SAM NLUR Working Group
Industry workshopQIS 2 to QIS 3
Johannesburg Country Club 13 June 2013
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Introduction
NLUR Workbook
Premium risk calibration
Reserve risk calibration
Natural catastrophe risk calibration
Man-made catastrophe risk calibrationo Hannes van Rensburgo Lisa Pines
(QIS 2 feedback on issues throughout)
Further issueso Premium definitiono Cash-back bonuseso Variable commission structureso Segmentation
Agenda
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Pillar 1 sub-committee request
Purposeo NLUR WG Update on changes to underwriting risk calculationo Facilitate STI industry discussion on underwriting risk issues o Strict time keepingo Methodology rather than numbers
NLUR WGo 31 memberso 14 qualified actuarieso 19 organisationso Many hourso Various sub-working groups:
FSB calibration team Workbook Premium risk Reserve risk Natural catastrophe risk Man-made catastrophe risk
Introduction
FSB Primary Insurers RI'ers & RI Brokers ConsultantsABSA Hannover Re DeloitteCGIC Guy Carpenter E&YHollard Willis KPMGM&F AON PWCNatsure DynamicModelOffi ceStandard Bank IACZurich GrailAfrica
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Separate NLUR workbooko Feedback from QIS 1o Completeness of reporting to FSBo Standard formula vs internal model
Issues from QIS 2 feedbacko Risk mitigation
o Complexo Not enough flexibilityo Allow calculations outside workbooko Etc
o Errorso Limited number of counterpartieso Lack of guidance
NLUR WorkbookQIS 2
5
Identified errors fixed
Reinsurance structureso Allowing more counterpartieso Multiple NLUR workbooks to allow for different portfolios covered by
different structureso Allow for features such as aggregate limits, deductibleso Guidance on NP adjustmento Allowance on man-made and nat cats for XL then prop then XL then prop
NLUR WorkbookProposed changes
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Guidanceo Guidance manualo Case studies with accompanied workbook exampleso NP adjustmento Two workbooks – one not protected; button to transfer to protected with
error outputo Unprotected version circulated beforehando Scaling of nat cat charge when splitting exposures
Automated summary sheet to aid analysis of results; capital allocation
NLUR WorkbookProposed changes
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How much freedom do we allow in a standard formula?
Data availability
Complexity
Other?
NLUR WorkbookOutstanding issues
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Structure
Volume measures by segment
Proportional RI %’s per counterparty per segment
NP volatility adjustment factor – optional!
Premium risk calibrationQIS 2 recap
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Compulsory data request – end of 2012o By segment (more detailed than QIS 2)o By accident year/underwriting yearo Earned premiumso Paid and reported claims triangleso Gross and net of reinsurance
Data cleaning and quality checko FSB; anonymityo Error correction; follow-up with individual companieso Re-run calibrationso Import key parameters into calibration toolo Exclusion of some outliers (e.g. very low loss ratios)o Graph all loss ratioso Confirm net of cat
Premium risk calibrationData collection
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Premium risk calibrationAnalyses by segment – 4 methods
Method 1 Method 2 Method 3 Method 4 Assumed distribution of Loss ratios and fitting method
Normal (Least squares)
Lognormal (Maximum Likelihood Estimation)
Lognormal (Maximum Likelihood Estimation)
Lognormal (Maximum Likelihood Estimation)
µ Fit LR Mean by undertaking
Fit LR Mean by undertaking
Fit LR mean across all undertakings
Fit LR Mean by undertaking
σ Fit LR sd by undertaking
Fit LR sd across all undertakings
Fit LR sd across all undertakings
Fit LR sd across all undertakings
E(Loss) and Var(loss)
E(Loss) α Prem sd(Loss) α sqrt (Prem)
E(Loss) α Prem sd(Loss) α sqrt (Prem)
E(Loss) α Prem sd(Loss) α sqrt (Prem)
E(Loss) α Prem sd(Loss) α Prem
Overfitting? In general: Fits more parameters – Highest level of overfitting – leads to lower parameters
In general: Fits more parameters – Overfitting – leads to lower parameters
Fits fewer parameters – underfitting – overstates volatility (will always give larger parameters)
In general: Fits more parameters – Overfitting – leads to lower parameters
Allows for diversification credit by volume (Diversification credit exists if larger co’s have lower variability)
Yes (more weight to larger companies)
Yes Yes? No
ELIMINATE IF LR’s are not the same for industry (Graph B)
There is evidence that larger companies have smaller sd’s (Graph C)
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Default method 2 Motor personal lines and Engineering
If negative relationship, eliminate method 4
Premium risk calibrationAnalyses by segment – sigma vs premium – method 2 vs 4
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Default method 2 If graph shows spread, eliminate method 3
Premium risk calibrationAnalyses by segment – histogram of average loss ratios – method 2 vs 3
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Usually only method 2 Indication of appropriateness of lognormal assumption
Usually indicates lognormal is too optimistic in tail Practicality of using different distribution?
