CAS 2007 Reinsurance Boot Camp on Pricing Techniques Catastrophe Modeling Jim Maher, FCAS MAAA Chief...

CAS 2007 Reinsurance Boot Camp on Pricing Techniques

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– 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)– Fault is at an angle to the surface of the earth– Movement of the rock is up or down– Great Kanto Earthquake (Japan 1923)


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

0

2

4

6

8

10

12

14

Aug-93 Mar-94 Sep-94 Apr-95 Oct-95

$B

N


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– 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


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


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 prediction

• Vulnerability and Financial Models


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 ScaleScale

NumberCentral

PressureWinds

Storm Surge

(Category)

mb (in.)mi/hr

(knots)ft (m)

1>980

(>28.94)74-95 (64-

82) 4-5 (~1.5)Damage mainly to trees, shrubbery and unanchored mobile homes

2

965-979 (28.50-28.91)

96-110 (83-95)

6-8 (~2.0-2.5)

Some trees blown down; major damage to exposed mobile homes; some damage to roofs of buildings

3

945-964 (27.91-28.47)

111-130 (96-113)

9-12 (~2.5-4.0)

Foliage removed from trees; large trees blown down; mobile homes destroyed; some structural damage to small buildings

4

920-944 (27.17-27.88)

131-155 (114-135)

13-18 (~4.0-5.5)

All signs blown down; extensive damage to roofs, windows, and doors; complete destruction of mobile homes; flooding inland as far as 10 km (6 mi); major damage to lower floors of structures near shore

5<920

(<27.17)>155

(>135)>18

(>5.5)

Severe damage to windows and doors; extensive damage to roofs of homes and industrial buildings; small buildings overturned and blown away; major damage to lower floors of all structures less than 4.5 m (15 ft) above sea level

Damage


Atlantic Basin Hurricanes

2001 - 2006 6 15.3 8.0


US Landfalling HurricanesAll Major

1 2 3 4 5 1,2,3,4,5 3,4,51851-1860 8 5 5 1 0 19 61861-1870 8 6 1 0 0 15 11871-1880 7 6 7 0 0 20 71881-1890 8 9 4 1 0 22 51891-1900 8 5 5 3 0 21 81901-1910 10 4 4 0 0 18 41911-1920 10 4 4 3 0 21 71921-1930 5 3 3 2 0 13 51931-1940 4 7 6 1 1 19 81941-1950 8 6 9 1 0 24 101951-1960 8 1 5 3 0 17 81961-1970 3 5 4 1 1 14 61971-1980 6 2 4 0 0 12 41981-1990 9 1 4 1 0 15 51991-2000 3 6 4 0 1 14 52001-2006 6 2 6 1 0 15 7

Avg. per decade 7.5 4.7 5.2 1.2 0.2 18.8 6.6

2001-2006 rate 10.0 3.3 10.0 1.7 0.0 25.0 11.7

DecadeSaffir Simpson Category


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

Long Term Average 2001-2006

% above average

Basin-wide 5.1 8.0 57%US Landfalling 1.9 2.5 33%US CAT 3-5 Landfalls 0.7 1.2 77%


Major Storms: 2004-05


2002 Season


2003

2003 Season


2004

2004 Season


2005 Season


2006 Season


2004 Hurricanes cost$BN PCS SigmaCharley 6.8 9.2 6.0 8.0 7.5 8.0 Frances 6.0 9.0 3.0 6.0 4.6 5.0 Ivan 3.5 5.9 3.0 6.0 7.1 11.0 Jeanne 5.9 9.9 4.0 8.0 3.7 4.0 Total 22.2 34.0 16.0 28.0 22.9 28.0

AIR Range RMS Range


2005 Hurricanes cost$BN PCSDennis 1.0 2.2 1.0 3.0 1.1 Katrina 18.0 25.0 10.0 20.0 40.7 Rita 4.0 5.5 3.0 5.0 5.6 Wilma 6.3 8.3 5.6 9.0 10.3 Total 29.3 41.0 19.6 37.0 57.7

