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CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
• Hazard Module
• Engineering Module (aka Vulnerability)
• Insurance (aka Financial) Module
• Event Set (and Year Set)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Hazard Module
• Seismology
• Meteorology
• Terrorism– Non random frequency– Non random severity
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Non-modeled perils
• Tsunami
• Meteor strike– Est. RP of 1,000 years for 10 megaton event– Most recent Siberia (1908)
• River Flood
• Wildfire
• Winterstorm
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Non-modeled coverages
• Life/Health– Personal Accident– Group Life– Disability
• Marine– Yachts– Offshore Oil Rigs– Cargo
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Earthquake
• Major Types of Earthquake
• Location of Earthquake Hazard
• Major Historical US Earthquakes
• Recent US Earthquakes
• Vulnerability and Financial Models
• Earthquake prediction (?)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Plate Boundaries & “Ring of Fire”
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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.
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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.
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Recent US Earthquakes
• Loma Prieta (1989)
• Northridge (1994)
• Nisqually/ (Seattle) (2001)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Northridge-PCS Estimates
0
2
4
6
8
10
12
14
Aug-93 Mar-94 Sep-94 Apr-95 Oct-95
$B
N
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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?
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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.
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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.
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Hurricanes
• Meteorology of Hurricanes
• Frequency of Hurricanes by category
• Recent Hurricane Activity
• Hurricane prediction
• Vulnerability and Financial Models
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Atlantic Basin Hurricanes
2001 - 2006 6 15.3 8.0
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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%
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Major Storms: 2004-05
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
2002 Season
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
2003
2003 Season
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
2004
2004 Season
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
2005 Season
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
2006 Season
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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*
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Modeling Issues raised by ‘04/05 storms
• Storm Surge
• Demand Surge
• Frequency Distribution of Hurricanes
• Offshore oil rig losses
• Caribbean Clash modeling
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Data/Modeling Issues
• Need for completeness
• Reinsurers need compensation for all risks being accepted
• Model all exposures
• Model all perils
• Run multiple models
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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 (?)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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%
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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%
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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%
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
Tail oriented Capital Metrics
• Approach also works for tail oriented capital metrics- e.g. TVAR
• Define capital = 3 x TVAR (80%)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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)
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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
CAS 2007 Reinsurance Boot Camp on Pricing Techniques
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