20% 5 - 20% 12 22% 42% 20 - 42% 23 22% 65% 42 - 65% 34 17% 82% 65 - 82% 45 10% 92% 82 - 92% 56 5% 97% 92 - 97% 6

Based on Poisson Distribution

Industry Simulated Hurricane FrequencyAverage Frequency = 3 Per Year

Year Percentile # of Events2012 17% 12013 36% 22014 85% 52015 97% 72016 14% 12017 2% 02018 15% 12019 52% 32020 78% 42021 34% 2

Landfall Location 1st Hurricane

Number of PercentileSegment Landfalls Probability Accumulative F(x) Segment

1 3 2% 2% 0 - 2% 12 3 2% 5% 2 - 5% 23 4 3% 8% 5 - 8% 34 10 8% 15% 8 - 15% 45 4 3% 18% 15 - 18% 56 3 2% 20% 18 - 20% 67 5 4% 24% 20 - 24% 78 6 5% 29% 24 - 29% 89 6 5% 33% 29 - 33% 910 3 2% 35% 33 - 35% 1011 2 2% 37% 35 - 37% 1112 4 3% 40% 37 - 40% 1213 3 2% 42% 40 - 42% 1314 19 14% 56% 42 - 56% 1415 17 13% 69% 56 - 69% 1516 3 2% 71% 69 - 71% 1617 2 2% 73% 71 - 73% 1718 1 1% 74% 73 - 74% 1819 5 4% 77% 74 - 77% 1920 2 2% 79% 77 - 79% 2021 3 2% 81% 79 - 81% 2122 10 8% 89% 81 - 89% 2223 1 1% 89% 89 - 89% 2324 2 2% 91% 89 - 91% 2425 1 1% 92% 91 - 92% 2526 5 4% 95% 92 - 95% 2627 1 1% 96% 95 - 96% 2728 5 4% 100% 96 - 100% 28

Total 133 100%

Industry Simulated Hurricane Location

Random (0,1)Hurricane Percentile Segment #

1 17% 52 36% 113 85% 224 97% 285 14% 46 2% 27 15% 48 52% 149 78% 2010 34% 10

Industry Simulated Hurricane EventsBased on 10,000 Years of Simulated Events

Year EventID Event Lat/Long Landfall1 11814 FL Hurricane Cat 1 26.1949/-80.03542 13602 LA Hurricane Cat 3 29.5352/-92.37302 22355 NC Hurricane Cat 5 35.2994/-76.15723 19188 MS Hurricane Cat 2 28.4666/-92.43523 34955 FL Hurricane Cat 3 26.2549/-90.34453 38175 FL Hurricane Cat 5 26.3555/-90.55533 3421 AL Hurricane Cat 4 27.3322/-92.55433 23037 SC Hurricane Cat 4 34.3335/-78.5555~ ~ ~ ~~ ~ ~ ~

9999 17044 GA Hurricane Cat 3 33.4444/-87.222510000 38889 FL Hurricane Cat 5 26.4444/-90.5555

Simulates Precise Location within Segment

Company XYZ Simulated Hurricane LossesBased on 10,000 Years of Simulated Events

Replacement Average Annual Policy # Type Address Lat/Long Location Value Loss

1000 Dwelling 1234 Washington 26.1949/-80.0354 100,000$ 100$ 1001 Apartment 1235 Washington 26.1950/-80.0360 15,000,000 10,000

~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~

1050 Dwelling 1500 Ash 26.1951/-80.0374 300,000 400 1051 Dwelling 1505 Ash 26.1953/-80.0380 400,000 550

Total 3,000,000$

Model Output

Company XYZ Simulated Hurricane Losses From LargestIn Thousands

Accumulated Gross Loss Gross Loss Net LossProbability Year EventID Event Amount Amount

0.0001 7779 16970 LA Hurricane 100,120 80,120 0.0002 3851 17065 NC Hurricane 99,500 79,500 0.0003 5447 40855 MS Hurricane 98,000 78,000

~~

0.0009 3354 35241 FL Hurricane 76,443 56,443 0.0010 1418 8130 FL Hurricane 75,150 55,150 0.0011 9004 34930 AL Hurricane 74,300 54,300

~~

0.0099 621 1617 SC Hurricane 40,253 37,752 0.0100 8782 13220 GA Hurricane 40,100 37,599 0.0101 4560 1172 FL Hurricane 39,980 37,479

