Catastrophe Modeling
Jim Maher, FCAS MAAA
Chief Risk Officer
Platinum Re US
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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 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)
• 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
14
12
$BN
10
8
6
4
2
0
Aug-93
Mar-94
Sep-94
Apr-95
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Oct-95
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 prediction
Vulnerability and Financial Models
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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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Safir-Simpson Scale
Scale
Central
Number Pressure
(Categor
mb (in.)
y)
1
Winds
mi/hr
(knots)
Storm
Surge
Damage
ft (m)
>980
74-95 (64Damage mainly to trees, shrubbery and unanchored mobile
(>28.94)
82)
4-5 (~1.5) homes
965-979
2
(28.5028.91)
96-110
(83-95)
3
945-964
(27.9128.47)
Foliage removed from trees; large trees blown down;
111-130 9-12 (~2.5- mobile homes destroyed; some structural damage to small
(96-113)
4.0)
buildings
920-944
(27.1727.88)
All signs blown down; extensive damage to roofs, windows,
and doors; complete destruction of mobile homes; flooding
131-155
13-18 inland as far as 10 km (6 mi); major damage to lower floors
(114-135) (~4.0-5.5) of structures near shore
4
5
<920
(<27.17)
>155
(>135)
6-8 (~2.0- Some trees blown down; major damage to exposed mobile
2.5)
homes; some damage to roofs of buildings
>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
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Atlantic Basin Hurricanes
2001 - 2006
6
15.3
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8.0
US Landfalling Hurricanes
Decade
1851-1860
1861-1870
1871-1880
1881-1890
1891-1900
1901-1910
1911-1920
1921-1930
1931-1940
1941-1950
1951-1960
1961-1970
1971-1980
1981-1990
1991-2000
2001-2006
1
8
8
7
8
8
10
10
5
4
8
8
3
6
9
3
6
Saffir Simpson Category
2
3
4
5
All
1,2,3,4,5
Major
3,4,5
6
1
7
5
8
4
7
5
8
10
8
6
4
5
5
7
5
6
6
9
5
4
4
3
7
6
1
5
2
1
6
2
5
1
7
4
5
4
4
3
6
9
5
4
4
4
4
6
1
0
0
1
3
0
3
2
1
1
3
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
19
15
20
22
21
18
21
13
19
24
17
14
12
15
14
15
0.2
18.8
6.6
25.0
11.7
Avg. per decade
7.5
4.7
5.2
1.2
2001-2006 rate
10.0
3.3
10.0
1.7
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0.0
Average & Recent Hurricane Activity
• To sum up: Average Hurricane numbers per year:
Long Term
Average
Basin-wide
US Landfalling
US CAT 3-5 Landfalls
2001-2006
5.1
1.9
0.7
• Cat Modeling Firms response:
– Alternate versions of their models
– Short Term vs. Long Term view
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8.0
2.5
1.2
% above
average
57%
33%
77%
Major Storms: 2004-05
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2002 Season
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2003 Season
2003
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2004 Season
2004
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2005 Season
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2006 Season
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2004 Hurricanes cost
$BN
Charley
Frances
Ivan
Jeanne
Total
AIR Range RMS Range PCS Sigma
6.8
9.2
6.0
8.0
7.5
8.0
6.0
9.0
3.0
6.0
4.6
5.0
3.5
5.9
3.0
6.0
7.1 11.0
5.9
9.9
4.0
8.0
3.7
4.0
22.2 34.0 16.0 28.0 22.9 28.0
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2005 Hurricanes cost
$BN
Dennis
Katrina
Rita
Wilma
Total
AIR Range
1.0
2.2
18.0
25.0
4.0
5.5
6.3
8.3
29.3
41.0
RMS Range*
1.0
3.0
10.0
20.0
3.0
5.0
5.6
9.0
19.6
37.0
* reflects RMS initial estimates:
later revised to $38-$55 BN for Katrina and $8-12 BN for Wilma
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PCS
1.1
40.7
5.6
10.3
57.7
Hurricane Prediction
2005 Hurricane Season
Forecast of Number of Hurricanes
Long Term Average is 6.0
Forecaster
Date
Number of 2005 Hurricanes
Dr. Mark Saunders 7/7/2005
8.8
Dr. William Gray
5/31/2005
8
NHC-NOAA
5/15/2005
7-9
Actual
15
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Hurricane Prediction, ctd.
2006 Hurricane Season
Forecast of Number of Hurricanes
Long Term Average is 6.0
Landfalling
Hurricanes Hurricanes
Forecaster
Accuweather
7.9
9.0
9.0
n/a
Actual
5.0
Dr. Mark Saunders
Dr. William Gray
NHC-NOAA
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2.1
n/a
3.0
5.0
0.0
Hurricane Prediction 2007
% above 1950-2006 Average
Forecast
Named Storms
Basin Hurricanes
Basin Severe Hurricanes
US Landfalling Hurricanes
Gray
17.0
9.0
5.0
#N/A
Saund
ers NOAA
16.1
15.0
8.9
8.5
4.0
4.0
2.3
2.1
19502006
Avg
10.3
6.2
2.7
1.5
Estimated from NOAA data
Forecasts are as of May for Saunders/NOAA, April for Gray
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Gray Saunders
65%
56%
45%
44%
85%
48%
#N/A
53%
NOAA
46%
37%
48%
40%
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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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
• 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 portfolio’s 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
Oceania Industry Excedence Freq Curve
Eurasia Industry Excedence Freq Curve
Event
Rate
Exced.
