eqecat u.s. hurricane loss model · presentation outline ... aties • for any given property, the...

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EQECATU.S. Hurricane Loss Model

FCHLPM Model Acceptability MeetingJune 1-3, 2005Tallahassee, FL

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Presentation Outline

General overview of the EQECAT modelSummary of changes relative to last year’s submission Summary of corrections made for deficienciesReview of the Standards

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Generalized Hurricane Loss Modeling

Catastrophe Modeling MethodologyStep One: Define the Hazard

HURRICANECentral PressureRadius to Max WindTranslational SpeedWind AttenuationTerrain

Gulf and Atlantic Hurricane Tracks, 1900 to 2003

Catastrophe Modeling MethodologyStep Two: Determine Site Hazard Severity

WIND SPEEDCalculated for ea Vw = f(Pc, d, regio

Gust Windspeed, mph

Like

lihoo

d

0%20%40%60%80%

100%

DM

G

Const 1 Const 2 Const 3

Vulnerability FunctionsCalculated damage for each Location

Estimate Damage for each Site:

Vulnerability curves for:• Structure / Appurtenant Structure• Contents• Loss of Use

Hazard Severity

Catastrophe Modeling Methodology Step Three: Estimate Ground up Damage

3 approaches for Vulnerability Function Development:

•Empirical ApproachHistorical Wind Fields and Claims Data

•Engineering ApproachDefine failure modes & estimate capacityCombine failure modes for overall capacity

•Expert opinion

Catastrophe Modeling MethodologyStep Four: Compute Insured Loss

Facultativeaties

• F or any g iven property , the insurer loss is the g reater o f tw o quan tities: (1 ) zero ,and (2 ) the dam age m inus the deductib le, bu t no t greater than the po licy lim it.B ecause the dam age is a random variab le, i.e ., it is associated w ith a p robabilityd istribu tion , so too is the insurer loss. H ow ever, w e can calcu late the averageinsurer loss (m athem atical expectation) by the fo llow ing expression:

D + L 1T IV • [ ∫ (x - D ) • f(x)dx + ∫ L • f(x)dx]

D D + L

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Outputs provided to FCHLPM

Core output used by insurers is the “Loss Cost”Loss cost varies

GeographicallyBy structure typeBy deductible level

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How is Loss Cost Generated?It is the sum of losses from all events affecting a location divided by the number of sampling years

It is the sum over all potential events of the product of the damage from an event times the annual frequency of each event

How is this done? A simplified example

∑=

2003

1900

)(104

1StormYear

allstormsSiteLossyears

dttftStormSiteLoss ttStorms

)()_(_∫ ∗

where )(tft = the annual frequency of one storm in the “probabilistic” event set

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Ground-up Loss Cost, example policy, using only historic events from 1990 to 2003

Opa

l

AndrewGeorges

Erin

Irene

High

Low

Relative Loss Cost

11


arry

Bob

Elena

High

Low

Relative Loss Cost

12


David

Eloi

se

Agnes

High

Low

Relative Loss Cost

13


Gerda

Cleo

Betsy

Gladys

High

Low

Relative Loss Cost

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King

How

Easy

Flor

ence

High

Low

Relative Loss Cost

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1944

-11

1945-01

1948-08

1946

-05

1941-05

1947-04

1945-09

1948

-07

1949-02

High

Low

Relative Loss Cost

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1930-02 1933-05

193

33-18

1934-03

1935-02

1936-05

939-02

High

Low

Relative Loss Cost

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1924-07 1926-0

1928-0

1921

-06

1924-04

1925

-02

1926-01

1929-02

High

Low

Relative Loss Cost

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1911-01

1912-03

1915-04

1916-01

High

Low

Relative Loss Cost

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1901-04

1903-03

High

Low

Relative Loss Cost

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Probabilistic loss costs

High

Low

Relative Loss Cost

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What is in a “probabilistic” set of events

The EQECAT Stochastic set contains permutations of storm intensity that are in overall agreement with regional meteorology and include permutations on

Storm intensityStorm trackMany other meteorological parameters

Example: Subset of storm tracks reaching northern Miami-Dade county, evaluation of track recurvature and time of maximum winds

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For entire stochastic set for Florida,number of hours before recurvature that wind peaks:mean=32 hours; sigma=79 hours

Recurvature versus location of maximum sustained winds

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How many years of simulations are necessary?

There are differences between the “historically derived”loss costs and the “probabilistic” loss costs

Goal is to produce results that do not change if the sampling period is increasedThe number of simulations is a function of the frequency and severity of loss inducing events

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Quantifying Modeling Uncertainty

Nassau County

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Nassau County Modeling Review

Calculate the average loss cost to the FHCF portfolio in Nassau county for varying probabilistic sets of storms

The meteorological characteristics of each set is the same(e.g., probability of severe storms)Only “refinement” is on the spacing of tracks, number of potential azimuths, how discretely storm intensity is modeled

Evaluate how “sensitive” model results are to increasing refinement of probabilistic set

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0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

0 1000 2000 3000 4000 5000number of events affecting Nassau county

expe

cted

ann

ual l

oss

Nassau County Aggregated PortfolioNassau County Aggregated Portfolio

90% confidence interval shown in red

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Nassau County Aggregated PortfolioNassau County Aggregated Portfolio

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

0 50,000 100,000 150,000 200,000Approximate number of annual simulations

expe

cted

ann

ual l

oss

90% confidence interval shown in red

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Reducing Modeling Uncertainty

Prior example showed a need for approximately 40,000 to 75,000 years of simulations to develop a stable average annual loss (loss cost)Is this the per-occurrence probability of loss non-exceedance curve more or less sensitive to this parameter?

