use of catastrophe models by general insurance companies · 2017-09-28 · session 191 pd - use of...

Session 191 PD - Use of Catastrophe Models by General Insurance Companies

Moderator:

Anthony E. Cappelletti, FSA, FCAS, FCIA

Presenter: Alan Frith, Are, CCM, CPCU

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1 CONFIDENTIAL ©2017 AIR WORLDWIDE

191 L - Use of Catastrophe Models by General

Insurance Companies Alan Frith, CPCU, ARe, CEEM


- What are cat models? - How are they structured? - What information do they provide? - How are they used by primary insurers?

Agenda


What is a Catastrophe Model? Mathematically represent the

characteristics of the peril

Computer programs

Inform event frequency and

severity

Industry standard practice

Quantify and price risk throughout the

industry


Traditional methods may not be good predictors of

possible loss

The constantly changing landscape of exposure data limits the usefulness of past

loss experience


Recent Historical Experience Informed the Baseline for What Might Happen

$- $500

$1,000 $1,500 $2,000 $2,500 $3,000 $3,500 $4,000

Historical Losses (before Andrew) Millions

Hurricane

Hugo

PCS Losses – Trended at 7%


Historical Losses Over a Short Term Do Not Capture the Potential for Future Losses

$- $2,000 $4,000 $6,000 $8,000

$10,000 $12,000 $14,000 $16,000 $18,000

Historical Losses (after Andrew) Millions

Hurricane

Hugo

PCS Losses – Trended at 7%


Exposure Changes


What Questions Are Catastrophe Models Designed to Answer?

Where are future events likely to

occur?

How intense are they likely to be?

For each potential event, what is the estimated range of

damage and insured loss?

What is the probability of a given level of loss for my book in a wide range of catastrophe

scenarios?

How frequently are they likely to occur?


AIR Catastrophe Modeling Framework


Hazard Module: Event Generation

Where are future events

likely to occur?

How frequently are they likely to occur?

How intense are they

likely to be?


Contains tens of thousands of potential

scenarios

Addresses uncertainty in the occurrence, location, size, and

other characteristics of the peril

Highest level of catastrophe risk

transparency


North Atlantic Tropical Cyclone Tracks Since 1900

More than 1,000 Historical Tracks (~9 Tracks per year)


Event Generation Begins with Collecting Key Variables of Historical Data

Lat. Long. Time Wind Speed Central Pressure Status

16.00°N 73.70°W 8/11/06z 55 999 TROPICAL STORM

16.30°N 75.40°W 8/11/12z 60 995 TROPICAL STORM

16.70°N 76.80°W 8/11/18z 65 993 CAT 1

17.40°N 78.10°W 8/12/00z 65 992 CAT 1

18.20°N 79.30°W 8/12/06z 75 988 CAT 1

19.20°N 80.70°W 8/12/12z 80 984 CAT 1

20.50°N 81.60°W 8/12/18z 90 980 CAT 2

21.70°N 82.20°W 8/13/00z 90 976 CAT 2

23.00°N 82.60°W 8/13/06z 105 966 CAT 3

24.40°N 82.90°W 8/13/12z 95 969 CAT 2


Historical Data Collection: Data Sources

Shanghai Typhoon Institute

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http://en.wikipedia.org/wiki/National_Oceanic_and_Atmospheric_Administration&ei=rsv1VMqmEIHtgwS0ooOgCA&bvm=bv.87269000,d.eXY&psig=AFQjCNHk22J0WMHKxugO3OPhBQqa9If93w&ust=1425480999943509

http://www.wibwnewsnow.com/national-weather-service-of-topeka-weather-update-for-today/

https://noaahrd.wordpress.com/2014/04/30/55th-anniversary-of-the-joint-typhoon-warning-center/

http://old.sti.org.cn/en/

http://www.town.motegi.tochigi.jp/motegi/nextpage.php?cd=010&syurui=1&lev=2&hidchangemoji=2

http://www.town.motegi.tochigi.jp/motegi/nextpage.php?cd=010&syurui=1&lev=2&hidchangemoji=2

http://de.wikipedia.org/wiki/National_Climatic_Data_Center


Stochastic Catalog: Sampling Distributions of Key Variables

Stochastic Catalog

Landfall Angle

Radius of Max. Winds

Forward Speed

Location Frequency

Min. Central Pressure

Annual Frequency


Simple Hurricane Track Using Conditional Probability Method

Storm Track Generation: Conditional Probability Method Stochastic Catalog Includes Complex