* reflects RMS initial estimates: later revised to $38-$55 BN for Katrina and $8-12 BN for Wilma

AIR Range RMS Range*


Hurricane Prediction

Forecaster Date Number of 2005 HurricanesDr. Mark Saunders 7/7/2005 8.8Dr. William Gray 5/31/2005 8NHC-NOAA 5/15/2005 7-9

2005 Hurricane SeasonForecast of Number of Hurricanes

Long Term Average is 6.0

Actual 15


Hurricane Prediction, ctd.

Forecaster HurricanesLandfalling Hurricanes

Dr. Mark Saunders 7.9 2.1 Dr. William Gray 9.0 n/aNHC-NOAA 9.0 3.0 Accuweather n/a 5.0

Actual 5.0 0.0

2006 Hurricane SeasonForecast of Number of Hurricanes

Long Term Average is 6.0


Hurricane Prediction 2007% above 1950-2006 Average

Forecast GraySaund

ers NOAA

1950-2006 Avg Gray Saunders NOAA

Named Storms 17.0 16.1 15.0 10.3 65% 56% 46%Basin Hurricanes 9.0 8.9 8.5 6.2 45% 44% 37%Basin Severe Hurricanes 5.0 4.0 4.0 2.7 85% 48% 48%US Landfalling Hurricanes #N/A 2.3 2.1 1.5 #N/A 53% 40%

Estimated from NOAA dataForecasts are as of May for Saunders/NOAA, April for Gray


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


Modeling Issues raised by ‘04/05 storms

• Storm Surge

• Demand Surge

• Frequency Distribution of Hurricanes

• Offshore oil rig losses

• Caribbean Clash modeling


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 SetsOceania Industry Excedence Freq Curve Eurasia Industry Excedence Freq Curve

Event RateExced.

Freq.Industry

LossRet.

Period Event RateExced.

Freq.Industry

LossRet.

Period

O_1 2.5% 2.5% 10,000 40 E_1 5.0% 5.0% 20,000 20

O_2 5.0% 7.5% 8,000 13 E_2 2.5% 7.5% 12,000 13

O_3 2.5% 10.0% 5,000 10 E_3 2.5% 10.0% 6,000 10

O_4 10.0% 20.0% 4,000 5 E_4 5.0% 15.0% 3,000 7

O_5 2.5% 22.5% 2,000 4 E_5 10.0% 25.0% 1,500 4


Create a set of Simulation YearsYear 1st Event 2nd Event 3rd Event

1 O_45 E_16 O_47 O_18 O_2 E_5

13 E_514 O_217 E_418 E_419 O_3 E_521 E_222 O_425 E_132 O_539 O_4 E_3 E_5


Check against Poisson

Combined annual mean frequencyfor the 10 events= 47.5%

# events Prob.

Expected number in

40 years

From Simulation

Set0 62.2% 24.9 251 29.5% 11.8 122 7.0% 2.8 2

3+ 1.3% 0.5 1


ContractsConsider that the following contracts are available in the open market:

Contract Territory Limit x RetentionReinstate

ments PremiumA Oceania 1,250 x 1,000 None 500 B Eurasia 1,250 x 750 None 300 C Both 5,000 x 1,000 None 2,000


Calc. Contract Losses by yearYear

Contract A Loss

Contract B Loss

Contract C Loss

1 1,250 - 3,000 5 - 1,250 5,000 6 1,250 - 3,000 7 1,250 - 5,000 8 1,250 750 5,000

13 - 750 500 14 1,250 - 5,000 17 - 1,250 2,000 18 - 1,250 2,000 19 1,250 750 4,500 21 - 1,250 5,000 22 1,250 - 3,000 25 - 1,250 5,000 32 1,000 - 1,000 39 1,250 1,250 5,000


