catastrophe risk (e) subgroup...and can cover multiple states and regions assess annual and...

© 2019 National Association of Insurance Commissioners

Date: 6/7/19

2019 Summer National Meeting New York, New York

CATASTROPHE RISK (E) SUBGROUP

Friday, August 2, 2019 5:00 – 6:30 p.m.

America’s Hall I – 3rd Level

ROLL CALL

Tom Botsko, Chair Ohio Robert Ridenour, Vice Chair Florida Susan Bernard California Mitchell Bronson Colorado Susan Gozzo Andrews/Wanchin Chou Connecticut Judy Mottar Illinois Gordon Hay Nebraska Anna Krylova New Mexico Gloria Huberman/Sak-man Luk New York Andy Schallhorn Oklahoma Will Davis South Carolina Nicole Elliott/Miriam Fisk Texas NAIC Support Staff: Eva Yeung/Jane Barr

AGENDA

1. Hear a Presentation from AIR Worldwide (AIR) on How the Aggregate and Occurrence Exceedance Probability Curves are Created Bases on the AIR Modeling Results—Christy Shang (AIR) Attachment A

2. Hear a Presentation from RMS on How the Aggregate and Occurrence Exceedance Probability is Calculated and a Comparison of the Results—Matthew Nielsen (RMS) Attachment B

3. Discuss Any Other Matters Brought Before the Subgroup—Tom Botsko (OH)

4. Adjournment w:\national meetings\2019\spring\tf\capadequacy\pcrbc\080219 cat risk agenda.docx

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1©2019 AIR Worldwide 1

Comparability of Aggregate and Occurrence Exceedance Probability Curves

NAIC 2019 Summer National Meeting Christy Shang, CEEM

Attachment A

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The AIR Models and Exceedance Probability (EP) Curves• AIR Model Framework• Aggregate EP Curve (AEP)• Occurrence EP Curve (OEP)

Comparability of AEP and OEP

Agenda

Attachment A

4


AIR Model Framework and EP Curve Generation

Attachment A

5


AIR Catastrophe Modeling Framework

HAZARD

ENGINEERING

FINANCIAL

Intensity Calculation

Exposure Information

Damage Estimation

Policy Conditions

Contract Loss Calculations

Event Generation

Simulations of What Could Happen in a Year

Calculate the physical effects at all locations Estimate property and

time element damage Estimate losses fromvarious perspectives

Attachment A

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Sample U.S. Hurricane Stochastic Catalog

Year Event ID Day LF Num SS LF Seg CP Max Wind SpeedLandfall

LatLandfall

LongRadius Max

WindForward

SpeedLandfall

Angle1 270000012 265 1 3 43 956 110.3 34.78 -76.6 39.4 15.4 -33.22 270000021 160 1 1 21 980.4 82.9 29.85 -84.17 23 8.5 29.72 270000042 272 1 1 8 978 91.1 28.89 -95.43 23.7 6.8 -30.13 270000061 216 1 3 8 958 113.9 28.83 -95.51 30.2 11 -32.73 270000062 216 1 1 38 989.2 79.1 32.27 -80.5 39.8 20.4 -72.63 270000077 280 1 2 30 971.9 106.3 25.87 -80.15 14.8 11.6 -101.34 270000089 198 1 3 16 911.6 126.1 30.36 -88.38 31.4 26.2 -17.57 270000181 220 1 3 17 962.8 113 30.37 -88.2 25.1 16.1 -7.68 270000203 205 1 1 42 977.3 90.3 34.56 -77.13 25.4 10.9 -38.88 270000216 261 1 2 42 967.5 99.9 34.23 -77.76 27.2 9 -22

11 270000300 259 1 3 14 973.6 110.5 29.19 -90.04 43.7 21.8 -1.611 270000301 260 1 2 39 968.8 106.4 32.69 -79.96 9.7 19 -31.911 270000301 260 2 1 55 986.8 86.9 41.48 -71.03 18.2 33.6 19.812 270000323 243 1 1 43 986.1 74.5 34.65 -76.93 39.5 8.5 -5.8

