Imperial CollegeLondonBusiness School
Some New Insights into Large Commercial Risks
Enrico Biffis
Imperial College London
CAS Seminar on Reinsurance
New York CityMay 22, 2014
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Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
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Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 3 / 38
Imperial CollegeLondonBusiness School
OVERVIEW
A new data source: Imperial-IICI dataset
Insurance Intellectual Capital Initiative (IICI)
Bronek Masojada (Hiscox), James Slaughter (Liberty Mutual), RobCaton (Hiscox)Lloyd’s of London
Focus on Large Commercial Risks (LCR)
Commercial Property, On-shore Energy; non-natural hazards
Implications for reserving and capital modeling (joint work with DavideBenedetti, Erik Chavez [Imperial]; with Andreas Milidonis [Nanyang] forAsia-Pacific region)
Tail risk estimation
Benchmarking exercise (market loss curves & scaling factors)
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Imperial CollegeLondonBusiness School
OVERVIEW
A new data source: Imperial-IICI dataset
Insurance Intellectual Capital Initiative (IICI)
Bronek Masojada (Hiscox), James Slaughter (Liberty Mutual), RobCaton (Hiscox)Lloyd’s of London
Focus on Large Commercial Risks (LCR)
Commercial Property, On-shore Energy; non-natural hazards
Implications for reserving and capital modeling (joint work with DavideBenedetti, Erik Chavez [Imperial]; with Andreas Milidonis [Nanyang] forAsia-Pacific region)
Tail risk estimation
Benchmarking exercise (market loss curves & scaling factors)
Overview Dataset Estimation Benchmarking Next Steps 4 / 38
Imperial CollegeLondonBusiness School
LCR
LCR largely non-modelled risks
Heterogeneity of exposures by type and size
Complex relation between hazard events and losses
Paucity of data for model estimation/validation
Implications
Considerable degree of judgment in pricing/reserving decisions
Reported claims may not reflect true risk of business
Pricing variability makes it difficult for corporates to budget for insurance
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AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
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DATASET
Around 3,200 FGU claims and exposures based on brokers’ submissions
Scope: worldwide, 1999-2012
Granular classification of exposures by three occupancy levels
Definitions based on Lloyd’s codes & individual syndicates’classification; can be related to ISO/PSOLD classification
Anonymized claim narratives available
Example:
Region Country Risk Code Occupancy 1 Occupancy 2 Occupancy 3NoA US P2 RE R 51
(Physical damage for (residential) (residential) (Large Hotels)primary layer property;
USA; excluding binders)
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Imperial CollegeLondonBusiness School
DATASET
Around 3,200 FGU claims and exposures based on brokers’ submissions
Scope: worldwide, 1999-2012
Granular classification of exposures by three occupancy levels
Definitions based on Lloyd’s codes & individual syndicates’classification; can be related to ISO/PSOLD classification
Anonymized claim narratives available
Example:
Region Country Risk Code Occupancy 1 Occupancy 2 Occupancy 3NoA US P2 RE R 51
(Physical damage for (residential) (residential) (Large Hotels)primary layer property;
USA; excluding binders)
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OCCUPANCY EXAMPLE - LEVEL 2 LIST
Code Definition Code DefinitionA Miscellaneous Q Offices/BanksB Manufacturers/Processors R ResidentialC Chemicals/Pharmaceuticals T TransportD Bridges/Dams/Tunnels/Piers U UtilitiesE Conglomerates V Telecoms and Data ProcessingF Food W Woodworkers (Sawmills, Papermills)G Grain X Onshore CrudeH General Mercantile/Shops Y Onshore GasPlantsJ Mines Z Onshore ConstructionK Crops 2 Hospital/Health care centresL Auto 4 Semiconductor/FabsM Metals 5 Motor ManufaturersO Municipal Property 6 WarehousesP Energy (Oil Refineries/Petrochemicals)
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GEOGRAPHICAL/OCCUPANCY SPLIT
AF (Africa), CA (Central Asia), EU (Europe),
LA (Latin America), ME (Middle East), AS
(Asia-Pacific), NoA (North America), OC
(Oceania), WW (Worldwide).
RE (Residential), CO (Commercial), MA
(Manufacturing), EON (Energy on-shore), Mi
(Miscellaneous).
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OCCUPANCY SPLIT BY CLAIM SIZE
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OCCUPANCY SPLIT BY TIV
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OCCUPANCY SPLIT BY LOCATION
North America Rest of the WorldFGU claims > USD 1m
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OCCUPANCY SPLIT BY LOCATION
North America Rest of the WorldFGU claims > USD 5m
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VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
All FGU claims
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VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
FGU claims > USD 1m
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VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
FGU claims > USD 5m
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VALIDATION - Cross-occupancy comparison
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
Source: National Fire Protection Association as compiled by ISO Verisk.
