London Market Pricing Framework

London Market Pricing Framework Hannes van Rensburg, Watson Wyatt Ryan Warren, Watson Wyatt GIRO 2009 - Edinburgh 8 October 2009 1

London Market Pricing Framework What we will cover Pricing framework Overview of pricing methods and where they fit in Interaction between main three functions involved: Underwriting Pricing or Analytics Central or Capital modelling team Title refers to London Market, but similar embedded process for other insurers.

Setting the scene Need for underwriting profit Financial climate means less investment income Recapitalisation expensive or not easily available Recent insurance results distorted by prior year releases

Setting the scene Need for underwriting profit Soft market conditions Need to know cost of risk to compete profitably Identify profitable segments Walk away

Setting the scene Need for underwriting profit Soft market conditions Lloyd s franchise directive Report benchmark rate on per risk basis Regulatory compliance vs value added

Setting the scene Need for underwriting profit Soft market conditions Lloyd s franchise directive Winners curse Imperfect information leads to loss making business London market exposed due to high level of competition and less than perfect information Party with the better information will outperform

Setting the scene Need for underwriting profit Soft market conditions Lloyd s franchise directive Winners curse Embedding capital and pricing Systematic risk vs. Diversifiable risk Capital allocation reflect risk profile and risk appetite set at company level

Setting the scene Need for underwriting profit Soft market conditions Lloyd s franchise directive Winners curse Embedding capital and pricing Solvency II requirements Actuarial opinion on underwriting function and reinsurance

The Rating Process Technical Premium Current premium Market conditions Benchmark Price Commercial premium Business Strategy

The Rating Process Pricing/Analytics Portfolio Analysis Market Data Analysis Capital/Central Modelling Underwriting Experience rating Large loss loadings Systematic Risk models Exposure base rates Product Design Risk Premium Other loadings Reinsurance Cost of capital Qualitative Factors Claims environment Technical Premium

The Rating Process Underwriting Pricing/Analytics Portfolio Analysis Market Data Analysis Experience rating Large loss loadings Analysis of portfolio/market data Predictive modelling Insurance scenario modelling (ISG) Segmentation Assisting underwriting Formalise exposure rates Derivation of ILFs Developing rating tools Experience rating Burning Cost analysis Frequency and severity fitting Simulating stochastic features Credibility models Adjust cost of capital per risk Risk measure Volatility, Expected Shareholder deficit

Portfolio Analysis Underwriting Pricing/Analytics Portfolio Analysis Market Data Analysis Experience rating Large loss loadings Predictive modelling Increasingly used in the London market Major limitations to date: Current data systems not set up to capture Heterogeneity Systems and awareness increasing Some of the classes where it is currently used: Marine Employers Liability Energy Motor Fleet Professional Indemnity Aviation Public Liability Yacht D&O

Predictive modelling- example With a reasonable amount of credible portfolio or market data: Derivation of base rates and rating differentials Probability models used to model attrition and large separately Simulate large loss and deductible discount curves by rating groups Predict profitability for change in business mix Monitor A v E (lift curves) for claims and portfolio mix

Marine Liability Example Objective Age Flag Vessel Tonnage Model Expected cost of claims Excess NCD

Marine Liability Example Modelling the cost of claims Car Freq x Amt = Cost 1 Col Freq x Amt = Cost 2 Pax Freq x Amt = Cost 3 Pol Freq x Amt = Cost 4 Oth Freq x Amt = Cost 5

Marine Examples Marine Cargo numbers model Marine Cargo numbers model 0.2 14% 12000 0 1% -7% -10% -11% -12% -14% -13% -4% 0% -7% -14% 10000-0.2-22% Log of multiplier -0.4-0.6-0.8-31% -44% 8000 6000 4000 Exposure (years) -1-1.2-72% 2000-1.4 0 to 1 1 to 3 3 to 5 5 to 7 7 to 9 9 to 11 11 to 13 13 to 15 15 to 18 18 to 21 21 to 23 23 to 25 25 to 28 28 to 33 33 to 43 Above 43 Vessel age 0 Oneway relativities Approx 95% confidence interval Unsmoothed estimate Smoothed estimate P value = 0.0% Rank 4/8

