Catastrophe Modeling Boot Camp Jim Maher, fcas maaa

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Catastrophe Modeling Boot Camp

  • Jim Maher, FCAS MAAA

  • Platinum Re


Cat Modeling

  • Basic Elements of Cat Models

    • Similarities/Differences of Cat Models
  • Data/Modeling Issues

  • Portfolio Management



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

    • Non random frequency
    • Non random severity


Non-modeled perils

  • Tsunami

  • Meteor strike

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

  • Wildfire

  • Winterstorm



Non-modeled coverages

  • Life/Health

    • Personal Accident
    • Group Life
    • Disability
  • Marine

    • Yachts
    • Offshore Oil Rigs
    • Cargo


Earthquake

  • Major Types of Earthquake

  • Location of Earthquake Hazard

  • Major Historical US Earthquakes

  • Recent US Earthquakes

  • Vulnerability and Financial Models

  • Earthquake prediction (?)



Major Types of Earthquakes

  • Strike-Slip

    • Rock on one side of fault slides horizontally
    • San Andreas Fault
  • Dip-Slip (subduction)



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)


Plate Boundaries & “Ring of Fire”





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.



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.



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




Recent US Earthquakes

  • Loma Prieta (1989)

  • Northridge (1994)

  • Nisqually/ (Seattle) (2001)



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



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



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





Northridge-PCS Estimates



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



Earthquake vulnerability factors

  • Building construction

  • 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


Financial model factors

  • CEA mini-policy

  • Earthquake sublimits on commercial

    • Per policy
    • Per location
    • Regional sublimits (e.g. CA only)
  • Interlocking clause



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


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?




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.



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



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.



Hurricanes

  • Meteorology of Hurricanes

  • Frequency of Hurricanes by category

  • Recent Hurricane Activity

  • Hurricane Andrew

  • Vulnerability and Financial Models

  • Hurricane prediction (?)



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





Safir-Simpson Scale



Atlantic Basin Hurricanes



US Landfalling Hurricanes



2004 Season



2003 Season



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

  • Jeanne:9/13-9/28, Crazy Cat 3 storm, same landfall as Frances but smaller & faster



2004 Hurricanes ctd.



Modeling Issues raised by 2004 storms

  • Storm Surge

  • Demand Surge

  • Frequency Distribution of Hurricanes

  • Offshore oil rig losses

  • Caribbean Clash modeling



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





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


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


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


Hurricane Prediction



Data/Modeling Issues

  • Need for completeness

  • Reinsurers need compensation for all risks being accepted

  • Model all exposures

  • Model all perils

  • Run multiple models



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 (?)


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


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



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



Event Sets



Create a set of Simulation Years



Check against Poisson



Contracts



Calc. Contract Losses by year



Compute AAL and expected profit for each contract



Distribution of profit/(loss)



Calculate return on capital



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



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


Portfolio ctd.



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


Return on Allocated Capital



Tail oriented Capital Metrics

  • Approach also works for tail oriented capital metrics- e.g. TVAR

  • Define capital = 3 x TVAR (80%)



Tail oriented ROAC



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



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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