ACE Tempest Re 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 =  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 # ofLayerTotal YrClaimLossAdj Prem k 1061k 49k k 1220k 176k 30 0k 1000k k 1247k 52k 35k 110k k 1491k 393k k 2445k 282k 229k 2k 26k 21k 596k k 2030k 664k 160k k 2500k 1003k 286k k 2500k 852k 387k k 2500k 90k 48k 83k 706k 1003k 95k 1003k k 2500k 1003k 522k 440k 421k 78k 1003k 381k 275k k 1498k 206k 193k 1, k 1492k 130k 112k 101k 16k 34k Total 1772M 2236M Expected Loss Ratio79%