Marine Examples Marine Cargo numbers model ABC Marine P&I clubs Cargo Cargo numbers model Log of multiplier 0.6 0.4 0.2 0-0.2-0.4 5% -10% -16% 28% 25% 10% -19% 0% -12% 7% 6% 20% 41% 28% 18000 16000 14000 12000 10000 8000 6000 Exposure (years) -0.6-51% 4000-0.8 2000-1 0 Japan Sweden Greece England Norway Cuba Denmark Flag state Germany Others China Liberia Panama Cyprus Bahamas Korea Approx 95% confidence interval Unsmoothed estimate Smoothed estimate P value = 0.0% Rank 3/4

Marine Liability Case Study Dealing with large claims Freq x Prob x Amt Freq x Amt

More Marine Examples Marine Probability of large Marinecargo model Example P&I Club Probability of large cargo model Cargo large proportion 0.6 Log of multiplier of p/(1-p) 0.3 0-0.3-0.6-0.9-1.2 3% 3% 3% 3% 5% 6% 6% 8% 8% 7% 6000 5000 4000 3000 2000 Exposure (years) -1.5 1000-1.8 <= 129 > 129 <= 349 > 349 <= 848 > 848 <= 1598 > 1598 <= 2592 > 2592 <= 4093 Gross tonnage > 4093 <= 6579 > 6579 <= 12800 > 12800 <= 24731 > 24731 0 Approx 95% confidence interval Unsmoothed estimate Smoothed estimate P value = 0.0% Rank 1/4

Predictive power of models Predictive power analysis Actual versus expected claim frequency (all claim types) on 2007 and 2008 year data 1000 8 900 7 800 6 700 Exposure 600 500 400 5 4 3 Claim frequency 300 200 2 100 1 0 0.000-0.060 0.120-0.180 0.240-0.300 0.360-0.420 0.480-0.540 0.600-0.660 0.720-0.780 0.840-0.900 0.960-1.020 1.080-1.140 1.200-1.260 1.320-1.380 1.440-1.500 1.560-1.620 1.680-1.740 Expected claims frequency (ultimate) 1.800-1.860 1.920-1.980 2.040-2.100 2.160-2.220 2.280-2.340 2.400-2.460 2.520-2.580 2.640-2.700 2.760-2.820 2.880-2.940 >=3.000 0 Total Actual claim frequency (to date) Expected claim frequency (ultimate) 20

Predictive power of models Predictive power analysis Actual versus expected burning cost (all claim types) on 2007 and 2008 year data 800 100000 700 90000 80000 600 70000 Exposure 500 400 300 60000 50000 40000 Burning cost 30000 200 20000 100 10000 0 0-1000 2000-3000 4000-5000 6000-7000 8000-9000 10000-11000 12000-13000 14000-15000 16000-17000 18000-19000 20000-21000 22000-23000 24000-25000 26000-27000 28000-29000 Expected burning cost (ultimate) 30000-31000 32000-33000 34000-35000 36000-37000 38000-39000 40000-41000 42000-43000 44000-45000 46000-47000 48000-49000 >=50000 0 Exposure Actual burning cost (to date) Expected burning cost (ultimate) 21

To simulate large loss curve from GLM Fit average cost per large claim distribution using traditional approach Select portfolio / subset for which total large claims cost distribution is to be generated for each policy record, determine expected number of claims and expected large claim probability from earlier fitted GLM For each policy record, simulate the number of claims For to each simulated claim, simulate a random number If the random number is less than or equal to probability of a large claim then simulate a large claim severity from a fitted distribution, otherwise use GLM severity for policy rating levels. Apply deductibles / coverage structure Cumulate large costs over the simulated claims over all policy records in each rating group Run sufficient simulations to obtain average cost for specified deductible Repeat for different deductibles to generate a loss curve

Portfolio analysis with less data Set framework in place for capturing exposure and claims data Supplement with market data Capture underwriting judgement as constraints in model and monitor emerging experience with subjective rates Start with simple one-way analysis and increase complexity Clustering of risks to more homogeneous rating groups

