Pricing Catastrophe Risk: Pricing Catastrophe Risk George R Walker Senior Risk Analyst Aon Re Australia 2003 Aon Re Australia Hazards Conference, Gold Coast, 18-19 August


Factors Affecting Catastrophe Risk Price: 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


Traditional Approach: 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


Modern Approach: Modern Approach Use Information Technology


GIS Earthquake Loss Model: GIS Earthquake Loss Model


Asset / Liability Modelling: Asset / Liability Modelling


Slide8: Minerva Earthquake Loss Sub-system Financial Management Sub-system EQC Building Costs Database External Databases & Systems Quotable Value Database Minerva Database User Interface CIMS Aon Soils Database Portfolio Model Minerva ISC Earthquake Database NZ Earthquake Commission’s Minerva


Characteristics: Characteristics Complex Expert Systems Expensive to Develop Cheap Relative to Potential Catastrophe Losses


Slide11: Theory of Risk Pricing


Slide12: Principal Flow of Money – Primary Reinsurance Company


Slide13: Average Loss Ratio Initial Capital For Specified Rate of Return For Specified Probability of Insolvency Maximum Average Loss Ratio Optimisation of Premium and Capital Requirements Optimum Initial Capital


Application to Reinsurance Pricing: 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


Process: 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


10 Worst Disaster Insurance Losses 1970 - 2002: 10 Worst Disaster Insurance Losses 1970 - 2002 Typhoon Bart Winterstorm Vivian European Storms & Floods Hurricane Hugo Winterstorm Lothar Winterstorm Daria Typhoon Mirelle Northridge Earthquake 911 Terrorist Attack Hurricane Andrew 0 5 10 15 20 Insured Loss (2002 USD Billion) From Sigma No 2/ 2003, Swiss Re


Slide18: Probability Plot - 34 Worst Natural Disaster Insurance Losses 1988 – 2002 (2002 Values in USD)


Slide21: Average Annual Loss (USD 12 Billion)  (USD 12 Billion) 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


Slide22: Layer Pricing – World Catastrophe Event Loss Level


Layer Capital – World Catastrophe Event Loss Level: Layer Capital – World Catastrophe Event Loss Level 0 2 4 6 8 10 12 14 0 5 10 15 20 25 30 35 40 45 50 Midpoint of Event Loss Range (USD Billion) Initial Capital / Average Annual Loss


Slide25: Australian Catastrophe Insurance Event Loss Risk


Slide26: Average Annual Loss (USD 9.6 Billion)  (USD 6.3 Billion) 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


Slide27: Average Annual Loss (USD 12 Billion)  (USD 12 Billion) 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


Slide28: Average Annual Loss (USD 9.6 Billion)  (USD 6.3 Billion) 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


Slide29: Average Annual Loss (AUD 0.45 Billion)  (AUD 1.7 Billion)


Australian Reinsurance Premium: 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 


Slide31: Estimated RoL = Average ALEL + 0.2 x Standard Deviation of ALEL ALEL = Annual Layer Event Loss Comparison of Actual & Estimated Australian Reinsurance Prices


EP Curves for Different Building Types: EP Curves for Different Building Types All D E A B Insured Loss ($) Return Period C


Analysis Of Building Type Risk: 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


Slide35: All 1 5 4 3 2 Location All I V IV III II Soil Type All a e d c b Policy Conditions Different Variables – EP Curves


Risk Factor Analysis: 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


Premium Rate Analysis: Premium Rate Analysis 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% 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


Conclusion: Conclusion Technology has provided the tools to take much of the uncertainty out of catastrophe risk pricing