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

Attachment A

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• Exceedance probability curves are calculated onan annual occurrence or annual aggregate basis

• Start with event losses by simulation year andprepare the data in one of two ways:– Occurrence basis: Obtain the largest loss within each

simulated year– Aggregate basis: Obtain the total of all losses within each

simulated year

Loss Exceedance Probability Curves

Attachment A

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Constructing an Occurrence Exceedance Probability Curve

• To build the EP curve, first compile all event losses for all years in simulation catalog:

Attachment A

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Step 1: Filter event losses by year (an occurrence EP curve utilizes the largest loss in each simulation year)

.

Event 2736 $2.45

Event 2735

$237.00

Event 2731 $3.50

Simulation Year 805

Occ. EP Curve Year 805 Loss = USD 237.00 Million


Event 2735

$237.00

Attachment A

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Step 2: Sort annual losses from highest to lowest. Rank each year.

Step 3: Compute exceedance probability as:

• Rank / (# Simulated Years)

Note that simulation year 805 contains the 20th largest ranked loss, this is your 0.20% exceedance probability or 500-year return period:

20/10000 = 0.20%


Attachment A

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Step 1: For an aggregate EP curve, sum event losses by year

Constructing an Aggregate Exceedance Probability Curve

.

Event 2736 $2.45

Event 2735

$237.00

Event 2731 $3.50

Simulation Year 805

Agg. EP Curve Year 805 Loss = USD 242.95 Million

Sum$242.95M

Attachment A

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• Step 2: Sort annual losses from highest to lowest. Rank each year.

• Step 3: Compute loss exceedance probability as:

• Rank / (# Simulated Years).

Note that simulation year 805 contains the 25th largest ranked loss, this is your 0.25% exceedance probability or 400-year return period:

25 / 10000 = 0.25%

Constructing an Aggregate Exceedance Probability Curve

Attachment A

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Comparability of AEP and OEP

Attachment A

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• Each stochastic year is asimulation of the hurricaneactivities in a given year

• It is common to have multipleloss-causing hurricanes in a year

• More likely to have events withhigh intensity in Florida than inthe Northeastern (NE) region

• Top simulated loss years ofFlorida are driven by singlemajor hurricane impacting thestate

• Top simulated loss years of theNE are driven by multiplehurricanes with lower intensitiesimpacting the region

Aggregate vs. Occurrence 100-Year Loss Case Studies - Hurricane

10%

7%

24%

45%

30 States andWashington D.C.

FL AL, LA and TX MA, NY and NJ

Agg_100Yr Occ_100Yr

Attachment A

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Aggregate vs. Occurrence 100-Year Loss Case Studies - Hurricane

8%

7%45%

4%

FL_Statewide FL_Monroe FL_Broward_Miami-Dade FL_Orange

Manufactured Home

Agg_100Yr Occ_100Yr

• The difference between Aggregate and Occurrence 100-year losses vary materiallydepending on the concentration of the exposure

Attachment A

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Aggregate vs. Occurrence 100-Year Loss Case Studies - Earthquake

• The earthquake model alsocontains stochastic yearswith multiple events

• The chance of having morethan 1 major earthquake inthe same year is relative lowcompared to hurricanes

• 100-Year OEP and AEP losslevels will vary materially forcompanies with exposuresin various seismic zones

4%

1%

13%

7%

50 States CA OR, WA CA, OR and WA

Agg_100Yr Occ_100Yr

Attachment A

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Aggregate vs. Occurrence EP Curves - Summary

• The difference between the aggregate andoccurrence EP curves would vary dependingon:– Peril (for example: hurricane vs. earthquake)– Company’s book of business (for example: regional vs.

countrywide carriers)

• Given the sensitivity of model estimates tounique portfolio characteristics, factor-basedadjustments to occurrence/aggregate lossestimates is not recommended

Attachment A

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1Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019

RMS PERSPECTIVE ON AEP AND OEPMatthew Nielsen – Government and Regulatory Affairs

Attachment B

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RMS AT A GLANCE

▪ RMS models and software help insurers, financial markets, corporations, and public

agencies evaluate and manage catastrophe risks throughout the world.