Experience rating Underwriting Pricing/Analytics Portfolio Analysis Market Data Analysis Experience rating Large loss loadings Individual account pricing needs sufficient historic exposure and claims data EL, PL, Motor, Marine, PI, Cash-in- Transit and the list goes on Limited information - can still use techniques, but use credibility approach to adjust portfolio rates: Burning cost or Frequency/Severity Capped burning cost Loss loading or discount scale

Experience rating Underwriting Pricing/Analytics Portfolio Analysis Market Data Analysis Experience rating Large loss loadings If you cap or exclude unusual experience, such as large claim, need to make a normal allowance: Portfolio analysis Catastrophe models ISG output/contingency models Select a claims rate to apply to expected future exposure Blend with view of other premiums Credibility approach to blend with portfolio view of premium based on: Number of years data, number of claims, incurred amounts Volatility of annual rates for risk compared to risks in overall portfolio

Experience rating Burning cost example UY Exposure Incurred Inflated Developed Capped Rate 2000 100 523 663 663 663 6.63 2001 103 514 632 632 632 6.14 2002 106 1212 1447 1447 847 7.99 2003 109 611 708 722 722 6.61 2004 113 450 506 532 532 4.73 2005 116 655 716 787 687 5.93 2006 119 525 557 668 668 5.60 2007 123 400 412 577 577 4.69 2008 125 755 6.04 Large loss allowance 88 0.70 Systematic Risk/Portfolio loadings 25 0.20 Projected Claims Cost for 2008 867 6.94 Portfolio (GLM) risk premium 813 6.50 Credibility Premium Factor (Z) 853 74%

Experience rating Frequency Severity modelling Inflate and trend historic claims and exposure to consistent basis Allow for future movement in case estimates (IBNER) and new reported (IBNR) claims separately [Workshop] Fit statistical distributions to the frequency and severity of claims London market policy features can be modelled by simulation Multiline or multiyear programmes Captive involvement with stop loss features Non proportional reinsurance and deductibles Aggregate limits and deductibles Bespoke features such as round-the-clock, multi-trigger Use simulations to adjust capital allocation to each component Volatility of each layer Var, TVar or ESD

Underwriting Underwriting process not only about price Product design and wording Risk assessment can be more valuable than pricing Claims environment adjustments Balanced Portfolio Underwriting Exposure base rates Product Design Qualitative Factors Claims environment Underwriting/pricing models Expert opinion based on experience Base rates for standard level of cover ILF curves to price higher layers Gross rates allowing for cost of risk, expenses, profit, reinsurance etc. Commonly used underwriting methods Return period (rate on line) Exposure curves set by loss elimination ratios Market loss Market share approaches

Underwriting Actuaries can add value even for portfolios with minimal data: Quantifying and formalising this judgement Break assumptions into different components Validating assumptions against claims experience and market losses Ensure risk premium change with policy design, portfolio mix and market trends Design data capture tools Feed Benchmark rate Underwriting Exposure base rates Product Design Qualitative Factors Claims environment

Capital/Central modelling Embed Capital modelling and pricing Assumptions consistent within pricing: expense allocations consistent with volumes Systematic Risk models Investment income consistent with expected returns Reinsurance cost and benefit allocated per policy Insurance Scenario Generators Catastrophes Economic claim influences Financial strength Latent claim models Global or market trend models Diversification of multi-line business Capital allocation and return on capital Reflect risk appetite and profit requirements Other loadings Capital/Central Modelling Reinsurance Use capital model simulation to allocate capital to line of business Pricing team can adjust these to reflect individual risks compared to portfolio Cost of capital

Integrated process Interaction between three functions: Underwriting Ensure portfolio is balanced Underlying risk changes Pricing or Analytics Base rates and large loss factors Experience rating and credibility Central or Capital modelling team Systematic risk models (ISG) Large portfolio losses and reinsurance All three parties play significant role and can bring valuable information to the table. build on strengths of each other

Conclusion Stating the obvious Imperfect information always a challenge, but can mitigate by having better information than peers Will never have data unless it is captured: It will take 3-5 years to capture sufficient data It will also in 3-5 years time! Value in modelling found in thought process and formalising the problem, not only in number crunching

Questions? ryan.warren@watsonwyatt.com hannes.van.rensburg@watsonwyatt.com