Catastrophe Models
December 2, 2010
Richard Bill, FCAS, MAAA
R. A. Bill Consulting
Bill.consulting@frontier.com
Overview
Use of Cat Models in:
• Exposure Management
• Ratemaking
Note: will use Hurricane as example
Cat Models
3
Exposure Management - In old days, pins were used to identify concentration of risk
RABill Consulting
4
Exposure Management – Pins in Map
•
Cumbersome practice was eliminated due to expense
considerations
• Billions of Dollars of Exposure is on or near the coast of the
US subject to severe hurricanes
• Likewise, for earthquake, the insurance industry exposure is
tremendous, particularly in California and the New Madrid
Area
----------------------------------------------------------------------• How do insurance companies judge how much business to
write in catastrophe prone areas such as on the coast of
Florida without exposing the company to bankruptcy????
Catastrophe Ratemaking Problem
•
A Hurricane is an unlikely event for a particular
location on the coast
• The experience period for making rates would need
to be very long to reflect the probability of a
Hurricane at a particular location
• Even if past history were available, it would not
reflect the increase in new construction on the coast
-------------------------------------------------------------------• How do Insurers decide how much to charge for
catastrophe prone areas????
Catastrophe Models evolved as a
solution to the problem
• AIR founded the catastrophe modeling
industry in 1987
• Models were not used much in the beginning
• Hurricane Hugo in 1989 and particularly
Hurricane Andrew in 1992 were wakeup
calls
• Many insurance companies had not realized
the extent of their exposure concentrations.
Cat Model Definition
Catastrophe modeling is the process
of using computer-assisted
calculations to estimate the losses that
could be sustained by a portfolio of
properties due to a catastrophic event
such as a hurricane or earthquake
Property Casualty Insurance Industry
Major Risk Factors
•
•
•
•
•
•
•
•
•
Hurricanes
Earthquakes
Terrorism Losses
Insufficient Reserves
Asbestos/Pollution or similar Exposure
Poor underwriting and/or Inadequate Rates
Collectibility of Reinsurance
High Expenses
Bad Investments
TYPES OF MODELS
• Earthquake
• Fire Following EQ
• Hurricane
• Storm Surge
• Tornado/Hail
• Winter Storm
• Terrorism
Catastrophe Models
• Catastrophe events are simulated for many
years (for example 10,000)
• Company submits detailed information on
their book of business
• Losses are calculated based on the
company’s book of business
• Losses are stated in terms of return time, i.e.
100 year event
Construction of Hurricane Model
•
•
•
•
•
The annual number of occurrences is generated from
the frequency distribution
Landfall Location of each Hurricane is determined
Simulation of Storm track after landfall
Hurricane severity simulation
• Wind Speed
• Size of Hurricane
The movement of the event across the affected area
is simulated, and dollar damages are calculated based
on insured value, type of building, deductible, etc.