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Case Study: Reducing Modeling Uncertainty

Background: The FHCLPM requires models loss costs to show no sensitivity to number of effective years of ‘storm’ simulations at the county loss cost.

Are other statistics more sensitive to model attributes?

Example: State of Texas, two ‘stochastic’ sets of hurricanes.• Set 1: 10,541 ‘events’• Set 2: 3,687 ‘events’

Analysis: Compare Ground-Up Loss cost at 5 km grid resolutionAnalysis: Compare Portfolio Probability of Loss non-exceedance curves

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Comparison of two stochastic sets

Set 1: 10,541 events Set 2: 3,687 events

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Comparison of two stochastic sets

Review of Stochastic SetsGalveston Bay

~20 miles

Review of Stochastic SetsGalveston Bay

~20 miles

Set 1: 10,541 events Set 2: 3,687 events

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Two Stochastic Storm Sets

Visually, the storms compare almost identicallyMeteorologically, the sets are the same

Distribution of Storm intensity with geography is the same (e.g., # CAT 4 events by 10 mile stretch of coast)Distribution of track angles is same

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Loss Cost Comparison

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Loss Cost discussion

State-wide loss costs compare to within 3%Smaller event set results are unstable – sometimes higher, sometimes lower than larger set

Differences are not based on physical modelDifferences are from insufficient number of simulations

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Comparing Per-Occurrence Probability of Loss non-exceedanceCurves

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

100,000

0 100 200 300 400 500 600 700 800 900 1,000

Return Period, Years

Per-

Occ

urre

nce

Loss

Abbreviated Stochastic SetComplete Stochastic Set

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Comparing Two Probability of Loss non-exceedance curves

The loss costs of the two ‘sets’ is quite close (within 3%)The non-exceedance curve for the abbreviated set has lower values for the lower probabilities of exceedance

The ‘bias’ of a lower non-exceedance curve is a physical property of a stochastic set that has insufficient resolution ofsimulationsThe ‘bias’ of being low is not consistent, but changes with degree of report resolution

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Logical Relationship to Risk

‘Risk’ varies with 3 primary componentsGeography (driven by hazard)Structure type (driven by vulnerability)Deductible

Does the model display consistent relativities to these factors?

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Masonry Ground-Up Loss Cost

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Frame Ground-Up Loss Cost

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Frame Loss Cost (2% Deductible)

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Masonry Loss Cost (2% deductible)

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EQECAT Hurricane Modeling

The basis of the EQECAT Hurricane model is empirical data from

MeteorologyEngineeringInsurance and actuarial science

It has been tested and compared to actual event outcomes to produce a reliable measure of risk

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Summary of Changes

Model Changes Since February 2004 Submittal

•The probabilistic hurricane database was regenerated to be consistent with the Commission's November 1, 2004 storm set.

•The gradient to sustained conversion and air density parameter were updated to be consistent with current scientific literatureand data.

•The distribution for hurricane frequency was changed from a Poisson to a Negative Binomial distribution.

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•One additional year with no hurricanes affecting FL (2003)

•Elena (1985) - upgraded from weak cat 3 (115 mph sustained) to strong cat 3 (127 mph sustained)

Official Hurricane Set - November 1, 2004

Gradient to Sustained Conversionand Air Density Parameter

•Gradient to sustained conversion •upper-level winds explicitly modeled

•Air density parameter updated to be•consistent with updated gradient to sustained conversion•based on the most recent full decade of SST data (1990-99)

•Impact on surface winds minimal (typically at most +/- 1 mph gust)

Negative Binomial Frequency Model

•Two parameters (mean, sigma) instead of the single parameter forPoisson (mean = variance) allows for better fit to the historical data

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Effect on Statewide Loss Costs

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Correction of Deficiencies

EQECAT Submissions to FCHLPM•Feb. 25, 2005 – original submission

•March 24, 2005 – submission to resolve deficiencies noted in March 11 letter from the Commission

•Editorial changes but no quantitative changes

•April 12, 2005 – provisional submission to address corrections noted in April 6 Professional Team report

•Editorial changes•Fig. 6 (p. 55) - revised units•Form M-1 (pp. 59-60) - revised frequencies in adjacent states•Form M-2 (pp. 62-63) - revised maps to use same locations•Form M-3 (pp. 64-65) - corrected minimum radius at 900 mb and updated figure to use full stochastic set instead of reduced set•Form A-4 (p. 119) - revised to correct for upgrade of Elena (1985)

•May 25, 2005 – submission to address corrections noted in April 6 Professional Team report and April 28 email from Donna Sirmons

•Further editorial changes but no further quantitative changes

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General Standards

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G-1 Scope of the Computer Model and Its Implementation

The computer model shall project loss costs for personal lines residential property from hurricane events.

USWIND projects loss costs for personal lines residential property from hurricane events.

For purposes of the Commission's review and determination of acceptability, the loss costs submitted for this review are expected losses resulting from hurricanes. Wind losses resulting from a hurricane are included even if wind speeds fall below hurricane force. The vulnerability functions are based to a large degree on hurricane claims data, which includes wind speeds above and below the hurricane threshold of 74 mph.

Expected loss costs include primary structure, appurtenant structures, contents, other covered personal property, and additional living expenses.