Premium risk calibrationAnalyses by segment – pp-plots of selected methods
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M2_Paid
M2_Reported
Theoretical
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M2_Reported
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Premium risk calibrationAnalyses by segment – initial parameters
SA QIS 2 Method 2 - original Method 2 - Industry benchmno of insurers (callibration) Paid Reported
Average pd/rep
Prop PL 26 8.2% 6.2% 5.7% 5.9%Motor PL 23 8.2% 5.7% 5.5% 5.6%Motor CL 23 8.2% 6.4% 6.1% 6.3%Prop CL 21 8.2% 12.6% 14.9% 13.8%Liability CL 19 13.9% 9.3% 14.9% 12.1%M&T 16 14.9% 14.5% 14.5% 14.5%Health 15 4.0% 18.6% 9.6% 14.1%Engineering 13 8.2% 9.4% 14.9% 12.1%Misc Other 13 12.8% 6.9% 7.8% 7.3%Warranty 6 12.8% 15.6% 16.8% 16.2%SuretyComm 5 11.7% 27.8% 27.0% 27.4%Legal expenses 3 6.5% 8.9% 9.4% 9.2%Aviation 2 14.9% 9.9% 11.4% 10.7%Travel 2 12.8% 9.2% 7.7% 8.4%Crop 2 12.8% 102.6% 109.8% 106.2%SuretyRetail 1 11.7% 17.9% 7.3% 12.6%
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Impact of excluding single companies
Paid vs reported
3 methods:o Company specific DFso Industry DFs chain laddero BF proxy
Consistency with reserve risk method
Credibilityo Number of submissions o Number of accident years (data points)o Percentage of industry by premium volumeo Size of segmento Other?o Proposed methods
Premium risk calibrationAnalyses by segment – other considerations
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Structure
Volume measures by segment
Total RI %’s per counterparty per segment – from best estimate technical
provisions calculation
No additional NP volatility adjustment factor
Reserve risk calibrationQIS 2 recap
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Compulsory data request – end of 2012
Data cleaning and quality checko Similar to premium risk calibration
Method typeso Premium risk type methods (3)o Triangulation type methods (3)
Similar considerations to premium risk calibration
Consistency between premium and reserve risk methods
Reserve risk calibrationData collection and analysis
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Natural catastrophe risk calibrationWorking group structure
Non
Life
Und
erw
riting
Ris
k Natural Catastrophe
Catastrophe Task Force
Catastrophe Modellers
Premium Risk
Reserve Risk
Man-made Catastrophe Risk
Workbook
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Natural catastrophe risk calibrationBackground
QIS1
• 2009 J statements adjusted for errors, Sum Insured by CRESTA Zone• Data modelled by cat modellers to get an industry view of the 1 in 200 year loss • Modelled factors were chosen by voting process within group
QIS2
•Exposures from industry template sent out in 2011, Sum Insured by Postal Code•EQ- Data modelled by cat modellers to get an industry view of the 1 in 200 year loss•EQ Motor- factors were based on model output for EQ Residential LOB and consensus view •HL- factors were based on consensus view by cat modellers
QIS3
• To be determined
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Postal codes were grouped in 19 new zones
Exposure data received from industry and modelled
Model output: Simulated losses by LOB and zone for 50 000 events
QIS5 Formula applied
Natural catastrophe risk calibrationQIS 2 calibration
rxc
cZONErZONEcrLOB WTIVWTIVAGGCAT ,,, **
rxc
cLOBrLOBcrEQEQ WTIVWTIVAGGQCAT ,,, **
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Market Factor: Rank total losses and determine the 1 in 200 year loss, disregarding multiple events in the same year