Simplified Example
Simulation of Frequency
• Assume average of 3 Hurricane Landfalls per year
• Assume Poisson Distribution
Probability of X Number of
Hurricanes , Avg Freq = 3 Per Year
# of
Hurricanes
0
1
2
3
4
5
6
Probability
5%
15%
22%
22%
17%
10%
5%
Based on Poisson Distribution
Accumulative
5%
20%
42%
65%
82%
92%
97%
Percentile
F(x)
0 - 5%
5 - 20%
20 - 42%
42 - 65%
65 - 82%
82 - 92%
92 - 97%
# of Simulated
Hurricanes
0
1
2
3
4
5
6
Industry Simulated Hurricane Frequency
Average Frequency = 3 Per Year
Year
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
Percentile
17%
36%
85%
97%
14%
2%
15%
52%
78%
34%
# of Events
1
2
5
7
1
0
1
3
4
2
Landfall Location 1st Hurricane
Segment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Total
Number of
Landfalls
3
3
4
10
4
3
5
6
6
3
2
4
3
19
17
3
2
1
5
2
3
10
1
2
1
5
1
5
133
Probability
2%
2%
3%
8%
3%
2%
4%
5%
5%
2%
2%
3%
2%
14%
13%
2%
2%
1%
4%
2%
2%
8%
1%
2%
1%
4%
1%
4%
100%
Accumulative
2%
5%
8%
15%
18%
20%
24%
29%
33%
35%
37%
40%
42%
56%
69%
71%
73%
74%
77%
79%
81%
89%
89%
91%
92%
95%
96%
100%
Percentile
F(x)
0 - 2%
2 - 5%
5 - 8%
8 - 15%
15 - 18%
18 - 20%
20 - 24%
24 - 29%
29 - 33%
33 - 35%
35 - 37%
37 - 40%
40 - 42%
42 - 56%
56 - 69%
69 - 71%
71 - 73%
73 - 74%
74 - 77%
77 - 79%
79 - 81%
81 - 89%
89 - 89%
89 - 91%
91 - 92%
92 - 95%
95 - 96%
96 - 100%
Segment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Industry Simulated Hurricane Location
Hurricane
1
2
3
4
5
6
7
8
9
10
Random (0,1)
Percentile
17%
36%
85%
97%
14%
2%
15%
52%
78%
34%
Segment #
5
11
22
28
4
2
4
14
20
10
Industry Simulated Hurricane Events
Based on 10,000 Years of Simulated Events
Simulates Precise
Location within Segment
Year
1
2
2
3
3
3
3
3
~
~
9999
10000
EventID
11814
13602
22355
19188
34955
38175
3421
23037
~
~
17044
38889
Event
FL Hurricane Cat 1
LA Hurricane Cat 3
NC Hurricane Cat 5
MS Hurricane Cat 2
FL Hurricane Cat 3
FL Hurricane Cat 5
AL Hurricane Cat 4
SC Hurricane Cat 4
~
~
GA Hurricane Cat 3
FL Hurricane Cat 5
Lat/Long Landfall
26.1949/-80.0354
29.5352/-92.3730
35.2994/-76.1572
28.4666/-92.4352
26.2549/-90.3445
26.3555/-90.5553
27.3322/-92.5543
34.3335/-78.5555
~
~
33.4444/-87.2225
26.4444/-90.5555
Company XYZ Simulated Hurricane Losses
Based on 10,000 Years of Simulated Events
Policy #
1000
1001
~
~
1050
1051
Total
Type
Dwelling
Apartment
~
~
Dwelling
Dwelling
Address
Lat/Long Location
1234 Washington 26.1949/-80.0354
1235 Washington 26.1950/-80.0360
~
~
~
~
1500 Ash
26.1951/-80.0374
1505 Ash
26.1953/-80.0380
Replacement
Average Annual
Value
Loss
$
100,000 $
100
15,000,000
10,000
~
~
~
~
300,000
400
400,000
550
$
3,000,000
Model Output
Company XYZ Simulated Hurricane Losses From Largest
In Thousands
Accumulated
Probability
0.0001
0.0002
0.0003
~
~
0.0009
0.0010
0.0011
~
~
0.0099
0.0100
0.0101
Year
7779
3851
5447
3354
1418
9004
Gross Loss
EventID
16970
17065
40855
Richard:
1000 Year Event
35241
8130
34930
Event
LA Hurricane
NC Hurricane
MS Hurricane
Gross Loss
Amount
100,120
99,500
98,000
Net Loss
Amount
80,120
79,500
78,000
FL Hurricane
FL Hurricane
AL Hurricane
76,443
75,150
74,300
56,443
55,150
54,300
SC Hurricane
GA Hurricane
FL Hurricane
40,253
40,100
39,980
37,752
37,599
37,479
Richard:
100 Year Event
621
8782
4560
1617
13220
1172
Company XYZ Cat Model Results
In Millions
Return
Period
25
50
100
250
500
1,000
10,000
Probability
4.00%
2.00%
1.00%
0.40%
0.20%
0.10%
0.01%
Avg Annual Loss
* After Reinsurance Recoveries
Direct Losses
Net Losses*
18
27
40
51
65
75
100
3
17
25
37
46
47
55
80
Return Period Perspective
• 250 Years-20 years before the Declaration of
Independence - 1756
• 500 Years- 14 years after Christopher Columbus
discovers America - 1506
• 1,000 Years-Leif Erickson discovers “Vinland”
(possibly New England - 1006?)