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VALIDATION - Cross-country comparison
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
Source: ISO Verisk.
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VALIDATION - NoA
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
Source: ISO Verisk.
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AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
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TAIL RISK
Tail index (α) estimation: P(Z > z) ∼ Cz−α
Existence of centered moments (mean, variance, etc.)
• Mean/Variance finite if and only if α > 1 (α > 2)
Extent of diversification benefits for quantile-based risk measures
Retain fractions w1, . . . , wn of risks X1, . . . , Xn
Resulting aggregate risk Z(w1,...,wn) =∑i wiXi
• V aRp(Z(1,0,...,0)) < V aRp(Z( 1n ,...,
1n )) for α ∈ (0, 1), p ∈ (0, 1/2), for
stable distributions (e.g., Ibragimov, 2009)
What do we find for LCR?
Heavy tails & significant heterogeneity across occupancy type
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Imperial CollegeLondonBusiness School
TAIL RISK
Tail index (α) estimation: P(Z > z) ∼ Cz−α
Existence of centered moments (mean, variance, etc.)
• Mean/Variance finite if and only if α > 1 (α > 2)
Extent of diversification benefits for quantile-based risk measures
Retain fractions w1, . . . , wn of risks X1, . . . , Xn
Resulting aggregate risk Z(w1,...,wn) =∑i wiXi
• V aRp(Z(1,0,...,0)) < V aRp(Z( 1n ,...,
1n )) for α ∈ (0, 1), p ∈ (0, 1/2), for
stable distributions (e.g., Ibragimov, 2009)
What do we find for LCR?
Heavy tails & significant heterogeneity across occupancy type
Overview Dataset Estimation Benchmarking Next Steps 21 / 38
Imperial CollegeLondonBusiness School
TAIL RISK
Tail index (α) estimation: P(Z > z) ∼ Cz−α
Existence of centered moments (mean, variance, etc.)
• Mean/Variance finite if and only if α > 1 (α > 2)
Extent of diversification benefits for quantile-based risk measures
Retain fractions w1, . . . , wn of risks X1, . . . , Xn
Resulting aggregate risk Z(w1,...,wn) =∑i wiXi
• V aRp(Z(1,0,...,0)) < V aRp(Z( 1n ,...,
1n )) for α ∈ (0, 1), p ∈ (0, 1/2), for
stable distributions (e.g., Ibragimov, 2009)
What do we find for LCR?
Heavy tails & significant heterogeneity across occupancy type
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RESIDENTIAL EXAMPLE (ALL TIVs)
Hill (1975) vs. Gabaix-Ibragimov (2011)’s log-log rank-size regression method with optimal
ranks shift -1/2 and correct standard errors.
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OCCUPANCY LEVEL 1 (ALL TIVs)
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OCCUPANCY LEVEL 1 (ALL TIVs)
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OCCUPANCY LEVEL 3 - Large Hotels
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OCCUPANCY LEVEL 3 - Institutional Housing, Condos, Housing
Associations
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OCCUPANCY LEVEL 2 - Chemicals, Metals, Mines
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AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
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BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
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BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
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BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
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LOSS CURVES HETEROGENEITY
Source: John Buchanan (ISO-Verisk).
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AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
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NEXT STEPS
New data source for LCR
Robust estimation of tail risk
Comparing claim costs across occupancy/TIV bands/location
Lessons from Imperial-IICI data collection, validation, and analysis
Link between claims and exposures crucial: Systematic storage of claims &exposures information (policy schedules & claims narratives in digital,compatible format) should be a priority
Macro-validation (e.g., Fire Protection Agencies) & micro-validation (e.g.,syndicate level) of data important for structural understanding of risk
Gains from data aggregation HUGE - please contribute!
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NEXT STEPS
New data source for LCR
Robust estimation of tail risk
Comparing claim costs across occupancy/TIV bands/location
Lessons from Imperial-IICI data collection, validation, and analysis
Link between claims and exposures crucial: Systematic storage of claims &exposures information (policy schedules & claims narratives in digital,compatible format) should be a priority
Macro-validation (e.g., Fire Protection Agencies) & micro-validation (e.g.,syndicate level) of data important for structural understanding of risk
Gains from data aggregation HUGE - please contribute!
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OCCUPANCY LEVEL 1 ‘CO’, α−1: AN INSURER
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OCCUPANCY LEVEL 1 ‘CO’, α−1: MULTIPLE DATA SOURCES
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WORK IN PROGRESS (ASIA-PACIFIC REGION) & NEXT STEPS
Insurance Risk & Finance Research Centreat Nanyang Business School Singapore
www.irfrc.com
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THANK YOU
Contact: [email protected]
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