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CAT MODELING, APPLICATION TO INSURANCE INDUSTRY: UNKNOWNS AND POSSIBLE SOURCES OF BIAS IN PRICING P . B a z z u r ro 1, M . Ko h ra n g i 2, A . Pa p a d o p o u l o s 2, S . Re d d y Ko t h a 3, O . O d a b a s i 4, D. Va mva t s i ko s 5

Internat ional Workshop on Advances in Assessment and Model ing of Earthquake Loss , I stanbul , Turkey, Nov 4-5, 2019

1Professor, University School for Advanced Studies IUSS Pavia, Italy 2 Ph.D., Risk Engineering + Development (RED), Italy 3 Ph.D., GFZ, Potsdam, Germany 4 PH.D. Candidate, University School for Advanced Studies IUSS Pavia, Italy 5 National Technical University of Athens

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Standard Output is a 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 Pr

obab

ility

0

50

100

150

200

250

300

350

10 20 50 100 250 500 1,000

Estimated Return Period

Loss

Amo

unt ($

millio

ns)

The Average Annual Loss (AAL) is the mean loss over many realizations of next year seismicity

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•Primary Insurance companies (buildings, crops, etc.) and Reinsurance Companies

•Investors/hedge funds

•Life, Accident, and Workers’ Compensation Insurers

•Catastrophe/relief funds and risk pools (e.g., TCIP, California Earthquake Authority, CCRIF)

•Rating Agencies (S&P, Moody’s, Fitch)

•Real estate management and investment

•Mortgage lending

-Fannie Mae, Freddie Mac and the secondary mortgage market

•Governments and their departments ( U.S. Department of Homeland Security, U.S. Navy, U.S.D.A., Mexican Government, Caribbean Caricom Governments, etc.)

•Major Corporations (Dow Chemical, Devon Energy, Arkema, Sony, General Motors, etc.)

•…

Typical Users of Cat Models

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Catastrophe Risk Models Are Used for Modeling a Wide Variety of Insurance Contracts

Enterprise Risk Management

Reinsurance Purchasing

Pricing

Underwriting

Claims

Portfolio Optimization

• Manage the impact of catastrophe risk on surplus • Communicate with ratings agencies • Accumulation/risk-aggregation management

• Use models to evaluate reinsurance purchases

• Streamline efficiency of communication with reinsurance intermediaries

• Use model outputs in rate filings and in pricing of individual policies or programs

• Identify areas to grow or retract based on model-based risk metrics

• Perform model-based analyses to understand and manage the drivers of catastrophe risk

• Advance planning, resource deployment, post-event communications

• Catastrophe model output used for risk selection and pricing at the point of sale

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Insurance Pricing is the last component of the Underwriting (UW) process Factors controlling the UW process are:

1. client selection (judgmental, nothing to do with cat modeling) 2. wordings acceptability (marginally related to cat modeling) 3. portfolio fit (e.g., risk diversification, diminish volatility, etc) 4. Price (cat models provide the quantitative support for pricing)

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Role of Cat Models in Insurance Pricing Objective: to determine how much to charge to cover the cost of the product and generate sufficient profit

Simplistically, the technical price consists of: 1. Expected loss (also called pure premium) 2. Expense loading (to account for internal operational costs, taxes, fees, commissions,

reinsurance and retrocession costs, cost of capital, etc.) 3. Profit loading 4. Risk loading (to account for unmodeled perils and unknowns)

NOTE: Technical price may differ from the market price, i.e., the price that the customer pays. The market price can be higher or lower than the technical price according to internal business strategies

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HAZARD

ENGINEERING

FINANCIAL

Intensity Calculation

Exposure Information

Damage Estimation

Policy Conditions

Insured Loss Calculations

Event Generation

Vulnerability/Fragility Curves for Classes of Buildings for classes of buildings

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Three Methods for developing vulnerability (or fragility curves) for classes of buildings

SEISMIC RISK AND LOSS ASSESSMENT 8

Expert opinion Empirical

Analytical

PREFERRED METHOD

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Mean Damage Function for California Wood Frame Buildings of given Vintage (Claims Data)

Company

Company

(1994 M6.7 Northridge

Earthquake)

10 10

Hazard analysis/Disaggregation

• Hazard source model from SHARE Project, hazard source model

• GMPE proposed by Boore and Atkinson (2008)

Istanbul

Ankara Erzincan

Excerpted from Kohrangi, Vamvatsikos, Bazzurro (2017)

Vulnerability/Fragility of 3 Identical 7story RC Buildings in Istanbul, Ankara and Erzincan

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Fragility Curves for Collapse are computed in five different ways: • Hazard consistent ground motion records at each one of the