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G-2 Qualifications of Modeler Personnel and Independent Experts

A. Model construction, testing, and evaluation shall be performed by modeler personnel or independent experts who possess the necessary skills, formal education, or experience to develop hurricane loss projection methodologies.

B. The model or any modifications to an accepted model shall bereviewed by modeler personnel or independent experts in the following professional disciplines, if relevant: structural/windengineering (licensed Professional Engineer (PE)), statistics (advanced degree), actuarial science (Associate or Fellow of Casualty Actuarial Society), meteorology (advanced degree), and computer/information science (advanced degree). These individuals shall abide by the standards of professional conduct if adopted by their profession.

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The model construction, testing, and evaluation was performed by a team of individuals who possess the necessary skills, formal education, and experience to develop hurricane loss projection methodologies, and who abide by the standards of professional conduct adopted by their profession.

The model and all modifications to it have been reviewed by modeler personnel or independent experts in the following professional disciplines, if relevant: structural/wind engineering (licensed Professional Engineer), statistics (advanced degree), actuarial science (Associate or Fellow of Casualty Actuarial Society), meteorology (advanced degree), and computer/information science (advanced degree). These individuals are signatories on Forms G-1 through G-6 as applicable and abide by the standards of professional conduct if adopted by their profession.

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•Professional vitae of new modeler personnel and independent experts

Anu Sandhu (product management)Krishnaraj Santhanam (atmospheric science)Pradeep Yalamanchi (computer science)

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G-3 Risk Location

A. ZIP Codes used in the model shall be updated at least every 24 months using information originating from the United States Postal Service. The United States Postal Service issue date of the updated information shall be reasonable.

The USWIND ZIP Code database was updated in February 2004, based on information originating from the United States Postal Service current as of October 2003. EQECAT will update the ZIP Code database in the USWIND model at least every 24 months.

B. ZIP Code centroids, when used in the model, shall be based on population data.

The ZIP Code centroids used in USWIND are derived using population.

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G-3 Risk Location

C. ZIP Code information purchased by the modeler shall be verified by the modeler for accuracy and appropriateness.

EQECAT verifies each new ZIP Code database through a suite of procedures, including automated numeric tests and visual tests.

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G-4 Units of Measurement

A. All units of measurement for model inputs and outputs shall be clearly identified.For entering user-defined storms, USWIND has a storm editor that clearly specifies units of measurement for all of the storm parameters:

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G-4 Units of Measurement

B. All model outputs of length, wind speed, and pressure shall be in units of statute miles, statute miles per hour, and millibars, respectively.

For output, wind speed maps are clearly labeled as mph gust.All model outputs of length, wind speed, and pressure are in units of statute miles, statute miles per hour, and millibars, respectively.

C. Wind inputs to the damage function shall be in units consistent with currently used wind measurement units and/or shall be converted using standard meteorological/engineering conversion factors.

Wind inputs to the damage function are in units consistent with currently used wind measurement units.

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G-5 Independence of Model Components

The meteorology, vulnerability, and actuarial components of the model shall each be theoretically sound without compensation forpotential bias from the other two components. Relationships within the model among the meteorological, vulnerability, and actuarial components shall be reasonable.

The meteorology, vulnerability, and actuarial components of USWIND have been independently developed, verified, and validated. The meteorology component, completely independent of the other components, calculates wind speed at each site.

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G-5 Independence of Model Components

The vulnerability component is entirely independent of all other calculations, e.g. meteorological, loss, etc. Validation of the vulnerability functions has been performed independently from other validation tests, e.g. whenever the vulnerability functions have been validated using claims data from a historical storm, the wind field for that storm has first been validated independently. If any of the other calculation modules were changed, no changes would be necessary to the vulnerability functions.

The loss distributions are calculated using the damage distribution at each site and the policy structure. Finally, the site distributions (damage and loss) are combined statistically to estimate the expected annual loss and the loss exceedance curve for the portfolio. All components together have been validated and verified to produce reasonable and consistent results.

•Validations of each model component presented to Professional Team in the relevant Standards sections•There have been no changes affecting independence of model components

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Meteorological Standards

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M-1 Official Hurricane Set

For landfall frequency analyses, the modeler shall use the latest updated Official Hurricane Set. Updates to HURDAT approved by the Tropical Prediction Center/National Hurricane Center are acceptable modifications to the Official Hurricane Set. Additional information from the National Hurricane Center or from peer reviewed atmospheric science literature can be used to justify modifications to the Official Hurricane Set.

The storm set used is the Official Hurricane Set provided by the Commission on November 1, 2004.

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M-2 Hurricane Characteristics

Methods for depicting all modeled hurricane characteristics, including but not limited to wind speed, radial distributions ofwind and pressure, minimum central pressure, radius of maximum winds, strike probabilities, tracks, and the spatial and time variant wind fields, shall be based on information documented by currently accepted scientific literature or modeler information accepted by the Commission.

The modeling of hurricane characteristics is based on information documented by currently accepted scientific literature or on EQECAT analyses of scientific information.

10 20 30 40 500

0.2

0.4

0.6

0.8

1

T at 1200 nmi

10 20 30 40 500

0.2

0.4

0.6

0.8

1

T at 1700 nmi

Probability Distribution and Chi-Square Test of Translational Speed (T)

CDF

T (knots) T (knots)

= 2.53 at 1200 nmiχ25

= 1.36 at 1700 nmiχ25

Near Ft. Meyers, FL Near Daytona Beach, FL

Lognormal distribution fits the empirical data at the 5% significance level

χ25P( < 11.1) = 0.95

USW Fits

NWS38 Data

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Goodness-of-Fit Test of Translational Speed (T) at Tampa

Kolmogorov-Smirnov TestTest Statistic: 12.4%

Critical Valueα=0.10 α=0.05 α=0.01

n=84 Years Data 13.3% 14.8% 17.9%

Lognormal model can not be rejected at the 10% level of Lognormal model can not be rejected at the 10% level of significance.significance.