LOB/Zone relativities: Express the share of the 1 in 200 year loss for zone (x) over the exposure for zone (x)o Zone (x)’s share is calculated as the Average Loss for zone (x)/ Average Loss
over all zones over a range (100 observations above and below the 1 in 200 year loss)
Aggregation Matrix: Solve the square root formula between each pair of zones/LOBs
Rescale relativities such that Market Factor * Exposure =
Natural catastrophe risk calibrationQIS 2 calibration
rxc
cLOBrLOBcr WTIVWTIVAGG ,,, **
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Model vs. Standard Formula o FSB sent scaled exposures for each co that submitted QIS2o Recalculate standard formula and compare to the modelled 1 in 200 year
loss per company
1 in 200 year loss per co
Natural catastrophe risk calibrationPost QIS 2 results
Base Scenario Count(-70% , -60%) 1
(-50% , -40%) 2
(-40% , -20%) 0
(-20% , -10%) 3
(-10% , 0%) 14
(0% , 10%) 15
(10% , 20%) 3
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Max (Base Scenario, Alternative Scenario) Count
(<-40%) 1
(-40% , -20%) 0
(-20% , -10%) 4
(-10% , 0%) 15
(0% , 10%) 15
(10% , 20%) 338
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Natural catastrophe risk calibrationPost QIS 2 results
Mkt Data (%) Calibration Data (%)0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Comparison of Mkt & Calibration Data(%)
Residential Buildings Commercial Buildings Contents Engineering Motor
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Natural catastrophe risk calibrationPost QIS 2 results
Residential Buildings Commercial Buildings Contents Engineering Motor
Comparison of Mkt & Calibration Data
Market Data (FSB) Calibration Data incl BI
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Horizontalo Template sent out to collect natural catastrophe claims over last 20-30
years from biggest companies, across all perilso FSB will collate and scale data to reflect industryo WG will analyse data and fit a curve to calibrate the 1 in 10 and 1 in 20 year
events
Verticalo Update exposures and re-run model?o Additional 2 CAT models to run and compare model results too Keep factors unchanged
Natural catastrophe risk calibrationQIS 3
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Premium and reserve risk segmentationo PL/CL split vs combinedo Aviation vs Marine and transport (vs pure transport)o Miscellaneous classeso Test alternatives in QIS3? – data split, FSB tests afterwardso Other segmentation concerns from industry – for discussion document
Volume measure – premium definition? Method 2 – volume measure square root – inconsistent with standard formula Allowance for loss absorbency of:
o Cash-back bonuseso Sliding scale/profit commission arrangements, both reinsurance, UMA’s,
cells, other?o Limited risk transfer
Allowance for additional risk caused by above? Lapse risk Contract boundaries Premium recognition
Premium and reserve riskFurther issues
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Factor based method – not as optional as industry might think it is
Postal code information o multiple risk addresses under one policyo solution: expected that industry addresses this, rather than changing
formula to allow for poor quality?o How should this be addressed? FSB should enforce at broker level?o Working group still to test impact of alternative zoning vs Cresta zones
Natural catastrophe risk calibrationData issues