Tracks Such as Jeanne’s (2004)


Simulate Thousands of Potential Hurricanes in the Stochastic Catalog for a Complete View of Risk


Annual Frequency of U.S. Hurricane Landfalls

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 1 2 3 4 5 6 7 8+

Rel

ativ

e Fr

eque

ncy

Number of Landfalls

Modeled Historical


After Sampling Variables: A Typical Hurricane Catalog

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

Speed Landfall Lat Landfall Long

Radius Max Wind

Forward Speed

Landfall Angle

1 1 280 1 1 7 984 80 28.291°N 96.492°W 12 15 20

3 2 231 1 3 22 963 113 29.472°N 83.236°W 11 14 23

4 3 269 1 2 43 979 96 34.891°N 76.420°W 13 23 32

4 4 230 1 2 5 969 102 27.048°N 97.297°W 12 19 45

5 5 285 1 2 4 975 97 26.002°N 97.160°W 14 18 34

8 6 289 1 4 10 944 132 26.689°N 93.713°W 9 20 18

8 7 204 1 1 39 987 76 32.689°N 79.563°W 16 18 19

9 8 245 1 3 30 957 114 25.952°N 80.131°W 12 16 23

11 9 290 1 2 43 979 98 34.930°N 76.330°W 18 16 20

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

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


Typical Earthquake Catalog Year Day Hour Event ID Source ID Mw Lat Long Azimuth Depth Rupture

Length Rupture Width Dip Angle Fault Type

1 45 8 1 2780 6.380 34.015°N 118.630°W 77 5.2 7.7 11.0 75 N

3 116 7 2 2747 6.563 34.086°N 117.791°W 70 6.0 17.0 13.0 75 N

4 187 7 8 1715 6.313 34.056°N 118.759°W -87 5.3 13.7 10.9 75 N

7 198 18 11 2815 6.664 34.376°N 118.631°W -76 6.5 12.6 14.1 55 N

8 225 12 12 2863 6.920 34.544°N 119.157°W 82 6.4 25.7 13.0 80 N

8 263 21 14 2932 6.700 34.285°N 118.997°W 81 7.1 21.4 13.9 60 N

11 271 15 16 2838 6.367 34.363°N 118.629°W -76 4.9 9.5 11.7 55 N

12 289 13 18 2817 6.663 34.348°N 118.561°W -85 5.8 14.9 14.2 55 N

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

Azimuth North

Foot Wall

Dip

Depth * Fault

slip

Azimuth

North

Foot Wall

Dip

Depth * Fault

slip


In 2015, which state in the contiguous U.S. had the most earthquakes?

A. Wyoming

B. Nevada

C. California

D. Oklahoma


D. Oklahoma

Source: USGS


Hazard Module: Intensity Calculation

What is the intensity of each event

at each location?

How do local

conditions affect the intensity?


Calculating Local Intensity: Understanding the Storm Wind Field

Eye

Storm Path

Storm Center

Left Side Right Side

R max Weaker Winds

Stronger Winds

Rmax


Creating a Simulated Wind Field: Calculating Local Wind Intensities

Function of:

Central Pressure

Peripheral pressure

Rmax

Latitude

Function of:

Rmax

Vmax

Latitude

Distance From Eye

Function of:

Roughness Length

Function of:

Forward Speed

Angle between storm direction

and wind direction

V1min,10m = 1-minute sustained wind speed at 10 m above ground level Vmax = upper level wind at Rmax GF = gust factor GWRF = gradient wind-reduction factor FwdAdj = forward speed adjustment FF = friction factor

Function of:

Distance from Eye

Peak Weighting

Factor

Wind speed formula for 1-minute sustained winds, at 10 meters above ground level:

V1-min,10 m = [Vmax * GF * GWRF * Radial Decay + FwdAdj] * FF Function of:

Roughness Length

Averaging Time


Terrain Impacts Ground-Level Wind Speeds Vg Vg Vg

Hg (smooth)

Hg (medium)

Hg (rough)

Very Flat Terrain Suburban Terrain Urban Terrain

H = Height V = Velocity


High-Resolution Land Use Data is Required

Commercial/Industrial

High-Intensity Residential

Low-Intensity Residential


Local Intensity for Earthquakes: Ground Motion Prediction Equations (GMPEs)

Ground Motion Prediction Equations mathematically describe the rate of decay in ground motion with distance

log(Y) = c1 + c2 * Mw + c3 * (Mwref - Mw)2 + (c4 + c5 * Mw) * log(R) + c6 * R + site effects + faulting mechanisms + basin effects...

Source

Path Effects Site Effects


What is the largest tropical cyclone, in diameter, on record?


Source: NOAA

1979 Super Typhoon Tip 1,380 miles (2,220 km) in diameter


Hazard Module: Exposure Data Input

What exposure

variables are being

modeled?


Exposure Data Relevant for Modeling Earthquakes

Location • Where is it?

Replacement value • How much is it?

Extra Characteristics • Foundation type • Foundation connection

Characteristics • What is it made of? • What is it used for? • When was it built? • How tall is it?


Engineering Module: Damage Estimation

What level of damage is

expected at each location given the

intensity of the peril?


Developing Hurricane Damage Functions: Component-Based Engineering Approach

ROOF: Wood, concrete, metal GLASS PERCENTAGE: 5, 20, 50, etc. DOORS: Double, single, sliding, etc.

PRIMARY BUILDING CHARACTERISTICS OCCUPANCY: Residential, commercial, industrial CONSTRUCTION: Wood frame, masonry, steel frame, etc. HEIGHT: Low-rise, mid-rise, high-rise AGE: In relation to regional building codes

SECONDARY BUILDING CHARACTERISTICS


Earthquakes: Component-Based Approach PRIMARY BUILDING CHARACTERISTICS

OCCUPANCY: Residential, commercial, industrial CONSTRUCTION: Wood frame, masonry, steel frame, etc. HEIGHT: Low-rise, mid-rise, high-rise AGE: In relation to regional building codes

BUILDING CONDITION BUILDING OPENINGS BUILDING SHAPE CHIMNEY BRACING TORSION

PARTITIONS RETROFIT SOFT STORY WALL SIDING WALL TYPE

SECONDARY BUILDING CHARACTERISTICS


Hurricane Wind Damage Function: Residential Wood Frame

Dam

age

Rat

io

Wind Speed

Roof Covering and Siding Damage

Damage to Envelope and

Cladding

Major Damage to Structural and Non-structural Elements


Hurricane Wind Damage Function: Commercial Structure

Roof Covering Damage

Glass/Cladding Damage

Major Damage to Non-structural Elements

Dam

age

Rat

io

Wind Speed


Earthquakes: Ground Motion Frequency and Intensity Are Important for Determining Damage

Tall structure responds to

long-period shaking

Short structure responds to short-period shaking

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.3 0.6 0.9 1.2 1.5 1.8

Time

Ag

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2

Time

Ag

Two different structures subjected to the same ground shaking


Engineering Module: Policy Conditions

What are the policy conditions in force for the

property?


Picture of ISO policy – what are we looking for?

Agent

AIR Insurance Agency LLC 545 Washington Boulevard

Jersey City, NJ 07310

Insured Katie Ward 131 Dartmouth Street Boston, MA 02116

131 Dartmouth Street, Boston, MA 02116


Financial Module: Insured Loss Calculation

What is the insured loss to

property, policy, or contract?


For an Actual Event, the Insured Loss Is Easily Calculated

Replacement Value =

USD 250,000

2% Deductible = USD 5,000

Damage Ratio = 50%

Damage Amount = USD 125,000 (“Ground-up Loss”)

Insurer’s Loss After Deductible = USD 120,000 (“Gross Loss”)

For an actual event, the damage is known:


For a simulated event, the damage is uncertain.

We need to consider all possible outcomes.