Freq.
Industry
Ret.
Loss 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
Event Rate
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Exced.
Freq.
Industry
Loss
Ret.
Period
Create a set of Simulation Years
Year
1
5
6
7
8
13
14
17
18
19
21
22
25
32
39
1st Event
O_4
E_1
O_4
O_1
O_2
E_5
O_2
E_4
E_4
O_3
E_2
O_4
E_1
O_5
O_4
2nd Event
3rd Event
E_5
E_5
E_3
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E_5
Check against Poisson
Combined annual mean frequency
for the 10 events=
47.5%
# events Prob.
0
62.2%
1
29.5%
2
7.0%
3+
1.3%
Expected
From
number in Simulation
40 years
Set
24.9
25
11.8
12
2.8
2
0.5
1
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Contracts
Consider that the following contracts are available
in the open market:
Contract
A
B
C
Territory
Oceania
Eurasia
Both
Limit
1,250
1,250
5,000
x
x
x
x
Retention
1,000
750
1,000
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Reinstate
ments Premium
None
500
None
300
None
2,000
Calc. Contract Losses by year
Year
1
5
6
7
8
13
14
17
18
19
21
22
25
32
39
Contract A
Loss
1,250
1,250
1,250
1,250
1,250
1,250
1,250
1,000
1,250
Contract B
Loss
1,250
750
750
1,250
1,250
750
1,250
1,250
1,250
Contract C
Loss
3,000
5,000
3,000
5,000
5,000
500
5,000
2,000
2,000
4,500
5,000
3,000
5,000
1,000
5,000
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Compute AAL and expected
profit for each contract
Contract
Territory
Limit
x
Retention
Premium
AAL
LR
E[Profit]
sd profit
A
Oceania
1,250
x
1,000
500
275
55%
225
518
B
Eurasia
1,250
x
750
300
244
81%
56
472
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C
Both
5,000
x
1,000
2,000
1,350
68%
650
2,017
Distribution of profit/(loss)
Distribution of Profit by year
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
(750)
500
500
500
500
(750)
(750)
(750)
500
500
500
500
500
(750)
500
500
500
500
(750)
500
B
300
300
300
300
(950)
300
300
(450)
300
300
300
300
(450)
300
300
300
(950)
(950)
(450)
300
C
(1,000)
2,000
2,000
2,000
(3,000)
(1,000)
(3,000)
(3,000)
2,000
2,000
2,000
2,000
1,500
(3,000)
2,000
2,000
(2,500)
2,000
Year
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A
500
(750)
500
500
500
500
500
500
500
500
500
(500)
500
500
500
500
500
500
(750)
500
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B
(950)
300
300
300
(950)
300
300
300
300
300
300
300
300
300
300
300
300
300
(950)
300
C
(3,000)
(1,000)
2,000
2,000
(3,000)
2,000
2,000
2,000
2,000
2,000
2,000
1,000
2,000
2,000
2,000
2,000
2,000
2,000
(3,000)
2,000
Calculate return on capital
Contract
A
Territory Oceania
Limit
1,250
x
x
Retention
1,000
Premium
500
AAL
275
LR
55%
E[Profit]
225
sd profit
518
Capital
1,037
ROC
21.7%
B
Eurasia
1,250
x
750
300
244
81%
56
472
944
6.0%
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C
Both
5,000
x
1,000
2,000
1,350
68%
650
2,017
4,033
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
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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.
Contract
Premium
AAL
E[Profit]
sd profit
Capital
ROC
Portfolio P+.1%A P+.1%*B P+.1%*C
230.0
230.5
230.3
232.0
146.9
147.2
147.1
148.2
83.1
83.4
83.2
83.8
211.0
211.4
211.3
213.0
422.0
422.9
422.6
425.9
19.7%
19.7%
19.7%
19.7%
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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
Contract
Net Premium
AAL
E[Profit]
Allocated Cap
ROAC
Stand-alone ROC
20%A 10%B
5%C
Portfolio
100
30
100
230
55
24
68
147
45
6
33
83
174
54
194
422
25.9%
10.3%
16.7%
19.7%
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
Distribution of Profit/(Loss)
%TILE
2.5%
5.0%
7.5%
10.0%
12.5%
15.0%
17.5%
20.0%
Portfolio
(395.00)
(345.00)
(320.00)
(270.00)
(270.00)
(170.00)
(170.00)
(170.00)
P+.1%A
(395.75)
(345.75)
(320.75)
(270.75)
(270.75)
(170.75)
(170.75)
(170.75)
P+.1%B
(395.95)
(345.45)
(320.45)
(269.70)
(269.70)
(169.70)
(169.70)
(169.70)
P+.1%C
(398.00)
(348.00)
(322.50)
(273.00)
(273.00)
(171.00)
(171.00)
(171.00)
TVAR
Capital
(263.75)
791.25
(264.50)
793.50
(263.79)
791.38
(265.94)
797.81
Allocated Cap
ROAC
P
791.25
10.5%
20%A
450.00
10.0%
10%B
13.12
42.9%
5%C
328.13
9.9%
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
CAS 2007 Reinsurance Boot Camp
on Pricing Techniques