Compute AAL and expected profit for each contract

Contract A B CTerritory Oceania Eurasia BothLimit 1,250 1,250 5,000 x x x xRetention 1,000 750 1,000 Premium 500 300 2,000 AAL 275 244 1,350 LR 55% 81% 68%E[Profit] 225 56 650 sd profit 518 472 2,017


Distribution of profit/(loss)Year A B C Year A B C

1 (750) 300 (1,000) 21 500 (950) (3,000) 2 500 300 2,000 22 (750) 300 (1,000) 3 500 300 2,000 23 500 300 2,000 4 500 300 2,000 24 500 300 2,000 5 500 (950) (3,000) 25 500 (950) (3,000) 6 (750) 300 (1,000) 26 500 300 2,000 7 (750) 300 (3,000) 27 500 300 2,000 8 (750) (450) (3,000) 28 500 300 2,000 9 500 300 2,000 29 500 300 2,000

10 500 300 2,000 30 500 300 2,000 11 500 300 2,000 31 500 300 2,000 12 500 300 2,000 32 (500) 300 1,000 13 500 (450) 1,500 33 500 300 2,000 14 (750) 300 (3,000) 34 500 300 2,000 15 500 300 2,000 35 500 300 2,000 16 500 300 2,000 36 500 300 2,000 17 500 (950) - 37 500 300 2,000 18 500 (950) - 38 500 300 2,000 19 (750) (450) (2,500) 39 (750) (950) (3,000) 20 500 300 2,000 40 500 300 2,000

Distribution of Profit by year


Calculate return on capitalContract A B CTerritory Oceania Eurasia BothLimit 1,250 1,250 5,000 x x x xRetention 1,000 750 1,000 Premium 500 300 2,000 AAL 275 244 1,350 LR 55% 81% 68%E[Profit] 225 56 650 sd profit 518 472 2,017 Capital 1,037 944 4,033 ROC 21.7% 6.0% 16.1%


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 portfoliosP+0.1% A

P+0.1% B

P+0.1% C


Portfolio ctd.

Contract Portfolio P+.1%A P+.1%*B P+.1%*CPremium 230.0 230.5 230.3 232.0 AAL 146.9 147.2 147.1 148.2 E[Profit] 83.1 83.4 83.2 83.8 sd profit 211.0 211.4 211.3 213.0 Capital 422.0 422.9 422.6 425.9 ROC 19.7% 19.7% 19.7% 19.7%


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

Contract 20%A 10%B 5%C PortfolioNet Premium 100 30 100 230 AAL 55 24 68 147 E[Profit] 45 6 33 83 Allocated Cap 174 54 194 422 ROAC 25.9% 10.3% 16.7% 19.7%Stand-alone ROC 21.7% 6.0% 16.1%


Tail oriented Capital Metrics

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

• Define capital = 3 x TVAR (80%)


Tail oriented ROAC

%TILE Portfolio P+.1%A P+.1%B P+.1%C2.5% (395.00) (395.75) (395.95) (398.00) 5.0% (345.00) (345.75) (345.45) (348.00) 7.5% (320.00) (320.75) (320.45) (322.50)

10.0% (270.00) (270.75) (269.70) (273.00) 12.5% (270.00) (270.75) (269.70) (273.00) 15.0% (170.00) (170.75) (169.70) (171.00) 17.5% (170.00) (170.75) (169.70) (171.00) 20.0% (170.00) (170.75) (169.70) (171.00)

TVAR (263.75) (264.50) (263.79) (265.94) Capital 791.25 793.50 791.38 797.81

P 20%A 10%B 5%CAllocated Cap 791.25 450.00 13.12 328.13

ROAC 10.5% 10.0% 42.9% 9.9%

Distribution of Profit/(Loss)


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

CAS 2007 Reinsurance Boot Camp on Pricing Techniques Catastrophe Modeling Jim Maher, FCAS MAAA Chief...

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