3 sites • Arbitrary set of scaled records from FEMA P695 • Two variants of ground motions consistent with hazard at all

three sites (on an average sense)

median

Building Vulnerability/Fragility Curves Are Site-dependent

SA(T1) Hazard curves for the 3 sites

benchmark

SAT1

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Fragility Curves for Collapse are computed in five different ways: • Hazard consistent ground motion records at each one of the 3 sites • Arbitrary set of scaled records from FEMA P695 • Two variants of ground motions consistent with hazard at all three sites

(on an average sense)

AvgSA

median

Using AvgSA decreases site-dependence of Building Vulnerability/Fragility Curves

AvgSA

AvgSA Hazard curves for the 3 sites

AVGSA in [0.2T1 – 2.0T1]≈[0.3s – 3.0s]

benchmark

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Moving towards empirical non-ergodic Ground Motion Prediction Equations (GMPEs)

HAZARD

BUILDING VULNERABILITY

FINANCIAL

Ground Motion Intensity

Calculation

Exposure Information

Damage Estimation

Policy Conditions

Loss Calculations

Earthquake Occurrence

Ground Motion Prediction Equations (GMPEs) or attenuation relationships

ln y = µ(M, R, θ) + εσT

≈

Classical Ergodic (site-generic) GMPE

Most of it is due to systematic effects rather than random unexplainable variability !

Gives mean and standard deviation of response-spectrum ordinate (at a particular frequency) as a function of magnitude distance, site conditions, and perhaps other variables.

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Towards non-Ergodic (site-specific) GMPEs

Courtesy: Dr. Norm Abrahamson

All sites have the same Vs30

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What is the impact on non-ergodic (site-specific) GMPEs on risk?

Site 3

Site 2

Site 1

N-E E

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Site-generic vs. Site-Specific Hazard Curves

Non-Ergodic (site-specific) Ergodic (site-generic)

Site#1

Site#2

Site#3

E>N-E E≈N-E E

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Site-generic vs. Site-Specific Response Hazard Curves (risk)

Site#1

Site#2

Site#3

E>N-E E≈N-E E

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Moving towards Broadband Ground Motion Simulations

HAZARD

BUILDING VULNERABILITY

FINANCIAL

Ground Motion Intensity

Calculation

Exposure Information

Damage Estimation

Policy Conditions

Loss Calculations

Earthquake Occurrence

20 20 http://visservices.sdsc.edu/projects/scec/terashake/imagery/

Beyond purely empirical GMPEs

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Why using ground motion simulation?

Where we need data the most!

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Broadband Physics-based Simulations

Excerpted from Paolucci et al (2017)

Gridded contours across the land indicate the PGV of the simulated (broadband) motions via the SPEED engine (http://speed.mox.polimi.it)

M7.2 on the North Anatolia Fault

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Effects of Physics-based Simulations on Risk: Tall Buildings in Istanbul

Analysis Sites

Three sites are selected for analysis - Esenyurt : Vs30=325m/s Rrup=15km - Atasehir : 500m/s 20km - Sisli : 870m/s 25km

Considered Earthquake Rupture Magnitude : Mw 7.2 Mechanism : strike-slip Dimensions : 84 × 15 km

Archetype Model We tested the 3D model of a 23-story reinforced concrete core shear wall building.

✓ force-based fiber elements ✓ aggregated shear hinges ✓ fixed base modelling × underground stories ignored

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Simulated vs Empirical ground motions Spectra

10-1

100

Period (s)

10-2

10-1

100

Spec

tral A

ccele

ration

(g)

Atasehir: Vs 3 0

=500 | Rr u p

=20

10-1

100

Period (s)

10-2

10-1

100

Spec

tral A

ccele

ration

(g)

Besiktas: Vs 3 0

=870 | Rr u p

=25

10-1

100

Period (s)

10-2

10-1

100

Spec

tral A

ccele

ration

(g)

Esenyurt: Vs 3 0

=325 | Rr u p

=15

Target median

Target ±2

Simulations median

Simulations ±2

Individual BBS

10-1

100

Period (s)

10-2

10-1

100

Spec

tral A

ccele

ration

(g)

10-1

100

Period (s)

10-2

10-1

100

10-1

100

Period (s)

10-2

10-1

100

Simulated: 15 ground-motion simulations for same M7.2 event but different rupture kinematics are generated using the SPEED engine (http://speed.mox.polimi.it).

Real: Real accelerograms are selected and scaled to match the M7.2 target spectrum and its variability

http://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.ithttp://speed.mox.polimi.it

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Higher Risk for Simulated Ground Motions

0 0.04 0.08 0.12 0.16 0.20

0.25

0.5

0.75

1

Loss ratio

CDF

BBS-EsenyurtBBS-AtasehirBBS-SisliRecordings-EsenyurtRecordings-AtasehirRecordings-Sisli

1. Simulated ground motions more aggressive for this M7.2 earthquake

2. Median loss ranged 2-7% of the total replacement cost

3. Simulated motions lead to 25-300% increase in the median losses.

P[lo

ss ra

tio ≥

L]

simulated

real

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Are there any source of bias in the pure premium estimates from EQ Cat Models?