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M-3 Landfall Intensity

Models shall use maximum one-minute sustained 10-meter wind speed when defining hurricane landfall intensity. This applies both to the Official Hurricane Set used to develop landfall strike probabilities as a function of coastal location and to the modeled winds in each hurricane which causes damage. The associated maximum one-minute sustained 10-meter wind speed shall be within the range of wind speeds (in statute miles per hour) categorized by the Saffir-Simpson scale.

USWIND uses maximum one-minute sustained 10-meter wind speed when defining hurricane landfall intensity.

The USWIND pressure-wind speed relationship generates wind speeds which are in agreement with the Saffir-Simpson category definition. Wind speeds developed for historical hurricanes are also consistent with the observed values.

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Revised Form M-1

•Revised the MS/AL and GA portions of Form M-1 (April 12, 2005):

•historicals had been double-counted in MS and AL

•issues with landfall states identified in Official Hurricane Set

•modeled frequencies were not determined correctly

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M-3 Landfall Intensity (Revised Form M-1)

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M-4 Hurricane Probabilities

A. Modeled probability distributions for hurricane intensity, forward speed, radii for maximum winds, and landfall angle shallbe consistent with historical hurricanes in the Atlantic basin.

The modeled probability distributions for hurricane intensity, forward speed, radii for maximum winds, and landfall angle are consistent with historical hurricanes in the Atlantic basin.

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M-4 Hurricane Probabilities

B. Modeled hurricane probabilities shall reasonably reflect the Official Hurricane Set through 2003 for category 1 to 5 hurricanes and shall be consistent with those observed for each coastal segment of Florida and neighboring states (Alabama, Georgia, and Mississippi).

Modeled hurricane probabilities reasonably reflect the Official Hurricane Set through 2003 for category 1 to 5 hurricanes and are consistent with those observed for each coastal segment of Florida, Alabama, Georgia, and Mississippi. Probabilities were developed along the Florida coast and adjacent areas using smoothed distributions of hurricane frequency and wind speed-defined intensity, fit to the Commission's Official Hurricane Set using scientific methods.

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GoodnessGoodness--ofof--Fit test (Negative Binomial)Fit test (Negative Binomial)

KolmogorovKolmogorov--Smirnov TestSmirnov TestTest Statistic: 0.0136Critical value at the 5% level of significance:0.174

ChiChi--Square TestSquare TestTest Statistic: 1.59Critical value, χ2(0.95;10-2) = 14.07

Model cannot be rejected at the 5% level of significance.Model cannot be rejected at the 5% level of significance.

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M-5 Land Friction and Weakening

A. The magnitude of land friction coefficients shall be consistent with currently accepted scientific literature relevant to current geographic surface roughness distributions and shall be implemented with appropriate geographic information system data.

USWIND uses land friction to produce a reduction of wind speeds over land which are consistent with the accepted scientific literature and with geographic surface roughness. A smooth transition is used to reduce onshore marine-exposure wind speeds to inland frictionally reduced wind speeds. Wind speeds between adjacent ZIP Codes, counties, or territories, also exhibit a smooth transition. Appropriate geographic information system data have been used to develop the USWIND land friction database.

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M-5 Land Friction and Weakening

B. The hurricane overland weakening rate methodology used by themodel shall be reasonable in comparison to historical records.

The hurricane overland weakening rate methodology used by USWIND for hurricanes in Florida is reasonable in comparison to historical records, and produces a result within twenty percent of the Kaplan-DeMaria filling rate.

•Revisions to submission (April 12, 2005):

•Revised units on Figure 6 on p. 55 of the submission (mph on vertical axis).

•Revised maps on Form M-2 to use same exposure locations

910 905 900 895

930 925 920 915

950 945 940 935

970 965 960 955

990 985 980 975

Hurricane Overland Weakening Rate• Mean filling rate µ based on J. Kaplan and M. DeMaria, A Simple

Empirical Model for Predicting the Decay of Tropical Cyclone Winds after Landfall, J. App. Met. 34 p. 2499-2512 (1995)

Velocity(mph)

Time (hr)20

170

0 25

= P0

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Revised Form M-2

Figure 9. Contour map - maximum winds for modeled version of Official Hurricane Set. Wind speeds are one-minute sustained mph.

75.0000 to 95.0000

40.0000 to 75.0000

140.0000 to 155.0000

130.0000 to 140.0000

110.0000 to 130.0000

95.0000 to 110.0000

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Revised Form M-2

Figure 10. Contour map - maximum winds for 100-year return period from stochastic storm set. Wind speeds are one-minute sustained mph.

75.0000 to 95.0000

40.0000 to 75.0000

140.0000 to 155.0000

130.0000 to 140.0000

110.0000 to 130.0000

95.0000 to 110.0000

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M-6 Logical Relationships of Hurricane Characteristics

A. The radius of maximum winds shall reflect historical hurricane characteristics.The distribution for radius of maximum winds used in USWIND reflects historical hurricane characteristics.

