Catastrophe modeling
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Catastrophe Modeling. Jim Maher, FCAS MAAA Chief Risk Officer Platinum Re US. Basic Elements of Cat Models. Hazard Module Engineering Module (aka Vulnerability) Insurance (aka Financial) Module Event Set (and Year Set). Hazard Module. Seismology Meteorology Terrorism

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Catastrophe Modeling

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Catastrophe modeling

Catastrophe Modeling

Jim Maher, FCAS MAAA

Chief Risk Officer

Platinum Re US

CAS 2007 Reinsurance Boot Camp on Pricing Techniques


Basic elements of cat models

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

Hazard Module

  • Seismology

  • Meteorology

  • Terrorism

    • Non random frequency

    • Non random severity

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Non modeled perils

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

Non-modeled coverages

  • Life/Health

    • Personal Accident

    • Group Life

    • Disability

  • Marine

    • Yachts

    • Offshore Oil Rigs

    • Cargo

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Earthquake

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

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

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

Plate Boundaries & “Ring of Fire”

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Catastrophe modeling

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Modified mercalli scale

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

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

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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Catastrophe modeling

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Recent us earthquakes

Recent US Earthquakes

  • Loma Prieta (1989)

  • Northridge (1994)

  • Nisqually/ (Seattle) (2001)

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Loma prieta 1989

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

Loma Prieta ctd.

  • Liquefaction

    • San Francisco’s 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

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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Catastrophe modeling

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Northridge pcs estimates

Northridge-PCS Estimates

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Nisqually seattle 2001

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

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

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

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

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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Catastrophe modeling

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Izmit quake ctd

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

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

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

Hurricanes

  • Meteorology of Hurricanes

  • Frequency of Hurricanes by category

  • Recent Hurricane Activity

  • Hurricane prediction

  • Vulnerability and Financial Models

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Meteorology of hurricanes

Meteorology of Hurricanes

  • Occur in both Northern and Southern Hemispheres

  • Don’t 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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Catastrophe modeling

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Safir simpson scale

Safir-Simpson Scale

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Atlantic basin hurricanes

Atlantic Basin Hurricanes

2001 - 2006 6 15.3 8.0

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Us landfalling hurricanes

US Landfalling Hurricanes

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Average recent hurricane activity

Average & Recent Hurricane Activity

  • To sum up: Average Hurricane numbers per year:

  • Cat Modeling Firms response:

    • Alternate versions of their models

    • Short Term vs. Long Term view

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Catastrophe modeling

Major Storms: 2004-05

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Catastrophe modeling

2002 Season

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Catastrophe modeling

2003 Season

2003

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Catastrophe modeling

2004 Season

2004

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Catastrophe modeling

2005 Season

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Catastrophe modeling

2006 Season

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2004 hurricanes cost

2004 Hurricanes cost

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2005 hurricanes cost

2005 Hurricanes cost

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Hurricane prediction

Hurricane Prediction

Actual 15

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Hurricane prediction ctd

Hurricane Prediction, ctd.

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Hurricane prediction 2007

Hurricane Prediction 2007

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Vulnerability model factors

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 factors1

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 models1

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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Modeling issues raised by 04 05 storms

Modeling Issues raised by ‘04/05 storms

  • Storm Surge

  • Demand Surge

  • Frequency Distribution of Hurricanes

  • Offshore oil rig losses

  • Caribbean Clash modeling

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Data modeling issues

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

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

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

Portfolio Management

  • Event Set framework is a powerful tool for portfolio management

  • Ability to model portfolio’s risk vs. return

  • Determine portfolio capital and allocate to individual deals

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Portfolio framework example

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

Event Sets

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Create a set of simulation years

Create a set of Simulation Years

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Check against poisson

Check against Poisson

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Contracts

Contracts

Consider that the following contracts are available

in the open market:

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Calc contract losses by year

Calc. Contract Losses by year

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Compute aal and expected profit for each contract

Compute AAL and expected profit for each contract

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Distribution of profit loss

Distribution of profit/(loss)

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Calculate return on capital

Calculate return on capital

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Portfolio effects

Portfolio Effects

  • Now assume that the reinsurer’s portfolio consists of certain shares of these 3 contracts

  • Want to calculate the overall portfolio capital and

  • Each contract’s share of this portfolio capital

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Portfolio

Portfolio

  • Consider the following portfolio:

    P = 20% A + 10% B + 5% C

  • Then consider 3 other portfolios

    P+0.1% A

    P+0.1% B

    P+0.1% C

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Portfolio ctd

Portfolio ctd.

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Allocating portfolio capital

Allocating Portfolio Capital

  • The portfolio capital can be allocated as follows:

    Cap[20%A]= 20%/0.1% * (422.89-422.02)=174

    Cap[10%B]= 10%/0.1% * (422.56-422.02)= 54

    Cap[5%C] = 5%/0.1% * (425.90-422.02)=194

    ----------------------

    Cap[Portfolio] = 422

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Return on allocated capital

Return on Allocated Capital

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Tail oriented capital metrics

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

Tail oriented ROAC

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Allocated capital calcs

Allocated Capital Calcs

  • As before, alloc. capital based on marginal

  • For example, for the 20%A contract:

    450 = (793.5-791.25)/0.1% * 20%

  • Portfolio Cap = Sum of Alloc. Capitals

  • N.B. according to this capital metric, 10%B has the highest ROAC in the portfolio

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Summary

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

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