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Long Term Reinsurance Buying Strategies modelled using a component based DFA Tool Astin July 2001 BENFIELD GREIG Introduction Investigate possible reinsurance strategies over several years. Two Strategies: • Constant Cover, but vary premium spend. • Constant Spend, but vary cover purchased. Use Monte Carlo Simulation to evaluate Risk / Return for an example company. Reinsurance Pricing Factors • Many potential ways to model changes in reinsurance pricing • Various factors including: Loss Experience Changes in exposure Reinsurance Market conditions • The method used here is based on Loss Experience, with exposure and market factors assumed to be constant. Example Company Example model is a property Cat XL programme with the following parameters (USD million): Premium Income 120 Expenses 30 Small Claims 48 Large Cat Loss Freq Poisson distribution with mean 1. • Large Cat Loss Size Lognormal distribution, mean 12, standard dev. 16. Example Company Reinsurance • The reinsurance programme consists of 4 layers as follows: • (USD million) Limit 10 20 50 50 Deductible Midpt Initial ROL 20 25 11.6 30 40 6.9 50 75 3.4 100 125 1.9 • All layers have 1 reinstatement at 100%. • Initial coinsurance for all layers is 25%. Different Strategies • Each Layer considered Separately • In Constant Cover strategies, coinsurance is fixed and premium paid varies. • In Constant Spend strategies, coinsurance varies to keep premium spend constant. Change in Reinsurance Pricing • The price of each layer in the reinsurance programme will vary, with an increase in price if the experience account (EA) for the layer is negative, and a reduction in price if the EA is positive and there are no losses in the previous year. • EA = reinsurance premiums and reinstatements – recoveries • if EA < 0 then premium = previous premium + EA * 10% • if EA > 0 then rate = previous rate * 90% • Initial EA = 0. Change ROL over time - Total Loss in Year 3 0.20 0.18 0.16 ROL 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0 1 2 3 Year 4 5 6 Model Implentation • Modelled Using ReMetrica II • Component Based Framework for risk analysis and DFA ( Dynamic Financial Analysis ) • Main Uses Include: – Reinsurance Pricing and Strategy – Risk Based Capital Modelling & Capital Allocation – Business Planning The Model Results • The graphs below show the cedant’s net underwriting result. As a measure of risk we show: Standard Deviation 1 in 100 result Probability of a negative UW result • As a measure of return we use expected UW result. • The numbers on the graph indicate the years 1 – 5. Results • The results were based on 20,000 simulations using stratified sampling of 10,000 strata • Performed sensitivity testing with further simulations ( 50,000 ) and different parameters. Risk Return - Standard Deviation Reinsurance Strategy - Risk Reward 29.40 5 5 29.20 29.00 4 4 28.80 28.60 28.40 12.4 3 3 2 12.6 12.8 13.0 13.2 13.4 1 13.6 2 13.8 14.0 Net UW Result (USD mill) - Standard Deviation Const Cover,Property,Net Underwriting Result Const Spend,Property,Net Underwriting Result Risk Return - 1 in 100 Reinsurance Strategy - Risk Reward 5 5 29.30 29.20 29.10 29.00 4 28.90 4 3 28.80 3 28.70 2 28.60 2 1 -19 -18 -17 -16 -15 28.50 -14 Net UW Result (USD m ill) - 1st Percentile Const Cover,Property,Net Underwriting Result Const Spend,Property,Net Underwriting Result -13 -12 28.40 -11 Risk Return - Probability Loss Reinsurance Strategy - Risk Reward 29.30 5 5 29.20 29.10 29.00 28.90 28.80 4 4 3 3 28.70 2 28.60 2 28.50 28.40 3.2% 3.4% 3.6% 3.8% 4.0% Probability negative Net UW Result Const Cover,Property,Net Underwriting Result Const Spend,Property,Net Underwriting Result 1 4.2% 4.4% Conclusions • Constant Spend strategy better than Constant Cover Strategy. • Return appears similar, but risk is less. • Consistent across different risk measures. Relevance • Constant Spend strategy is similar to the following strategy: – Buy core programme down from a top PML ( probable maximum loss ) figure and buy lower down on an opportunistic basis. • Opposite strategy reduces reinsurance when cost is low and buys more when costs are high. I call this the ‘short memory’ strategy. • Constant Cover is neutral. • This analysis indicates that buying down from your PML as far as your budget will allow is a good strategy. ( In practice, will still need a core programme. ) • This analysis may help a reinsurance manager defend against the ‘short memory’ strategy.