B. The magnitude of asymmetry shall increase as the translation speed increases, all other factors held constant.The magnitude of asymmetry in USWIND increases as the translation speed increases, all other factors held constant.

C. The wind speed shall decrease with increasing surface roughness (friction), all other factors held constant.The wind speed in USWIND decreases with increasing surface roughness (friction), all other factors held constant.

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Revised Form M-3Central Pressure (mb) Range of Rmax (mi)

900

4-24

910

4-33

920

5-42

930

6-60

940

6-60

950

6-60

955

6-60

960

6-60

965

6-60

970

6-60

975

6-60

980

6-60

985

6-60

990

6-60

Revision April 12, 2005: corrected minimum radius at 900 mb

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Revised Form M-3

Revision April 12, 2005: updated figure to use full stochastic set instead of reduced set

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Vulnerability Standards

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V-1 Derivation of Vulnerability Functions

A. Development of the vulnerability functions is to be based on a combination of the following: (1) historical data, (2) tests, (3) structural calculations, (4) expert opinion, or (5) site inspections. Any development of the vulnerability functions based on structural calculations or expert opinion shall be supported by tests, siteinspections, or historical data.

USWIND vulnerability functions are based on historically observed damage (in terms of both claims data and post-hurricane field surveys), and experimental research conducted by Professors Kishor Mehta and James McDonald at Texas Tech.

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The claims data analyzed is from two basic sources: (1) claims data from all major storms during the period 1954 - 1994 analyzed by Dr. Don Friedman and JohnMangano while managing the Natural Hazard Research Service (NHRS) effort for The Travelers Insurance Company; and (2) claims data from Hurricanes Alicia (1983), Elena (1985), Gloria (1985), Juan (1985), Kate (1985), Hugo (1989), Bob (1991), Andrew (1992), Iniki (1992), Erin (1995), and Opal (1995) provided to EQECAT by the insurance companies assisting with the development of USWIND.

EQE / EQECAT teams have conducted post-disaster field surveys for several storms in the past few years, including Hurricanes Andrew (1992), Iniki (1992), Luis (1995), Marilyn (1995), Opal (1995), Georges (1998), Irene (1999), Lili(2002), Fabian (2003), Isabel (2003), Charley (2004), Frances (2004), Ivan (2004), and Jeanne (2004); Typhoon Paka (1997); and the Oklahoma City (1999), Fort Worth (2000), and Midwest (2003) tornado outbreaks. In addition, the research of Professors Mehta and McDonald incorporates a large amount of investigation into the effects of all major storms in roughly the last 25 years.

84


B. The method of derivation of the vulnerability functions shall be theoretically sound.

The method of derivation of the USWIND vulnerability functions is theoretically sound.

C. Any modification factors/functions to the vulnerability functions or structural characteristics and their corresponding effects shall be clearly defined and be theoretically sound.

Modification factors/functions to the vulnerability functions are applied in the secondary structural component of the model. The effects of particular structural characteristics are clearly defined and theoretically sound.

85


D. Construction type and construction characteristics shall be used in the derivation and application of vulnerability functions.USWIND allows a user to account for the unique features of individual buildings, including construction type and construction characteristics. Such features modify the vulnerability functions.

E. In the derivation and application of vulnerability functions,assumptions concerning building code revisions and building codeenforcement shall be reasonable and be theoretically sound.The EQECAT model accounts for building code revisions using the year of construction (next slide). The model does not explicitly incorporate building code quality or enforcement into the vulnerability functions because at this time no reliable or accurate source of information is available. USWIND does allow a user to account for the unique characteristics of individual buildings, which are often related to code enforcement: roof-to-wall anchorage, foundation anchorage, and debris potential from nearby buildings for example.

86


Mobile Homes •Pre 1974•1974-1994•Post 1994

All Other Structures•Pre 1955•1955-1972•1973-1982•1983-1995•1996-1998•1999-2002•Post 2002

The model provides a set of modification functions to the vulnerability functions on the basis of year of construction, in terms of the following age ranges:

87


F. Vulnerability functions shall be separately derived for building structures, mobile homes, appurtenant structures, contents, and additional living expense.

The USWIND vulnerability functions separately compute damages for building structures, mobile homes, appurtenant structures, contents, and additional living expense.

G. The minimum wind speed that generates damage shall be reasonable.

The USWIND vulnerability functions calculate damage for all peak gust wind speeds greater than or equal to 40 miles per hour.

88

V-2 Mitigation Measures

A. Modeling of mitigation measures to improve a building's wind resistance and the corresponding effects on vulnerability shall be theoretically sound. These measures shall include fixtures or construction techniques that enhance:

· Roof strength· Roof covering performance· Roof-to-wall strength· Wall-to-floor-to-foundation strength· Opening protection· Window, door, and skylight strength.

The USWIND model allows for modifications to the vulnerability curves in the secondary structural component of the model if additional knowledge about the construction characteristics is available.

89

V-2 Mitigation Measures

B. Application of mitigation measures shall be reasonable both individually and in combination.

The application of modifications to the vulnerability curves in the secondary structural component of USWIND is reasonable both individually and in combination.

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Actuarial Standards

91

A-1 Modeled Loss Costs

Modeled loss costs shall reflect all damages starting when damage is first caused in Florida from an event modeled as a hurricane at that point in time and will include all subsequent damage in Florida from that event.

Any variations in modeled loss costs shall be justified.

Modeled loss costs reflect all damages starting when damage is first caused in Florida from an event modeled as a hurricane at that point in time and will include all subsequent damage in Florida from that event.