A Modeling Perspective: Uncertainty in the Loss, Given the Event

Damage Ratio Probability Ground-up Loss Gross Loss0% 0.4415 - - 2% 0.0643 5,000 - 5% 0.0607 12,500 7,500 7% 0.0561 17,500 12,500

10% 0.0510 25,000 20,000 12% 0.0457 30,000 25,000 15% 0.0405 37,500 32,500

… … … …90% 0.0002 225,000 220,000 93% 0.0002 232,500 227,500 95% 0.0001 237,500 232,500 98% 0.0001 245,000 240,000 100% 0.0006 249,975 244,975

Replacement Value = USD 250,000 2% Deductible = USD 5,000

Intensity (e.g., wind speed, ground motion)

Dam

age

Rat

io


Developing the AIR EP Curve

Event ID Simulated Year Company Loss Event Info

111410752 9294 $25,628,808 Mw 6.9 EQ New Madrid 270012443 3699 $23,725,256 Class 5 Hurr FL NC VA SC PQ 270071140 1364 $21,812,737 Class 4 Hurr NY NJ CT PA MA 110952564 3264 $21,668,433 Mw 6.3 EQ New Madrid 270012636 3760 $21,456,324 Class 4 Hurr NY NJ CT PA MA 270029462 8794 $21,189,431 Class 5 Hurr FL LA GOM BF MS 270082612 4842 $20,943,015 Class 4 Hurr NY NJ CT MA PA 270042893 2912 $20,669,393 Class 5 Hurr FL SC NC GA BF 270072504 1794 $20,639,935 Class 4 Hurr NY NJ CT PA MA 270087106 6144 $20,569,005 Class 4 Hurr NY NJ CT MA PA 270093974 8178 $20,329,354 Class 4 Hurr NY NJ CT PA MA 270159424 7740 $20,244,536 Class 5 Hurr FL TX GOM BF LA 270112697 3828 $20,195,153 Class 4 Hurr NY NJ CT PA MA 270017212 5144 $19,906,853 Class 5 Hurr FL AL MS GOM LA 270042988 2935 $19,761,670 Class 5 Hurr FL GOM LA BF TX 270133994 121 $18,923,299 Class 4 Hurr NY NJ CT MA PA 270125384 7570 $18,568,895 Class 4 Hurr NY NJ CT PA MA 270106416 1925 $17,171,431 Class 5 Hurr FL GOM 270142249 2640 $17,148,883 Class 5 Hurr FL AL MS BF GOM 270058503 7554 $16,842,286 Class 5 Hurr FL NC SC GOM GA 270060242 8075 $16,555,698 Class 5 Hurr FL AL MS GOM LA 270006467 1895 $16,513,774 Class 4 Hurr NY NJ CT MA PA

. . . .

. . . .

Event Output Sorted Event Output Event ID Simulated Year Company

Loss Event Info

110000053 2 $153,819 Mw 6.3 EQ Los Angeles 110000061 3 $40,609 Mw 6.4 EQ San Francisco 110000078 3 $43,988 Mw 6.8 EQ San Francisco 110000153 5 $716,394 Mw 7.5 EQ Los Angeles 110000162 5 $28,271 Mw 5.1 EQ New Madrid 110000197 7 $22,876 Mw 5.9 EQ TX OK NM 110000263 9 $22,193 Mw 7.1 EQ New England 110000287 10 $49,814 Mw 5.6 EQ WA 110000497 17 $274,992 Mw 6.8 EQ San Francisco 110000507 17 $31,813 Mw 5.5 EQ SC 110000576 19 $131,771 Mw 5.7 EQ New Madrid 110000601 20 $57,694 Mw 6.1 EQ San Francisco 110000623 21 $24,305 Mw 5.6 EQ New England 110000702 23 $609,635 Mw 6.9 EQ New Madrid 110000705 23 $53,690 Mw 5.6 EQ San Francisco 110000751 25 $20,586 Mw 5.3 EQ San Francisco 110000760 25 $76,837 Mw 7.2 EQ San Francisco 110000842 28 $37,797 Mw 6.7 EQ Los Angeles 110000863 29 $535,234 Mw 6.6 EQ San Francisco 110000866 29 $36,560 Mw 7.2 EQ San Francisco 110000874 29 $25,638 Mw 5.5 EQ New England 110000922 31 $593,052 Mw 6.6 EQ Los Angeles

. . . .

