Catastrophe Modeling Boot Camp

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Catastrophe Modeling Boot Camp

• Jim Maher, FCAS MAAA
• Platinum Re

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Cat Modeling

• Basic Elements of Cat Models
• Similarities/Differences of Cat Models
• Data/Modeling Issues
• Portfolio Management

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Basic Elements of Cat Models

• Hazard Module
• Engineering Module (aka Vulnerability)
• Insurance (aka Financial) Module
• Event Set (and Year Set)

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Hazard Module

• Seismology
• Meteorology
• Terrorism
• Non random frequency
• Non random severity

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Non-modeled perils

• Tsunami
• Meteor strike
• Est. RP of 1,000 years for 10 megaton event
• Most recent Siberia (1908)
• River Flood
• Wildfire
• Winterstorm

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Non-modeled coverages

• Life/Health
• Personal Accident
• Group Life
• Disability
• Marine
• Yachts
• Offshore Oil Rigs
• Cargo

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Earthquake

• Major Types of Earthquake
• Location of Earthquake Hazard
• Major Historical US Earthquakes
• Recent US Earthquakes
• Vulnerability and Financial Models
• Earthquake prediction (?)

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Major Types of Earthquakes

• Strike-Slip
• Rock on one side of fault slides horizontally
• San Andreas Fault
• Dip-Slip (subduction)
• Fault is at an angle to the surface of the earth
• Movement of the rock is up or down
• Great Kanto Earthquake (Japan 1923)

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Location of Earthquakes

• Plate Boundaries
• 90 of worlds earthquakes occur here
• Seven Major Crustal Plates on the Earth
• Rocks usually weaker, yield more to stress than
  Examples California, Japan, etc.
• Ring of Fire
• Intra-plate Earthquakes
• New Madrid (1812)
• Newcastle, Australia (1989)
• Charleston (1886)

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Plate Boundaries Ring of Fire
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Modified Mercalli Scale

• IV Felt by many indoors but by few outdoors.
  Moderate
• V Felt by almost all. Many awakened. Unstable
  objects moved.
• VI Felt by all. Heavy objects moved. Alarm.
  Strong.
• VII General alarm. Weak buildings considerably
  damaged. Very strong.
• VIII Damage general except in proofed buildings.
  Heavy objects overturned.

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Modified Mercalli ctd.

• IX Buildings shifted from foundations, collapse,
  ground cracks. Highly destructive.
• X Masonry buildings destroyed, rails bent,
  serious ground fissures. Devastating.
• XI Few if any structures left standing. Bridges
  down. Rails twisted. Catastrophic.
• XII Damage total. Vibrations distort vision.
  Objects thrown in air. Major catastrophe.

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Major Historical US Quakes

• San Francisco (1906)
• Magnitude 7.8, 3000 deaths
• Significant fire following element
• Charleston (1886)
• Magnitude 7.3, 100 deaths
• New Madrid (1811/12)
• 12/16/1811 Northeast Arkansas
• 1/23/1812 2/7/1812 New Madrid, Missouri
• Estimated Magnitude 8.0
• Destroyed New Madrid, severe damage in St. Louis,
  rang church bells in Boston

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Recent US Earthquakes

• Loma Prieta (1989)
• Northridge (1994)
• Nisqually/ (Seattle) (2001)

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Loma Prieta (1989)

• Magnitude 6.9 on San Andreas Fault
• Largest since 1906 earthquake
• 63 deaths, 3,757 injuries, 6 BN economic damage,
  1.0 BN insured damage
• Severe property damage in Oakland and San
  Francisco
• Collapse of Highways, viaducts

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Loma Prieta ctd.