92

A-2 Underwriting Assumptions

A. When used in the modeling process or for verification purposes, adjustments, edits, inclusions, or deletions to insurance company input data used by the modeler shall be based upon accepted actuarial, underwriting, and statistical procedures.

• Review claims data for consistency, correct any errors and determine all elements included within the claims data

• Group data by class, ensure consistency between insurers including relevant underwriting practices

• Correct data for underinsurance, if any

93

A-2 Underwriting Assumptions

B. For loss cost estimates derived from or validated with historical insured hurricane losses, the assumptions in the derivations concerning (1) construction characteristics, (2) policy provisions, (3) claim payment practices, and (4) relevant underwriting practices underlying those losses, as well as any actuarial modifications, shall be reasonable and appropriate.

• Calculate ground up loss using paid claim and prorated deductible, removing demand surge if applicable

• Apply corrections for unreported data• Assign windspeed using best available historical information• Perform regression analysis• Validate damage functions using loss experience

94

A-3 Loss Cost Projections

A. Loss cost projections produced by hurricane loss projection models shall not include expenses, risk load, investment income,premium reserves, taxes, assessments, or profit margin.

B. Loss cost projections shall not make a prospective provision foreconomic inflation.

C. Loss cost projections shall not explicitly include demand surge.

• Loss cost projections produced do not include expenses, risk load, investment income, premium reserves, taxes, assessments or profit margin.

• The model does not make a prospective provision for economic inflation, with regard to either losses or policy limits.

• Loss cost projections do not explicitly include demand surge.

95

A-4 User Inputs

All modifications, adjustments, assumptions, and defaults necessary to use the inputs in the model shall be actuarially sound and included with the model output. Treatment of missing valuesfor user inputs required to run the model shall be actuarially sound and described with the model output.

Any assumption or method used by EQECAT's hurricane loss projection model that relates to a specific insurer's inputs to the model, if any, for the purposes of preparing the insurer's rate filing shall be clearly identified. EQECAT will disclose any implicit assumptions relating to insurance to value, the prevalence of appurtenant structures, or demographic risk characteristics.

96

A-5 Logical Relation to Risk

A. Loss costs shall not exhibit an illogical relation to risk, nor shall loss costs exhibit a significant change when the underlying riskdoes not change significantly

B. Loss costs produced by the model shall be positive and non-zero for all valid Florida ZIP Codes

C. Loss costs cannot increase as friction or roughness increase, all other factors held constant

D. Loss costs cannot increase as the quality of construction type, materials and workmanship increases, all other factors held constant

E. Loss costs cannot increase as the presence of fixtures or construction techniques designed for hazard mitigation increases, all other factors held constant

F. Loss costs cannot increase as the quality of building codes and enforcement increases, all other factors held constant

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A-5 Logical Relation to Risk

G. Loss costs shall decrease as deductibles increase, all other factors held constant.

H. The relationship of loss costs for individual coverages, (e.g., structures, appurtenant structures, contents, and loss of use/additional living expense) shall be consistent with thecoverages provided.

Loss costs exhibit logical relation to risk. Loss costs are positive for all ZIP Codes. All other factors held constant, loss costs do not increase: as friction or roughness increase; as the quality of construction type increases, as materials and workmanship increase; fixtures or construction techniques designed for hazard mitigation are present; as the quality of building codes and enforcement increases. All other factors held constant, loss costs decrease as deductibles increase. Relationships among the loss costs forcoverages A,B,C,D are consistent with the coverages provided.

Revised Form A-4 to correct for upgrade of Elena (1985).

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A-6 Deductibles and Policy Limits

A. The methods used in the development of mathematical distributions to reflect the effects of deductibles and policy limits shall be actuarially sound.

B. The relationship among the modeled deductible loss costs shall be reasonable.

USWIND provides an actuarially sound mathematical representationof the distribution of losses to reflect the effects of deductibles and policy limits.

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A-7 Contents

A. The methods used in the development of contents loss costs shall be actuarially sound.

B. The relationship between the modeled structure and contents loss costs shall be reasonable, based on the relationship between historical structure and contents losses.

EQECAT’s model calculates damage to contents separately from damage to buildings and appurtenant structures. Content vulnerability curves in USWIND are based on claims data.

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A-8 Additional Living Expense (ALE)

A. The methods used in the development of Additional Living Expense (ALE) loss costs shall be actuarially sound.

B. ALE loss cost derivations shall consider the estimated time required to repair or replace the property.

C. The relationship between the modeled structure and ALE loss costs shall be reasonable, based on the relationship between historical structure and ALE losses.

EQECAT’s model calculates damage to additional living expense (ALE) as a function of building and content damage. ALE vulnerability curves in USWIND are based on claims data.

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A-9 Output Ranges

A. Output Ranges shall be logical and any deviations supported. The output ranges produced by the model are logical and any deviations are supported.

B. All other factors held constant:

1. Output ranges produced by the model shall have a pattern of declining loss costs with increasing deductibles.The output ranges produced by the model have a pattern of declining loss costs with increasing deductibles.

2. Output ranges produced by the model shall reflect lower loss costs for masonry construction versus frame construction.The output ranges produced by the model reflect lower loss costs for masonry construction versus frame construction, subject to the discussion in Disclosure 1.

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A-9 Output Ranges

3. Output ranges produced by the model shall reflect lower loss costs for residential risk exposure versus mobile home risk exposure.The output ranges produced by the model reflect lower loss costs for residential risk exposure versus mobile home risk exposure.

