On The Cost of Financing
Catastrophe Insurance
Presentation to the
Casualty Actuarial Society
Dynamic Financial Analysis Seminar
By
Glenn Meyers and John Kollar
Insurance Services Office, Inc.
July 13 &14 , 1998
Catastrophes and Insurer
Capital
• Two major insurers lost more than their
“capital” in Hurricane Andrew
• They are solvent today, because they
had “rich” parents.
• You need a LOT of capital to cover
catastrophes.
• Is holding sufficient capital to cover
catastrophes efficient?
Capital Substitutes
• Reinsurance
– Does not have the capacity to cover the
really big catastrophes
– Cat Limits are usually small compared to
surplus
• Securitization
– Large potential capacity
– Index trading has been slow
– Recent over the counter deals are insurer
specific, like reinsurance
Potential Advantages of
Catastrophe Indices
•
•
•
•
Low transaction costs
No counter-party risk
Ease of entry for investors and insurers
Liquidity
Problems with
Catastrophe Indices
• Investors don’t understand the risk
• Insurers don’t know how much their risk
will be reduced (i.e. basis risk)
• The insurer-specific deals have found
investor support because they could
quantify the risk using a catastrophe
model on the insurer’s exposures.
ISO’s Contribution
• Quantify risk for investors
• Quantify risk for insurers
• Use a catastrophe model and
underlying exposure for catastrophe
indices and insurers.
• Agreements with AIR and RMS
• Can use GCCI or PCS options
A Quick Explanation of
Hurricane Models
• Multiple Events
• Each Event
– Affects a collection of ZIP codes
– Each ZIP code has a wind speed
• Insurer
– Has exposure for each class and ZIP code
A Quick Explanation of
Hurricane Models
• For each event
– For each ZIP
• Get wind speed
• For each class
–Get Value of buildings
–Get Damage Ratio for wind speed
–Loss = Value × Damage ratio
– Add up all losses for the event
The Guy Carpenter
Catastrophe Index (GCCI)
• Consists of the combined experience of
39 insurers who report their data to ISO
• Contracts on the GCCI are traded on
the Bermuda Commodities Exchange
(BCOE)
• The underlying exposures are available,
so it is possible to use a catastrophe
model to quantify the risk to both
investors and insurers.
The GCCI Index
Homeowners Wind Losses
GCCI Index 
 10,000
Insured Value
Bermuda Commodities Exchange
Traded GCCI Contracts
Covered Events
• Aggregate Loss
• Largest Event
• Second Largest Event
• Contracts pay $5000 if
Index exceeds the
posted strike price
Geographic Regions
• National
• Southeast
• Northeast
• Mid/West
• Florida
• Gulf
Strike prices traded on BCOE - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
15, 20, 25, 30, 35, 40, 45, 50, 100, 150, 200, 250, 300,
350, 400, 450, 500, 550, 600, 650, 700
The Examples Use an Illustrative
Index Similar to the GCCI
• Programming GCCI rules is under way
• Used proxy GCCI for now.
– Ran cat model through 50 insurers
– Set the largest event = 100
• Industry Equivalent - 100 Billion +
– Maximum event contracts for $1,000
– Strike prices at 5,10, …, 95,100
Maximum Event Catastrophe Options
Probability of
Excercising Option
Information for Investors
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
20
40
60
Strike Price
80
100
120
Catastrophe Options vs
Other Investments
One way to compare risk and cost
• Moody’s - Projected 12-month default
rate of speculative-grade bonds is 2.5%.
• Average spread of speculative-grade
bonds over risk-free bonds is 3.5%
• Probability of exercising a catastrophe
option with a strike price of 20 is 2.3%
Insurer Objectives
Using Catastrophe Options
• Reduce the cost of financing insurance
– Expected insurer costs
– Cost of Capital
– Cost of Capital Substitutes
• Reinsurance
• Contracts on a catastrophe index
• Find the right mix of capital and capital
substitutes
Quantifying the Cost of Capital
• Depends on the variability of the insurer’s business
• Standards will depend on the insurer management
• An “easy” formula
Cost of Capital = K  T  
Where:
 = Standard deviation of total insurer loss
T = Factor reflecting risk aversion
K = Rate of return needed to attract capita
Quantifying Basis Risk
Ran hurricane model through insurers and index.