HAZARD

BUILDING VULNERABILITY

FINANCIAL

Exposure Information

Damage Estimation

Policy Conditions

Loss Calculations

Earthquake Occurrence

Ground Motion Intensity

Calculation

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Only mainshocks are considered in EQ cat risk models

1932–2010 SCEC catalogue in Southern California.

3368 events with M>3.8 in 78 years (43 events per year on average)

913 mainshock events with M>3.8 in 78 years (11 events per year on average)

all events Mainshock only (after declustering)

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And then, after declustering, there were one…

Only one event per sequence is retained after earthquake

catalog declustering!

Central Italy 2016-17 sequence (one M6.5 but 9 M5+ in the sequence)

Emilia 2012 Sequence (two M5.9 but 7 M5+ in the sequence) [Courtesy of INGV]

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Amatrice, Central Italy 2016

Damage Accumulation

24 August 2016 End of the sequence

Excerpted from Sextos et al. (2018)]

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Evolution of damage states during the 2016-17 Central Italy Sequence Adapted from GEER

(2017), Report No. GEER-050D

Damage state (0= no damage; 5= complete collapse)

Amatrice

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Larger Footprint of Damaged Building Stock Max PGA Shakemap from

Mw=5.8, 20/5/2012 Emilia earthquake

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Max PGA Shakemap from Mw=5.8, 20/5/2012 Emilia earthquake Mw=5.6, 29/5/2012 Emilia earthquake

Larger Footprint of Damaged Building Stock

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Generation of stochastic catalogues with all earthquakes

[Excerpted from Papadopoulos and Bazzurro, 2019

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Administrative Level 3 - Municipalities 30 arc-sec resolution

[Excerpted from Papadopoulos, 2019 [Courtesy of RED]

Residential Exposure in Italy

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Seismic risk in Umbria region with all earthquakes

Year 2018 after 2016-17 sequence Average year

[Excerpted from Papadopoulos and Bazzurro, 2019

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Systematic Underestimation of AAL’s

[Excerpted from Papadopoulos and Bazzurro, 2019

First year after the sequence Average year

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• For 25+ years now Cat Risk Models have been underpinning many decisions regarding risk assessment

of portfolios of buildings including pricing

• Premium computations is based on AAL from these models plus loading factors that include, among

others, unmodeled sources of risk (e.g., earthquake induced landslides or ground failure) and unknowns

• Many are the sources of bias and volatility in the current models, we explored four

• Clustered seismicity cannot be excluded any longer from seismic risk assessment

• Hazard-consistent vulnerability functions for classes of buildings to avoid biased loss estimates

• Future ground motion predictions tools will remove sources of bias in loss estimates from current

models

Final Remarks

Cat Modeling, Application to Insurance Industry: unknowns and possible sources of bias in pricingStandard Output is a Loss Exceedance Probability CurveSlide Number 3Catastrophe Risk Models Are Used for Modeling a Wide Variety of Insurance ContractsInsurance Pricing is the last component of the Underwriting (UW) processRole of Cat Models in Insurance PricingSlide Number 7Three Methods for developing vulnerability (or fragility curves) for classes of buildingsMean Damage Function for California Wood Frame Buildings of given Vintage (Claims Data) �Vulnerability/Fragility of 3 Identical 7story RC Buildings in Istanbul, Ankara and Erzincan�Building Vulnerability/Fragility Curves �Are Site-dependentUsing AvgSA decreases site-dependence of Building Vulnerability/Fragility Curves Moving towards empirical non-ergodic Ground Motion Prediction Equations (GMPEs)Slide Number 14Towards non-Ergodic (site-specific) GMPEsWhat is the impact on non-ergodic (site-specific) GMPEs on risk?Site-generic vs. Site-Specific Hazard Curves Site-generic vs. Site-Specific �Response Hazard Curves (risk)Moving towards Broadband Ground Motion Simulations Slide Number 20Why using ground motion simulation?Slide Number 22Slide Number 23Slide Number 24Slide Number 25Are there any source of bias in the pure premium estimates from EQ Cat Models?Only mainshocks are considered in EQ cat risk modelsSlide Number 28Slide Number 29Slide Number 30Larger Footprint of Damaged Building StockLarger Footprint of Damaged Building StockSlide Number 33Slide Number 34Seismic risk in Umbria region with all earthquakesSystematic Underestimation of AAL’s Slide Number 37