• Liquefaction
• San Franciscos Marina district
• loosely consolidated, water saturated soils.
• Loosely consolidated soils tend to amplify
  shaking and increase structural damage.
• Water saturated soils compound the problem due to
  their susceptibility to liquefaction and
  corresponding loss of bearing strength.
• Unreinforced masonry construction
• Engineered buildings performed well

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Northridge (1994)

• Magnitude 6.8 earthquake
• Occurred on previously unknown fault
• 60 killed, 7,000 injured, 20,000 homeless, 40,000
  buildings damaged
• 15 BN insured damage, 44 BN economic
• Fires caused damage in San Fernando Valley,
  Malibu, Venice
• Liquefaction at Simi Valley

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Northridge-PCS Estimates
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Nisqually/(Seattle) (2001)

• Magnitude 6.8, 400 people injured
• Major damage in Seattle-Tacoma area
• Insured Damage 305 Million
• Max. intensity VIII in Pioneer Square area
• Landslides in the Tacoma area
• Liquefaction and sand blows

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Earthquake vulnerability factors

• Building construction
• Unreinforced masonry vs. seismic designed
• Building height
• Taller buildings vulnerable to long-period waves
• Soft story (hotel lobby) increases vulnerability
• Building location
• Soil type is critical
• Fire following losses can be very significant

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Financial model factors

• CEA mini-policy
• Earthquake sublimits on commercial
• Per policy
• Per location
• Regional sublimits (e.g. CA only)
• Interlocking clause
• Reduces event loss across multiple treaty years
• Hard to model

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Differences between models

• Detailed vs. Aggregate
• Detailed models better capture these
  vulnerability and financial considerations
• Fire Following
• Significant difference in modelers
• New Madrid
• Significant difference in return period

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Earthquake prediction

• Earthquakes not a Poisson process
• Poisson implies inter-arrival times are
  exponentially distributed (memory-less)
• 1999 Izmit (Turkey) Earthquake
• Increased risk for a quake in Istanbul
• San Andreas Fault
• Is an earthquake due? Where on fault?

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Izmit Quake ctd.

• 60 chance of Istanbul earthquake in next 30
  years - Thomas Parsons, USGS
• Researchers took into account the stress transfer
  from a magnitude 7.4 earthquake in Izmit, Turkey
  in August 1999.

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San Andreas Fault

• Over the past 1,500 years large earthquakes have
  occurred at about 150-year intervals on the
  southern San Andreas fault.
• As the last large earthquake on the southern San
  Andreas occurred in 1857, that section of the
  fault is considered a likely location for an
  earthquake within the next few decades
• The San Francisco Bay area has a slightly lower
  potential for a great earthquake, as less than
  100 years have passed since the great 1906
  earthquake

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Cat Models and Earthquake Pred.

• At least one cat modeling firm has variable
  earthquake rate (changes with calendar date)
• Annual model updates allow for changing
  earthquake rate with time.

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Hurricanes

• Meteorology of Hurricanes
• Frequency of Hurricanes by category
• Recent Hurricane Activity
• Hurricane Andrew
• Vulnerability and Financial Models
• Hurricane prediction (?)

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Meteorology of Hurricanes

• Occur in both Northern and Southern Hemispheres
• Dont occur on the equator
• Factor in the 2004 Tsunami tragedy
• Coriolis Force
• spin clockwise in southern hemisphere
• spin counter-clockwise in northern hemisphere
• Need warm sea surface temperatures
• Always travel from east to west

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Safir-Simpson Scale
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Atlantic Basin Hurricanes
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US Landfalling Hurricanes
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2004 Season
2004
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2003 Season
2003
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2004 Hurricanes

• Charley 8/9-14, Small storm- strengthened
  rapidly to Cat 4 just before FL landfall
• Frances 8/25-9/8, Larger storm, weakened from
  Cat 4 to Cat 2 before FL landfall
• Ivan 9/2-9/24, Long-lived, Cat 5 storm, weakened
  to Cat 3 before AL landfall
• Jeanne9/13-9/28, Crazy Cat 3 storm, same
  landfall as Frances but smaller faster

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2004 Hurricanes ctd.
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Modeling Issues raised by 2004 storms

• Storm Surge
• Demand Surge
• Frequency Distribution of Hurricanes
• Offshore oil rig losses
• Caribbean Clash modeling