Richard:1000 Year Event

Richard:100 Year Event

Company XYZ Cat Model Results In Millions

ReturnPeriod Probability Direct Losses Net Losses*

25 4.00% 18 17 50 2.00% 27 25

100 1.00% 40 37 250 0.40% 51 46 500 0.20% 65 47

1,000 0.10% 75 55 10,000 0.01% 100 80

Avg Annual Loss 3

* After Reinsurance Recoveries

Return Period Perspective

• 250 Years-20 years before the Declaration of Independence - 1756

• 500 Years- 14 years after Christopher Columbus discovers America - 1506

• 1,000 Years-Leif Erickson discovers “Vinland” (possibly New England - 1006?)

• 10,000 Years – 8000 B.C. - ??????

Industry % of Insured Value in Coastal Counties

• 79% in Florida

• 63% in Connecticut

• 61% in New York

• 54% in Massachusetts

• 16% Nationwide

Top 10 Most Costly Hurricanes in US History, (Insured Losses, $2005)

$3.5 $3.8 $4.8 $5.0$6.6 $7.4 $7.7 $8.4

$21.6

$40.0

$0

$5

$10

$15

$20

$25

$30

$35

$40

$45

Georges(1998)

Jeanne(2004)

Frances(2004)

Rita (2005)

Hugo(1989)

Ivan (2004)

Charley(2004)

Wilma(2005)

Andrew(1992)

Katrina(2005)

$ B

illio

ns

From III Presentation on HurricanesSources: ISO/PCS; Insurance Information Institute.

Seven of the 10 most expensive hurricanes in US history

occurred in the 14 months from Aug. 2004 – Oct. 2005:

Katrina, Rita, Wilma, Charley, Ivan, Frances & Jeanne

Exposure Management

• Component of Insurance Company’s Enterprise Risk Management (ERM)

• Make sure that a catastrophe does not wipe out the company

• Maintain financial strength after an event

• Maintain financial ratings

• Smooth earnings (publicly held companies)

Accumulation Management

• Manage accumulation during underwriting process

• Limit new business

• Non renewals

• Increase business in lower risk areas

Exposure Management (cont.)

• Rating Agencies are placing a lot more reliance on cat management since the hurricanes of 2004 and 2005

• A Company can either purchase more reinsurance or reduce exposure or raise prices or a combination

Industry Reaction

• More demand for reinsurance

• Many companies are pulling back from coastal areas particularly, the gulf states

• Insurance Rates for coastal properties have skyrocketed

Ratemaking

Pricing for Hurricane

“When hurricane rating analyses were first expanded from five to 30 years of storm experience, the technique was applauded as a vast improvement, which is was. The 30 years were replaced by 100,000 years and real life events were replaced by silcon-prompted simulations. “

Company XYZ Simulated Hurricane LossesBased on 10,000 Years of Simulated Events

In Thousands

Gross Loss Net LossYear EventID Event Lat/Long Location Amount Amount

1 11814 FL Hurricane 26.1949/-80.0354 283 283 2 13602 LA Hurricane 29.5352/-92.3730 400 400 2 22355 NC Hurricane 35.2994/-76.1572 40 40 3 19188 MS Hurricane 28.4666/-92.4352 300 300 3 34955 FL Hurricane 26.2549/-90.3445 10,000 9,500 3 38175 FL Hurricane 26.3555/-90.5553 640 640 3 3421 AL Hurricane 27.3322/-92.5543 100 100 3 23037 SC Hurricane 34.3335/-78.5555 829 829 4 17044 GA Hurricane 33.4444/-87.2225 214 214 4 38889 FL Hurricane 26.4444/-90.5555 589 589 ~ ~ ~~ ~ ~

Total 30,000,000

Average Annual Loss (Divide by 10,000) 3,000$

Average Annual Loss• Indicates what needs to be charged each year

to cover hurricane losses over the long run• Can be calculated for each individual building-

useful for pricing large commercial buildings• Can be calculated at a zip code level or even

finer to be used in pricing – example, all dwellings within 1 mile of the coast

• Risk charge can be calculated as an additional charge

How Models Are UsedUnderwriting

Establish guidelines

Differentiate risks

Develop pricing

Portfolio Management

Determine risk drivers

Evaluate capital adequacy

Allocate capital

Estimate post-event losses

Accumulation Management

Risk Transfer

Determine reinsurance needs

Structure and price of reinsurance