. . . .

Losses (000’s) Rank EP (Rank/Catalog Size)

Return Period (Catalog Size/Rank)

$25,628,808 1 1/10,000 = .01% 10,000 $23,725,256 2 2/10,000 = .02% 5,000 $21,812,737 3 3/10,000 = .03% 3,333 $21,668,433 4 4/10,000 = .04% 2,500 $21,456,324 5 5/10,000 = .05% 2,000

. . . . $11,739,235 40 40/10,000 = .4% 250

. . . . $8,700,892 100 100/10,000 = 1.0% 100

. . . .


Main Catastrophe Modeling Output Loss Perspectives and Definitions

– Ground Up Losses • Losses prior to the application of limits, deductibles, etc.

– Gross Losses • Losses after the application of limits and deductibles, or direct losses to the primary insurer

– Retained Loss • Losses that are paid by the insured, typically defined as [Ground Up Loss – Gross Loss]

– Net Loss • Losses to the primary insurer after the application of limits, deductibles, and reinsurance

– Expected Loss (a.k.a. Average Annual Loss) • E[L] = ΣXi / n = sum of losses from all simulated years/number of years not events.

– Standard Deviation • Summary measure of variability across entire loss distribution


Catastrophe Models Provide a Wide Range of Loss Outputs

Exceedance Probability (EP) Curve - Occurrence

0%1%2%3%4%5%6%7%8%9%

10%

0 50 100 150 200 250 300 350 400Loss Amount ($ millions)

Exc

eed

ance

Pro

bab

ility

050

100150200250

300350

10 20 50 100 250 500 1,000Estimated Return Period

Lo

ss A

mo

un

t ($

mil

lio

ns)


Average Annual Loss & Loss Cost


Loss Exceedance Probability Curve

Exceedance Probability (EP) Curve - Occurrence

0%1%2%3%4%5%6%7%8%9%

10%

0 50 100 150 200 250 300 350 400Loss Amount ($ millions)

Exce

edan

ce P

roba

bilit

y

050

100150200250

300350

10 20 50 100 250 500 1,000Estimated Return Period

Loss

Am

ount

($m

illio

ns)


– Second, 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 = $237.00M

Constructing an Occurrence Exceedance Probability Curve

Event 2735

$237.00


- For an aggregate EP curve, the second step requires you 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 = $242.95M

Sum $242.95M


Assess Your Risk in the Exceedance Probability Curve

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

- 50 100 150 200 250 300 350Loss

Exc

eeda

nce

Prob

abili

ty

Losses (USD billions)

Tail value at risk (TVaR): average of all simulated event losses at and beyond specified probability, such as 1.0% or 0.4%

TVaR is a standard output of Touchstone® and CATRADER®


How AIR’s Clients Use Our Software

Enterprise Risk Management

Risk Transfer

Pricing

Underwriting

Claims

Portfolio Optimization


Risk Transfer & Enterprise Risk Management

Evaluate Reinsurance

Purchase

Communicate With Ratings

Agencies

Manage Impact on Surplus

Streamline Communication

w/ Intermediaries

Accumulation Management


- Eliminate volatility in loss costs

- Appropriately allocate cost of reinsurance or capital

- Account for exposure changes

Pricing Existing Portfolio


- Exposure classes that aren’t in the existing portfolio

- Evaluate relativities with no bias • Construction • Occupancy • Deductibles/Limits • Mitigation

Pricing w/ Notional Portfolios


- Distance to Coast • (Wind)

- Flood Zone

• (Flood)

- Elevation • (Wind & Flood)

- Soil Type

• (Earthquake)

Underwriting – Hazard Metrics


- Average Annual Loss

- Standard Deviation

- Return Periods

- TVaR

Underwriting – Account Loss Metrics


- Return Periods - TVaR - Window VaR

Underwriting – Marginal Impact on Portfolio


- Advance planning - Resource deployment - Post-event communications

Claims


- Identify areas to grow or retract

- Understand and manage the drivers of catastrophe risk

Portfolio Optimization


Questions?

use of catastrophe models by general insurance companies · 2017-09-28 · session 191 pd - use of...

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