Event
1
2
3
4
5
…
1001
1002
1003
1004
1005
Index
Value
100.00
89.04
87.56
83.48
83.20
…
15.84
15.83
15.79
15.74
15.67
Event
Probability
0.00000121
0.00000121
0.00000181
0.00000702
0.00000702
…
0.00000050
0.00002730
0.00001610
0.00015000
0.00006420
Max Event
Contract
Direct
Reinsurance Event Loss
Probability
Value
Insurer Loss
Recovery
Given Max
0.00000121 1,164,300,000 1,212,550,269 13,000,000
35,250,269
0.00000121 1,052,700,000 1,509,161,589 13,000,000 443,461,589
0.00000181 1,052,700,000 1,303,694,653 13,000,000 237,994,653
0.00000702
971,300,000
761,956,629 13,000,000 (222,343,371)
0.00000702
971,300,000
734,137,782 13,000,000 (250,162,218)
…
…
…
…
…
0.00000048
142,200,000
168,534,466 13,000,000
13,334,466
0.00002630
142,200,000
137,088,005 13,000,000 (18,111,995)
0.00001551
142,200,000
191,606,795 13,000,000
36,406,795
0.00014452
142,200,000
141,627,163 13,000,000 (13,572,837)
0.00006184
142,200,000
117,419,238 13,000,000 (37,780,762)
+ about 9000 more
• Compare variability before and after
• Is the risk reduction worth the cost?
Minimize Sum of
Cost Elements
• Insurer Capital
Cost of Capital = K  T  (Net Losses)
• Reinsurance
Transaction Cost + Expected Cost
• Cat index contracts
Transaction Cost + Expected Cost
Use cat model results to back out transaction costs.
Analysis of Three Insurers
• Insurer #1 - A medium national insurer
Highly correlated with the index
• Insurer #2 - A large national insurer
Moderately correlated with the index
• Insurer #3 - A small regional insurer
Slightly correlated with the index
Search for Best Strategy to
Minimize Cost of Financing
Insurance
• Search for the combination of index and
reinsurance purchases that minimizes
total cost of providing insurance.
Questions
• How many index contracts at each
strike price?
• What layer of reinsurance?
Results of Search
Contract
Range
5-20
25-40
45-55
60-70
75-85
90-100
Number of Index Contracts @ $1,000
Insurer #1
Insurer #2
Insurer #3
47,400
93,100
0
74,400
118,100
6,300
59,500
67,900
0
47,600
28,600
0
81,400
545,100
0
37,200
634,800
0
Retention
Limit
Reinsurance
73,000,000 457,000,000 54,000,000
13,000,000 36,000,000 105,000,000
Financing With Reinsurance
and Catastrophe Options
Expected Net Loss
Cost of Capital
Cost of Reinsurance
Cost of Catastrophe Options
Cost of Financing Insurance
Insurer #1
Insurer #2
Insurer #3
16,315,629
62,086,995
1,464,410
47,905,407 143,662,761 12,914,922
2,132,070
1,848,530
1,726,342
22,252,015
42,409,101
249,427
88,605,121 250,007,387 16,355,100
Financing Without Reinsurance
and Catastrophe Options
Expected Net Loss
Cost of Capital
Cost of Reinsurance
Cost of Catastrophe Options
Cost of Financing Insurance
Insurer #1
Insurer #2
Insurer #3
34,839,348
95,417,229
2,385,629
62,095,747 166,962,499 15,356,683
0
0
0
0
0
0
96,935,095 262,379,728 17,742,312
Differences in Costs
Without Reins & Options
With Reins & Options
Difference
Pct Difference
Insurer #1
Insurer #2
Insurer #3
96,935,095 262,379,728 17,742,312
88,605,121 250,007,387 16,355,100
8,329,975 12,372,340 1,387,212
8.6%
4.7%
7.8%
The Marginal Cost of
Financing Catastrophe Insurance
• The effect of Catastrophe Options and
reinsurance in rates.
• Calculate the cost of financing with and
without catastrophe coverage.
Marginal Cost with Reinsurance
and Catastrophe Options
Cost of Financing without Cats
Cost of Financing with Cats
Marginal Cost of Cats
Marginal Cost/Expected Loss
Insurer #1
Insurer #2
Insurer #3
43,908,324 103,258,865 10,764,807
88,605,121 250,007,387 16,355,100
44,696,797 146,748,522 5,590,293
1.283
1.538
2.343
Marginal Cost without Reinsurance
and Catastrophe Options
Cost of Financing without Cats
Cost of Financing with Cats
Marginal Cost of Cats
Marginal Cost/Expected Loss
Insurer #1
Insurer #2
Insurer #3
43,908,324 103,258,865 10,764,807
96,935,095 262,379,728 17,742,312
53,026,771 159,120,863 6,977,505
1.522
1.668
2.925
The Next Steps
• Analyze regional and state indices
• Embed catastrophe options within
reinsurance contracts
• Reinsurer hedges combined risk of its
primary insurers
• Reinsurer covers customized indices —
adverse selection is not an issue.