Određivanje cijene reosiguranja viška štete za zelenu kartu / Pricing of Green Card XL Reinsurance

Transcription

1 Određivanje cijene reosiguranja viška štete za zelenu kartu / Pricing of Green Card XL Reinsurance Dr. Torsten FISCHER Domenico SEMERARO September 1st, 2009 Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

2 1 Overview of the Pricing Process for Green Card XL 2 3 Calculation of the Price for XL Reinsurance 4 Outlook on Refined Loss Modelling 5 Discussion Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

3 Overview of the Pricing Process for Green Card XL 1. Submission of pricing request by cedent / broker: description of portfolio, slip, (rates). 2. Creation of a loss model for single large losses. 3. Calculation of a price for reinsurance based on model and contract features. Possible: quotation for alternative layerings, using the same model. 4. Negotiations, finalization of the contract. 3

4 1 Overview of the Pricing Process for Green Card XL 2 3 Calculation of the Price for XL Reinsurance 4 Outlook on Refined Loss Modelling 5 Discussion Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

5 Fictitious Example for Green Card XL Reinsurance Reinsurance for 3 layers: 1. Layer: EUR xs EUR 2. Layer: EUR xs EUR 3. Layer: unlimited xs EUR. Data: new contract period: 2009 same portfolio for 10 years loss history for the years : complete list of all losses above EUR. What is the price for reinsurance? Problem: We do not know the future losses. 5

6 Approach: Create and apply a model for the (future) losses, based on the loss history. What should the model predict? 1. number of losses above the priority ( EUR), 2. the severity (loss amount) distribution. Assumptions (for simplicity): no inflation of premiums or losses, no development of losses (final incurreds are known). For more realistic assumptions, see below. 6

7 Loss Amount in EUR Fictive Loss History (above EUR in ) Accident Year 7

8 Number All Loss Amounts above EUR, ordered Loss Amount in EUR 8

9 Cumulative Probability Empiric Severity Curve 100% 80% 60% 40% 20% 0% Loss Amount in EUR 9

10 Cumulative Probability Empiric Severity Curve and Pareto Fit 100% 80% 60% 40% The largest historic loss is below 1 mio. In the Pareto model also losses above 1 mio are possible. 20% 0% Loss Amount in EUR 10

11 Number of Large Losses Number of Losses above EUR per Year History Average 5, Accident Year 11

12 We have estimated the parameters of a frequency-severity-model: 1. Model threshold: EUR 2. Frequency: average 5,4 losses (above EUR) per year Poisson-distribution (not shown here) 3. Severity (loss amount) Pareto-distribution Pareto-alpha: 2,3. In this model even very large losses are possible, e.g. loss amounts above 5 mio EUR. 12

13 1 Overview of the Pricing Process for Green Card XL 2 3 Calculation of the Price for XL Reinsurance 4 Outlook on Refined Loss Modelling 5 Discussion Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

14 Cumulative Probability Calculation of the Price for XL Reinsurance Expected Loss to each Layer = Area * Frequency 5,4 100% 80% 60% 40% 20% 0% Loss Amount in EUR 14

15 Cumulative Probability Calculation of the Price for XL Reinsurance Annual Loss per Layer 100% 80% 60% 40% 20% With probability 88% the 3. layer has no annual loss. With probability 56% the 1. layer has an annual loss of EUR or less. 1. Layer 0,2 xs 0,2 2. Layer 0,6 xs 0,4 3. Layer unlimited xs 1 0% Loss Amount in EUR 15

16 Costs in EUR Calculation of the Price for XL Reinsurance 1. layer: working layer, mainly driven by expected loss. Expected Costs per Layer layer: rarely hit, small expected loss mainly driven by cost of capital Cost of Capital Internal Expenses Brokerage Expected Loss 0 0,2 xs 0,2 0,6 xs 0,4 unlimited xs 1 Layer 16

17 1 Overview of the Pricing Process for Green Card XL 2 3 Calculation of the Price for XL Reinsurance 4 Outlook on Refined Loss Modelling 5 Discussion Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

18 Outlook on Refined Loss Modelling Loss Inflation: How much would a historic loss cost today? Possible approach: loss amounts are inflated like the wages or medical costs in the country of occurrence. Loss development: Consider that the ultimate loss amount for an accident is unknown for a long time. Split of loss into paid and reserved. Discount of later payments, capital allocation for period of uncertainty. Application of market models: in particular if the cedent s data is sparse, not suitable for modelling; application to non-working layers. 18

19 Outlook on Refined Loss Modelling Separate models for different type of risks: segmentation by type of vehicle, destination - however: one needs a lot of good data for that. Comparison of historic portfolios: - Inflation of premiums, e.g. by Premium Index (tariff changes). - Preferred exposure measure: number of vehicles or vehicle years. 19

20 Outlook on Refined Loss Modelling Consideration of structural changes: - changes in the cedent s portfolio, e.g. from passenger cars to trucks, merger with another company, change in underwriting policy. - changes in law: higher limits, change in jurisdiction estimation of quantitative effect is difficult. Facit: Refined Loss Modelling leads to a better estimation of the fair price for Reinsurance. The better the data (level of information, number of reported years, ) the better the model. 20

21 1 Overview of the Pricing Process for Green Card XL 2 3 Calculation of the Price for XL Reinsurance 4 Outlook on Refined Loss Modelling 5 Discussion Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009

22 Hvala na pažnji! - Thank you for your attention! Dr. Torsten FISCHER Phone: TFischer@scor.com Domenico SEMERARO Phone: DSemeraro@scor.com Pricing of Green Card XL Reinsurance - Sarajevo September 1st, 2009