some new insights into large commercial risks · 2017. 10. 20. · imperial college london business...
TRANSCRIPT
Imperial CollegeLondonBusiness School
Some New Insights into Large Commercial Risks
Enrico Biffis
Imperial College London
CAS Seminar on Reinsurance
New York CityMay 22, 2014
Overview Dataset Estimation Benchmarking Next Steps 1 / 38
Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 2 / 38
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)
Overview Dataset Estimation Benchmarking Next Steps 4 / 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)
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
Overview Dataset Estimation Benchmarking Next Steps 5 / 38
Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 6 / 38
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)
Overview Dataset Estimation Benchmarking Next Steps 7 / 38
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)
Overview Dataset Estimation Benchmarking Next Steps 7 / 38
Imperial CollegeLondonBusiness School
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)
Overview Dataset Estimation Benchmarking Next Steps 8 / 38
Imperial CollegeLondonBusiness School
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).
Overview Dataset Estimation Benchmarking Next Steps 9 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY SPLIT BY CLAIM SIZE
Overview Dataset Estimation Benchmarking Next Steps 10 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY SPLIT BY TIV
Overview Dataset Estimation Benchmarking Next Steps 11 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY SPLIT BY LOCATION
North America Rest of the WorldFGU claims > USD 1m
Overview Dataset Estimation Benchmarking Next Steps 12 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY SPLIT BY LOCATION
North America Rest of the WorldFGU claims > USD 5m
Overview Dataset Estimation Benchmarking Next Steps 13 / 38
Imperial CollegeLondonBusiness School
VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
All FGU claims
Overview Dataset Estimation Benchmarking Next Steps 14 / 38
Imperial CollegeLondonBusiness School
VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
FGU claims > USD 1m
Overview Dataset Estimation Benchmarking Next Steps 15 / 38
Imperial CollegeLondonBusiness School
VALIDATION
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
FGU claims > USD 5m
Overview Dataset Estimation Benchmarking Next Steps 16 / 38
Imperial CollegeLondonBusiness School
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.
Overview Dataset Estimation Benchmarking Next Steps 17 / 38
Imperial CollegeLondonBusiness School
VALIDATION - Cross-country comparison
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
Source: ISO Verisk.
Overview Dataset Estimation Benchmarking Next Steps 18 / 38
Imperial CollegeLondonBusiness School
VALIDATION - NoA
Imperial-IICI data vs. Property Size-of-Loss Database (PSOLD) [JohnBuchanan (ISO-Verisk)]
Source: ISO Verisk.
Overview Dataset Estimation Benchmarking Next Steps 19 / 38
Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 20 / 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
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
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
Overview Dataset Estimation Benchmarking Next Steps 21 / 38
Imperial CollegeLondonBusiness School
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.
Overview Dataset Estimation Benchmarking Next Steps 22 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 1 (ALL TIVs)
Overview Dataset Estimation Benchmarking Next Steps 23 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 1 (ALL TIVs)
Overview Dataset Estimation Benchmarking Next Steps 24 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 3 - Large Hotels
Overview Dataset Estimation Benchmarking Next Steps 25 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 3 - Institutional Housing, Condos, Housing
Associations
Overview Dataset Estimation Benchmarking Next Steps 26 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 2 - Chemicals, Metals, Mines
Overview Dataset Estimation Benchmarking Next Steps 27 / 38
Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 28 / 38
Imperial CollegeLondonBusiness School
BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
Overview Dataset Estimation Benchmarking Next Steps 29 / 38
Imperial CollegeLondonBusiness School
BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
Overview Dataset Estimation Benchmarking Next Steps 30 / 38
Imperial CollegeLondonBusiness School
BENCHMARKING EXERCISE - A SPECIFIC TIV BAND
Overview Dataset Estimation Benchmarking Next Steps 31 / 38
Imperial CollegeLondonBusiness School
LOSS CURVES HETEROGENEITY
Source: John Buchanan (ISO-Verisk).
Overview Dataset Estimation Benchmarking Next Steps 32 / 38
Imperial CollegeLondonBusiness School
AGENDA
1 Overview
2 Dataset
3 Estimation
4 Benchmarking
5 Next Steps
Overview Dataset Estimation Benchmarking Next Steps 33 / 38
Imperial CollegeLondonBusiness School
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!
Overview Dataset Estimation Benchmarking Next Steps 34 / 38
Imperial CollegeLondonBusiness School
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!
Overview Dataset Estimation Benchmarking Next Steps 34 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 1 ‘CO’, α−1: AN INSURER
Overview Dataset Estimation Benchmarking Next Steps 35 / 38
Imperial CollegeLondonBusiness School
OCCUPANCY LEVEL 1 ‘CO’, α−1: MULTIPLE DATA SOURCES
Overview Dataset Estimation Benchmarking Next Steps 36 / 38
Imperial CollegeLondonBusiness School
WORK IN PROGRESS (ASIA-PACIFIC REGION) & NEXT STEPS
Insurance Risk & Finance Research Centreat Nanyang Business School Singapore
www.irfrc.com
Overview Dataset Estimation Benchmarking Next Steps 37 / 38
Imperial CollegeLondonBusiness School
THANK YOU
Contact: [email protected]
Overview Dataset Estimation Benchmarking Next Steps 38 / 38