• 10,000 Years – 8000 B.C. - ??????
Industry % of Insured Value
in Coastal Counties
•
•
•
•
•
79% in Florida
63% in Connecticut
61% in New York
54% in Massachusetts
16% Nationwide
Top 10 Most Costly Hurricanes in US History, (Insured
Losses, $2005)
$45
$40
$35
$ Billions
$30
$25
$20
$15
Seven of the 10 most expensive
hurricanes in US history
occurred in the 14 months from
Aug. 2004 – Oct. 2005:
Katrina, Rita, Wilma, Charley,
Ivan, Frances & Jeanne
$10
$5
$40.0
$3.5
$3.8
Georges
(1998)
Jeanne
(2004)
$4.8
$5.0
Frances
(2004)
Rita
(2005)
$21.6
$6.6
$7.4
$7.7
$8.4
Hugo
(1989)
Ivan
(2004)
Charley
(2004)
Wilma
(2005)
$0
From III Presentation on Hurricanes
Sources: ISO/PCS; Insurance Information Institute.
Andrew
(1992)
Katrina
(2005)
Exposure Management
• Component of Insurance Company’s
Enterprise Risk Management (ERM)
• Make sure that a catastrophe does not wipe
out the company
• Maintain financial strength after an event
• Maintain financial ratings
• Smooth earnings (publicly held companies)
Accumulation Management
• Manage accumulation during
underwriting process
• Limit new business
• Non renewals
• Increase business in lower risk
areas
Exposure Management (cont.)
• Rating Agencies are placing a lot more
reliance on cat management since the
hurricanes of 2004 and 2005
• A Company can either purchase more
reinsurance or reduce exposure or raise
prices or a combination
Industry Reaction
• More demand for reinsurance
• Many companies are pulling back from
coastal areas particularly, the gulf states
• Insurance Rates for coastal properties have
skyrocketed
Ratemaking
Pricing for Hurricane
“When hurricane rating analyses were first
expanded from five to 30 years of storm
experience, the technique was applauded as a
vast improvement, which is was. The 30 years
were replaced by 100,000 years and real life
events were replaced by silcon-prompted
simulations. “
Company XYZ Simulated Hurricane Losses
Based on 10,000 Years of Simulated Events
In Thousands
Year
1
2
2
3
3
3
3
3
4
4
~
~
EventID
11814
13602
22355
19188
34955
38175
3421
23037
17044
38889
Event
FL Hurricane
LA Hurricane
NC Hurricane
MS Hurricane
FL Hurricane
FL Hurricane
AL Hurricane
SC Hurricane
GA Hurricane
FL Hurricane
Gross Loss
Amount
283
400
40
300
10,000
640
100
829
214
589
~
~
30,000,000
Lat/Long Location
26.1949/-80.0354
29.5352/-92.3730
35.2994/-76.1572
28.4666/-92.4352
26.2549/-90.3445
26.3555/-90.5553
27.3322/-92.5543
34.3335/-78.5555
33.4444/-87.2225
26.4444/-90.5555
Total
Average Annual Loss (Divide by 10,000)
$
3,000
Net Loss
Amount
283
400
40
300
9,500
640
100
829
214
589
~
~
Average Annual Loss
• Indicates what needs to be charged each year
to cover hurricane losses over the long run
• Can be calculated for each individual buildinguseful for pricing large commercial buildings
• Can be calculated at a zip code level or even
finer to be used in pricing – example, all
dwellings within 1 mile of the coast
• Risk charge can be calculated as an additional
charge
How Models Are Used
Underwriting
Establish guidelines
Differentiate risks
Develop pricing
Portfolio Management
Determine risk drivers
Evaluate capital adequacy
Allocate capital
Estimate post-event losses
Accumulation Management
Risk Transfer
Determine reinsurance needs
Structure and price of reinsurance