4. Output ranges produced by the model shall reflect lower loss costs, in general, for inland counties versus coastal counties.The output ranges produced by the model reflect lower loss costs, in general, for inland counties versus coastal counties.

5. Output ranges produced by the model shall reflect lower loss costs, in general, for northern counties versus southern counties.The output ranges produced by the model reflect lower loss costs, in general, for northern counties versus southern counties.

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A-9 Output Ranges

6. Output ranges produced by the model shall reflect lower loss costs for contents versus structures.The output ranges produced by the model reflect lower loss costs for contents versus structures, subject to the discussion in Disclosure 1.

7. Output ranges produced by the model shall reflect lower loss costs for additional living expense versus structures.The output ranges produced by the model reflect lower loss costs for additional living expense versus structures, subject to the discussion in Disclosure 1.

8. Output ranges produced by the model shall be positive and non-zero for all given risk exposures.The output ranges produced by the model are positive and non-zero for all given risk exposures.

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Statistical Standards

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S-1 Modeled Results and Goodness-of-Fit

A. The use of historical data in developing the model shall be supported by rigorous methods published in currently accepted scientific literature.

EQECAT’s use of historical data in developing USWIND is supported by rigorous methods published in currently accepted scientific literature.

B. Modeled and historical results shall reflect agreement using currently accepted scientific and statistical methods.

Modeled and historical results reflect agreement using currently accepted scientific and statistical methods.

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S-1 Modeled Results and Goodness-of-Fit

•The validation and verification of the model is based on the claims data from Hurricanes Alicia (1983), Elena (1985), Gloria (1985), Juan (1985), Kate (1985), Hugo (1989), Bob (1991), Andrew (1992), Iniki (1992), Erin (1995) and Opal (1995).

•USWIND-generated peak gust wind patterns have been validated with the actual peak gust observations for eleven landfalls of nine notable hurricanes since 1960.

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S-2 Sensitivity Analysis for Model Output

The modeler shall have assessed the sensitivity of temporal and spatial outputs with respect to the simultaneous variation of input variables using currently accepted scientific and statistical methods and have taken appropriate action.

•EQECAT has assessed the sensitivity of temporal and spatial outputs with respect to the simultaneous variation of input variables using currently accepted scientific and statistical methods, and has taken appropriate action.

•Sensitivity analyses have been performed on track spacing, on the number of attack angles given landfall, on the number of wind speed class intervals given landfall and attack angle.

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S-3 Uncertainty Analysis for Model Output

The modeler shall have performed an uncertainty analysis on the temporal and spatial outputs of the model using currently accepted scientific and statistical methods and have taken appropriate action. The analysis shall identify and quantify the extent that input variables impact the uncertainty in model output as the input variables are simultaneously varied.

EQECAT has performed uncertainty analysis on the temporal and spatial outputs of the model using currently accepted scientific and statistical methods and has taken appropriate action. The analysis has identified and quantified the extent that input variables impact the uncertainty in model output as the input variables are simultaneously varied.

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S-4 County Level Aggregation

At the county level of aggregation, the contribution to the error in loss costs estimates attributable to the sampling process shall be negligible.

USWIND estimates loss costs in the mainland United States from Texas to Maine on the basis of 511,500 stochastic hurricane events. Of these, about 160,000 are Florida landfalling or bypassing events. Given the high resolution of the stochastic storm database, the contribution to the error in loss cost estimates induced by the sampling process is negligible.

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S-5 Replication of Known Hurricane Losses

The model shall reasonably replicate incurred losses on a sufficient body of past hurricane events, including the most current data available to the modeler. This Standard applies separately to personal residential and, to the extent data are available, to mobile homes. Personal residential experience may be used to replicatebuilding-only and contents-only losses. The replications shall be produced on an objective body of loss data by county or an appropriate level of geographic detail.

•USWIND reasonably replicates incurred losses on a sufficient body of past hurricane events, including the most current data available to EQECAT.

•Five validation comparisons have been provided in Form S-6 for four different companies for hurricane Andrew, Opal and Alicia.

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S-6 Comparison of Estimated Hurricane Loss Costs

The difference, due to uncertainty, between historical and modeled annual average statewide loss costs shall be statistically reasonable.

•The difference, due to uncertainty, between historical and modeled annual average statewide loss costs is statistically reasonable.

•Validation of the expected annual loss estimate has been carried out by checking each component of the model separately – frequency of the storm, severity of the storm, loss calculation.

•Loss estimate by USWIND compared against the alternative method of estimating the annual loss.

•Carried out convergence tests to ensure stability of the results.

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Computer Standards

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C-1 Documentation

A. The modeler shall maintain a primary document binder, containing a complete set of documents specifying the model structure, detailed software description, and functionality. Development of each section shall be indicative of accepted software engineering practices.

EQECAT maintains all such documentation, and it was reviewed by the Professional Team.

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C-1 Documentation

B. All computer software (i.e., user interface, scientific, engineering, actuarial, data preparation, and validation) relevant to the modeler's submission shall be consistently documented.


C. Documentation shall be created separately from the source code.


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C-2 Requirements

The modeler shall maintain a complete set of requirements for each software component as well as for each database or data file accessed by a component.

EQECAT maintains a set of documents describing the specifications and product requirements for user interfaces, database schema, client customizations, security considerations, user manuals, and references. This documentation was reviewed by the Professional Team.