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Hurricane Andrew

• Period 8/16-8/28 1992
• Small, intense CAT 5 Cape Verde storm
• Affected Bahamas, S. Florida, Louisiana
• Damage 25 BN, 15.5 Insured US damage
• Central Pressure 992 mb, third lowest since 1900

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Vulnerability model factors

• Construction
• Concrete bunkers vs. mobile homes
• Location
• Properties near ocean very vulnerable to storm
  surge
• Secondary modifiers
• E.g. Roof tie downs

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Financial model factors

• percentage deductibles can be very significant
• New season deductible in FL
• What is a risk?
• Issue for per-risk treaties
• For hurricanes, widely dispersed buildings on one
  policy often considered one risk
• E.g. school district

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Differences between models

• Detailed vs. Aggregate models
• Location (distance to coast) is critical
• Need detailed model to properly assess
• Northeast Hurricane
• Significant difference between modelers
• Caribbean clash
• Not all modelers facilitate this analysis

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Hurricane Prediction
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Data/Modeling Issues

• Need for completeness
• Reinsurers need compensation for all risks being
  accepted
• Model all exposures
• Model all perils
• Run multiple models

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Missing exposures

• Sometimes only get tier 1 wind counties
• Sometimes only certain states
• E.g. CA, Pacific NW, New Madrid only
• Other shake exposure ignored (e.g. East Coast)
• Fire following exposures ignored
• Sometimes entire books of business are missing
• Must cross-check cat model exposure data
• Premium often n.a. , policy counts (?)

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Modeling Tricks

• Failing to load for LAE
• Failing to consider demand surge
• Abuse of secondary modifiers
• Really, all my policyholders have roof
  tie-downs!
• Running all the models and providing the lowest
• different modeling firms
• Aggregate vs. detailed models

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Portfolio Management

• Event Set framework is a powerful tool for
  portfolio management
• Ability to model portfolios risk vs. return
• Determine portfolio capital and allocate to
  individual deals

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Portfolio Framework Example

• Consider two countries
• Oceania and Eurasia
• 5 possible events for each country
• Industry losses specified
• Goal-determine risk vs. return for various
  reinsurance portfolios

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Event Sets
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Create a set of Simulation Years
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Check against Poisson
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Contracts
Consider that the following contracts are
available in the open market
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Calc. Contract Losses by year
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Compute AAL and expected profit for each contract
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Distribution of profit/(loss)
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Calculate return on capital
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Portfolio Effects

• Now assume that the reinsurers portfolio
  consists of certain shares of these 3 contracts
• Want to calculate the overall portfolio capital
  and
• Each contracts share of this portfolio capital

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Portfolio

• Consider the following portfolio
• P 20 A 10 B 5 C
• Then consider 3 other portfolios
• P0.1 A
• P0.1 B
• P0.1 C

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Portfolio ctd.
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Allocating Portfolio Capital

• The portfolio capital can be allocated as
  follows
• Cap20A 20/0.1 (422.89-422.02)174
• Cap10B 10/0.1 (422.56-422.02) 54
• Cap5C 5/0.1 (425.90-422.02)194
• -------------- --------
• CapPortfolio 422

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Return on Allocated Capital
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Tail oriented Capital Metrics

• Approach also works for tail oriented capital
  metrics- e.g. TVAR
• Define capital 3 x TVAR (80)

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Tail oriented ROAC
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Allocated Capital Calcs

• As before, alloc. capital based on marginal
• For example, for the 20A contract
• 450 (793.5-791.25)/0.1 20
• Portfolio Cap Sum of Alloc. Capitals
• N.B. according to this capital metric, 10B has
  the highest ROAC in the portfolio

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Summary

• CAT Models provide a powerful tool for portfolio
  management
• Can be used to derive capital for a contract
  within a portfolio and ROC
• There is no contract order issue as is
  sometimes thought
• Portfolio can then be optimized to maximize ROC