Transcript Handout 2
Numerical Examples – Adjustable Features Jeanne Lee Ying ACE Tempest Re Basic Steps Build aggregate loss distribution Lognormal is a common distribution used for aggregate loss distribution Model frequency and severity separately Usually assume the independence between frequency and severity Apply specific treaty adjustable features to the loss distribution curve generated or to each simulated year Reasonability check ACE Tempest Re Numerical Examples Profit Commission Loss Ratio Corridors Loss Ratio Caps Swing Rate ACE Tempest Re Profit Commission Example A Casualty Prorata Treaty Subject Premium: 50M Loss Ratio: 70% Weighted average based on all year on level loss ratios Ceding commission: 22% Brokerage: 0% Profit Commission: 30% after 15% of reinsurer’s margin Profit Commission formula = 0.3 x (premium-loss-expense-reinsurer’s margin) What is the expected profit commission for the deal? ACE Tempest Re Modeling A Lognormal Distribution Model a Lognormal Aggregate Distribution Parameters: Loss Ratio (mean): 70%, Standard Deviation (SD): 20% CV (Coef. of Varitation)= Standard Deviation / Mean = 0.2 / 0.7 = 0.2857 Sigma = SQRT (LN((CV^2 +1)) = 0.28 Mu = LN(mean) – (Sigma^2)/2 = 17.3 Determine loss ratios with their associated probability EXCEL Function Lognormdist (X, Mu, Sigma) ACE Tempest Re Profit Commission Example ACE Tempest Re Profit Commssion -Key Observation Cost of expected profit commission (1.2%) does not equal to the cost of profit commission at the expected loss ratio (0%) For Casualty lines, historical data may not reflect a full range of possibilities Adjusting CV using judgement to account for more variability ACE Tempest Re Loss Corridor Example A Casualty Pro Rata Treaty Loss Ratio: 70% Weighted average based on all year on level loss ratios Ceding commission: 22% Brokerage: 0% A Loss Corridor between 80%-90% loss ratio What is the expected loss ratio net of the corridor? ACE Tempest Re Loss Corridor ACE Tempest Re Loss Ratio Cap Example A Casualty Pro Rata Treaty Loss Ratio: 75% with standard deviation of 30% Ceding commission: 22% Brokerage: 0% A Loss Ratio Cap at 110% What is the expected loss ratio net of loss ratio cap? ACE Tempest Re Loss Ratio Cap ACE Tempest Re Modeling Frequency and Severity Separately A Casualty Excess of Loss Treaty Assume frequency and severity are independent Simulate Severity to the Layer Simulate on level frequency ACE Tempest Re Swing Rated Example A General Liability Excess of Loss Treaty 750K xs 250K Layer with 10M Subject Premium Premium is adjusted based on 100/80 loading factor subject to a minimum rate of 10% and a maximum rate of 25% Expected burn cost: 18% Adjusted Premium= Minimum of Layer Loss x 100/80 + Minimum Rate x Subject Premium Maximum Rate x Subject Premium ACE Tempest Re Swing Rated Example A General Liability Excess of Loss Treaty For each year, simulate Claim Count Using Poisson. In this case, Lamda=4.4 For each claim count, assign a loss severity based on simulation of Lognormal or Pareto distribution. We used a 5 parameter truncated Pareto distribution. For this example, we simulated 1000 years ACE Tempest Re Simulation Summary # of Layer Total Claim Loss Adj Prem 1 1 1 49k 1061k 49k 2 1 176k 1220k 176k 3 0 0k 1000k 4 3 198k 1247k 52k 5 1 393k 1491k 393k 6 6 1156k 2445k 7 2 824k 8 2 Yr 2 3 4 5 6 35k 110k 282k 229k 2k 26k 21k 596k 2030k 664k 160k 1289k 2500k 1003k 286k ----- - - ----- - - 7 996 2 1239k 2500k 852k 387k 997 7 3029k 2500k 90k 48k 83k 706k 1003k 95k 1003k 998 8 4122k 2500k 1003k 522k 440k 421k 78k 1003k 381k 999 2 399k 1498k 206k 193k 1,000 5 393k 1492k 130k 112k 101k 16k 34k 1772M 2236M Total Expected Loss Ratio 8 275k 79% ACE Tempest Re