Pricing Catastrophe Risk

1
Pricing Catastrophe Risk
2003 Aon Re Australia Hazards Conference, Gold
Coast, 18-19 August

• George R Walker
• Senior Risk Analyst
• Aon Re Australia

2
Background
3
Factors Affecting Catastrophe Risk Price

• Probable Maximum Loss (PML)
• Expected Annual Loss
• Spread of Risk
• Historical Experience
• Expenses Premiums, Claims, Tax
• Competition
• Solvency
• Profitability
• Uncertainty - Loss Occurrence
  Magnitude
• Portfolio Data
• Risk Tolerance

4
Traditional Approach
Insurance in General Actuarial Analysis Based on
Projection of Past Losses
Problem of Catastrophic Losses Sparse Past
Losses Made Actuarial Analysis Unreliable
Consequence for Pricing of Catastrophe
Risk Avoided by Insurers through Transfer to
Reinsurers Based on Intuition Empirical
Heuristic Approaches
5
Modern Approach
Use Information Technology
6
GIS Earthquake Loss Model
7
Asset / Liability Modelling
8
NZ Earthquake Commissions Minerva
Minerva
Minerva
External Databases Systems
Quotable Value Database
EQC Building Costs Database
Portfolio Model
Minerva Database
Financial Management Sub-system
Aon Soils Database
Earthquake Loss Sub-system
ISC Earthquake Database
CIMS
User Interface
9
Characteristics
Complex Expert Systems Expensive to
Develop Cheap Relative to Potential Catastrophe
Losses
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Theory
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Theory of Risk Pricing
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Principal Flow of Money Primary Reinsurance
Company
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Optimisation of Premium and Capital Requirements
For Specified Rate of Return
For Specified Probability of Insolvency
Average Loss Ratio
Maximum Average Loss Ratio
Optimum Initial Capital
Initial Capital
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Example
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Application to Reinsurance Pricing
Assumed Characteristics of Reinsurance Company

• Uniform exposure to total reinsurance risk
• Target annual rate of return on capital
  15
• Maximum risk of insolvency 4 in next 10
  years
• Expected annual growth in exposure 4
• Average return on invested funds 5
• Expenses including tax 30 of premium
  income

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Process

• Establish Risk Characteristics
• - EP Curve Annual Aggregate Losses
• - Will base on Swiss Re Sigma data
• Model Financial Performance over Time
• - DFA model
• - Will model over 10 years
• Determine Optimum Values
• - Average loss ratio
• - Initial capital

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10 Worst Disaster Insurance Losses 1970 - 2002
Hurricane Andrew
911 Terrorist Attack
Northridge Earthquake
Typhoon Mirelle
Winterstorm Daria
Winterstorm Lothar
Hurricane Hugo
European Storms Floods
Winterstorm Vivian
Typhoon Bart
0
5
10
15
20
Insured Loss (2002 USD Billion)
From Sigma No 2/ 2003, Swiss Re
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Probability Plot - 34 Worst Natural Disaster
Insurance Losses 1988 2002 (2002 Values in USD)
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• Optimum for Industry
• Average Loss Ratio 0.5
• ie Premium Ratio 2 ? 1
• Initial Capital USD 30 Billion
• ie 2.5 x Average Annual Loss

Average Annual Loss (USD 12 Billion)
? (USD 12 Billion)
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Layer Pricing World Catastrophe Event Loss Level
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Layer Capital World Catastrophe Event Loss Level
14
12
10
8
Initial Capital / Average Annual Loss
6
4
2
0
0
5
10
15
20
25
30
35
40
45
50
Midpoint of Event Loss Range (USD Billion)
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Australia
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Australian Catastrophe Insurance Event Loss Risk
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• Optimum for Industry
• Average Loss Ratio 0.57
• ie Premium Ratio 1.75 ? 1.2
• Initial Capital USD 14 Billion
• ie 1.5 x Average Annual Loss

Average Annual Loss (USD 9.6 Billion)
? (USD 6.3 Billion)
27

• Optimum for Industry
• Average Loss Ratio 0.5
• ie Premium Ratio 2 ? 1
• Initial Capital USD 30 Billion
• ie 2.5 x Average Annual Loss

Average Annual Loss (USD 12 Billion)
? (USD 12 Billion)
28

• Optimum for Industry
• Average Loss Ratio 0.57
• ie Premium Ratio 1.75 ? 1.2
• Initial Capital USD 14 Billion
• ie 1.5 x Average Annual Loss

Average Annual Loss (USD 9.6 Billion)
? (USD 6.3 Billion)
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Average Annual Loss (AUD 0.45 Billion)
? (AUD 1.7 Billion)
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Australian Reinsurance Premium
Required Premium from Australia 0.03 x
9.6 / 0.57 USD 0.5 Billion AUD 0.75
Billion AUD 0.45 0.30 Billion ?
1.2 ?
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Comparison of Actual Estimated Australian
Reinsurance Prices
Estimated RoL Average ALEL 0.2 x Standard
Deviation of ALEL ALEL Annual Layer Event
Loss
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Premium Rating
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EP Curves for Different Building Types
All
C
B
Insured Loss ()
A
E
D
Return Period
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Analysis Of Building Type Risk
If Total Insured Value Iv Annual
Average Loss AAL
Building Type Risk Contribution Insured
Value A 0.15 x AAL 0.2 x Iv B 0.20
0.2 C 0.50 0.2 D 0.05
0.2 E 0.10 0.2
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Different Variables EP Curves
All
I
II
III
IV
V
Soil Type
All
All
1
a
2
b
3
c
4
d
5
e
Location
Policy Conditions
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Risk Factor Analysis
Building Type A B C D E Risk
Contribution 0.15 0.2 0.5 0.05 0.1 Proportion
of Insured Value 0.2 0.3 0.2 0.1 0.1 Location
1 2 3 4 5 Risk Contribution 0.3 0.4 0.05
0.1 0.15 Proportion of Insured
Value 0.5 0.2 0.1 0.15 0.05 Soil Type I
II III IV V Risk Contribution 0.02 0.08 0.2 0
.5 0.2 Proportion of Insured Value 0.1 0.25 0.4 0
.2 0.05 Policy Conditions a b c d e Risk
Contribution 0.3 0.25 0.2 0.2 0.05 Proportion
of Insured Value 0.05 0.15 0.25 0.4 0.15
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Premium Rate Analysis
Assume Average Total Annual Loss 600
million Total Insured Value 120
billion
Require Premium Rate for following combination
Building Type A Location 3 Soil
Type IV Policy Conditions d
Pure Risk Premium Rate 0.15 x 0.05 x 0.5
x 0.2 x 600/(0.2 x 0.1 x 0.2 x 0.4 x 120,000)
for A/3/IV/d 0.16
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Conclusion
Technology has provided the tools to take much of
the uncertainty out of catastrophe risk pricing
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Thank You