▪ RMS models integrate and synthesize the relevant science, data, engineering

knowledge, and actual loss experience in the aftermath of a catastrophe, to provide

an unbiased and consistent measure of risk. Risk metrics and analytics are

harnessed by insurers and reinsurers, the financial markets, policymakers, and

others, to make informed risk management and mitigation decisions.

Attachment B

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KEY APPLICATIONS

• Determine risk drivers• Evaluate Capital Adequacy• Estimate post-event losses

Portfolio Management

• Determine reinsurance needs• Structure and price risk transfer• Used as a “common currency”

Risk Transfer

• Analyze policy structures• Differentiate risks• Establish guidelines • Develop rating

Underwriting

Attachment B

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4Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019Copyright © 2016 Risk Management Solutions, Inc..Copyright © 2019 Risk Management Solutions, Inc..

CATASTROPHE MODELS CALCULATE USEFUL FINANCIAL METRICS

▪ Probability that losses from the single largest occurrence in a year will exceed a given threshold

▪ Each point represents a loss threshold and a probability of exceeding that threshold for one event

OEP

AEPQ: What is the probability of any single event in a year exceeding $500,000 in loss?

Annu

al P

roba

bilit

y of

Exc

eeda

nce

Loss Amount ($)

A: 0.009 = 0.9%or 1 in 111 years

OEP CurveAEP Curve

Attachment B

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5Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019Copyright © 2016 Risk Management Solutions, Inc..Copyright © 2019 Risk Management Solutions, Inc..

CATASTROPHE MODELS CALCULATE USEFUL FINANCIAL METRICS

▪ Probability that losses from all occurrences in a year will exceed a given threshold

▪ Each point represents a loss threshold and a probability of exceeding that threshold for all events in a year

OEP

AEP

Annu

al P

roba

bilit

y of

Exc

eeda

nce

Loss Amount ($)

OEP CurveAEP Curve

Q: What is the probability of all events in a year exceeding $500,000 in loss?

A: 0.039 = 3.9%or 1 in 25.6 years

Attachment B

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HOW TO CALCULATE EP CURVES - STEPSFor each coverage type at each location for each stochastic event: multiply the damage ratio (including loss amplification as appropriate) by the value of the property à yields a mean loss and coefficient of variation

Fit beta distributions to each stochastic event à yields the severity distribution that describes the distribution of the size of losses, given that an event has occurred.

A Poisson distribution is used for event frequency with the mean frequency obtained as the sum of all the event rates à yields the frequency distribution

The OEP curve is calculated on an occurrence basis and is obtained from the severity distribution along with the overall mean frequency

The AEP curve is calculated on an aggregate basis, showing the probability that aggregate losses in a year (the sum of losses from all occurrences in a year) will be greater than a given loss threshold. Thus, multiple occurrences in a year are considered for which the severity distribution is convolved as many times as occurrences may happen in a year. Uses the Fast Fourier Transform methodology described in Robertson (Proceedings of the Casualty Actuarial Society, Vol. LXXIX, 1992)

Attachment B

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7Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019 77Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019 7

COMPARISON OF OEP TO AEP RESULTS:

EARTHQUAKE

Attachment B

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▪ Coverage across North America

▪ Incorporates seismic source data from USGS 2014 National Seismic Hazard Mapping Project, including UCERF3

▪ More than 3,800 unique vulnerability functions for U.S. building shake coverage

▪ Soil amplification model includes largest available mapping of Vs30 data

▪ Includes Shake, Fire Following, Sprinkler Leakage and Tsunami Accumulation Footprints

EARTHQUAKE

Key Features

Attachment B

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9Copyright © 2019 Risk Management Solutions, Inc. All Rights Reserved. July 10, 2019Copyright © 2016 Risk Management Solutions, Inc. .Copyright © 2019 Risk Management Solutions, Inc. .