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C-3 Model Architecture and Component Design

The modeler shall maintain and document (1) detailed control anddata flow diagrams and interface specifications for each software component, and (2) schema definitions for each database and datafile. Documentation shall be to the level of components that make significant contributions to the model output.

The design levels of the software have been documented, including software components and interfaces, data files, and database elements. This documentation was reviewed by the Professional Team.

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C-4 Implementation

A. The modeler shall maintain a complete procedure of coding guidelines consistent with accepted software engineering practices.

EQECAT maintains such a procedure, and it was reviewed by the Professional Team.

B. The modeler shall maintain a complete procedure used in creating, deriving, or procuring and verifying databases or datafiles accessed by components.

EQECAT maintains such a procedure, and it was reviewed by the Professional Team.

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C-4 Implementation

C. All components shall be traceable, through explicit componentidentification in the flow diagrams, down to the code level.

All components are traceable in this manner. This aspect of the EQECAT software was reviewed by the Professional Team.

D. The modeler shall maintain a table of all software componentsaffecting loss costs, with the following table columns: (1) Component name, (2) Number of lines of code, minus blank and comment lines; and (3) Number of comment lines.

EQECAT maintains such a table. This aspect of the EQECAT software was reviewed by the Professional Team.

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C-4 Implementation

E. Each component shall be sufficiently and consistently commented so that a software engineer unfamiliar with the code shall be able to comprehend the component logic at a reasonable level of abstraction.Yes, the source code is commented in this manner. Also, EQECAT maintains live intranet source code documentation for the analysis engines. The model is based upon published research modified as appropriate by EQECAT’s meteorological, engineering, and statistical personnel. System data is organized and maintained in tables, binary files, or flat files, depending upon the type of analysis. The underlying model including algorithm implementation and technical assumptions along with the procedures used for updating the system data will be available for review by the professional team during the on-site visit. The overall system design has been implemented using standard software engineering techniques. System documentation is maintained to define critical system functionality in terms of Data Flow Diagrams, Structure Charts, and the corresponding narratives which describe how each module functions. This information was reviewed by the Professional Team.

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C-5 Verification

A. GeneralThe modeler shall maintain procedures for verification, such as code inspections, reviews, calculation crosschecks, and walkthroughs,sufficient to demonstrate code correctness.

The models have been extensively tested to verify that calculated results are consistent with the intended simulation approach. A variety of methods have been employed. These include algorithm verification through comparison to independently developed software packages, hand calculations, and sensitivity analyses.

Extensive validation testing of the software generated wind fields has been performed to confirm that generated wind speeds are consistent with observations. Numerous analyses have been conducted using actual insurance portfolio data to confirm the reasonableness of resulting answers.

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C-5 Verification

B. Component Testing1. The modeler shall use testing software to assist in documenting and analyzing all components.Testing software is used to assist in documenting and analyzing all components.

2. Unit tests shall be performed and documented for each component.Unit tests have been performed and documented for each component relevant to residential hurricane loss costs in Florida.

3. Regression tests shall be performed and documented on incremental builds.A suite of automated regression tests is regularly run on the software to ensure integrity of the various components as well as the results produced by the integrated system. Quality assurance documentation includes a description of each test case from the regression testing suite.

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C-5 Verification

B. Component Testing4. Aggregation tests shall be performed and documented to ensurethe correctness of all components, defining the model.A suite of automated regression tests is regularly run on the software to ensure integrity of the various components as well as the results produced by the integrated system.

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C-5 Verification

C. Data Testing1. The modeler shall use testing software to assist in documenting and analyzing all databases and data files accessed by components.Testing software is used to assist in documenting and analyzing all databases and data files accessed by components.

2. The modeler shall perform and document integrity, consistency, and correctness checks on all databases and data files accessed by the components.Client data is extensively tested during the import process into the EQECAT system to confirm its accuracy. Field level validation is performed to confirm that every data element within each record falls within known ranges. Data not falling within known ranges is marked as an error or a warning in a log depending upon the severity of the problem. Child/parent and other key relationships are also checked. A summary log is displayed at the end of import process denoting the number records which have warnings or errors.

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C-6 Model Maintenance and Revision

A. The modeler shall maintain a clearly written policy for modelrevision, including verification and validation of revised components, databases, and data files.

EQECAT has a clearly written policy for model revision with respect to methodologies and data, including verification and validation of revised components, databases, and data files. This policy was reviewed by the Professional Team.

B. A revision to any portion of the model that results in a change in any Florida residential hurricane loss cost shall result in a new model version number.

A revision to any portion of the model that results in a change in any Florida residential hurricane loss cost results in a new model version number.

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C-6 Model Maintenance and Revision

C. The modeler shall use tracking software to identify all errors, as well as modifications to code, data, and documentation.

EQECAT uses tracking software to identify all errors, as well as modifications to code, data, and documentation. EQECAT's policies and procedures for model revision were reviewed by the Professional Team.

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C-7 Security

The modeler shall have implemented and fully documented securityprocedures for: (1) secure access to individual computers where the software components or data can be created or modified, (2) secure operation of the model by clients, if relevant, to ensure that the correct software operation cannot be compromised, (3) anti-virus software installation for all machines where all components and data are being accessed, and (4) secure access to documentation,software, and data in the event of a catastrophe.

In accordance with standard industry practices, EQECAT has in place security procedures for access to code, data, and documentation, including disaster contingency, and for maintenance of anti-virus software on all machines where code and data are accessed. Procedures are also in place to ensure that licensees of the model cannot compromise the correct operation of the software.

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