FACTORS TO ADJUST OEP TO AEP

Low frequency of earthquake peril leads to small gap between OEP and AEP

California dominates US activity, therefore matches overall US average

All US Residential: 1.03

California Residential: 1.03

Washington Residential: 1.01

Missouri Residential: 1.00

Attachment B

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COMPARISON OF AEP TO OEP RESULTS:

HURRICANE

Attachment B

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▪ Basin-wide event set

includes wind and storm surge coverage for 14 states

▪ Over 2,000 distinct risk types represented

▪ Model incorporates wind and storm surge

▪ Clustering reflected in event set

Key Features

HURRICANEAttachment B

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The ratio to gross to AEP is slightly higher than quake due to possibility of clustering

Florida has highest frequency of storms and higher tendency for clustering


Florida Residential: 1.07

New York Residential: 1.01

Attachment B

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COMPARISON OF AEP TO OEP RESULTS:

SEVERE CONVECTIVE STORM

Attachment B

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▪ SCS represents 1/3 of the U.S. AAL

▪ Model Coverage: 48 states & Canada

▪ Loss due to: hail, tornado, straight-line wind, lightning

▪ Events can last from minutes to days, and can cover multiple states and regions

▪ Assess annual and aggregate risk

against the complete spectrum of cat-

and non-cat events

– Two event sets: high and low frequency (both used for this analysis)


Key Features

Large Event Losses Annual Losses

Hail

TornadoStraight-line

WindTornado

Hail

Straight-line

Wind

Based on Claims Data

Attachment B

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▪ Low-frequency events

– Thunderstorms, straight-line winds, tornadoes, lightning

– Typical “catastrophic” event (most similar to PCS

event)

▪ High-frequency events

– Isolated thunderstorms, downbursts, hailstorms

– Thousands occur across the continent per year


Hazard Modeling

Tornado Wind HailModeled using

Fujita Scale intensity

Modeled using kinetic energy

estimates related to hail stone size and

density

Modeled using 3-second peak gust intensity, swaths 3 miles to 100+ miles

wide

Typical Low Frequency Event

Typical High Frequency Event

Attachment B

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Severe Convective Storm events are very frequent

OEP to AEP factor higher than almost all other perils


Texas Residential: 1.45

Attachment B

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CONCLUSIONS

Factors to adjust OEP to AEP depend on:

• Peril • Hurricane, Earthquake, Severe Convective Storm, etc

• Geographic Scope• All US, by State, by county, by ZIP• California vs. East Coast vs. Gulf Coast vs. Midwest, etc

• Portfolio composition• Construction, occupancy, year built, building height, etc

• Insurance structure• Deductibles, endorsements, exclusions, etc

Attachment B

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ABOUT RMSRMS is the world’s leading provider of products, services, and expertise for thequantification and management of catastrophe risk. More than 400 leadinginsurers, reinsurers, trading companies, and other financial institutions rely onRMS models to quantify, manage, and transfer risk. As an established provider ofrisk modeling to companies across all market segments, RMS provides solutionsthat can be trusted as reliable benchmarks for strategic pricing, risk management,and risk transfer decisions.

©2019 Risk Management Solutions, Inc. RMS and the RMS logo are registeredtrademarks of Risk Management Solutions, Inc. All other trademarks are propertyof their respective owners.


ABOUT RMS

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ABOUT RMS

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Attachment B

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080219 Cat Risk agendaAttA_AIR_Comparability_AEP_and_OEP_NAICCatRisSub_20190703AttB_NAIC_AEPOEP_Aug2019_vFinal

catastrophe risk (e) subgroup...and can cover multiple states and regions assess annual and...

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