loss model - Bosna RE

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Pricing of Green Card XL
Reinsurance
Dr. Torsten FISCHER
Domenico SEMERARO
September 1st, 2009
Pricing of Green Card XL Reinsurance - Sarajevo
September 1st, 2009

1
Overview of the Pricing Process for Green Card XL
2
Simple Stochastic Model for Large Losses
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

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

1
Overview of the Pricing Process for Green Card XL
2
Simple Stochastic Model for Large Losses
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

Simple Stochastic Model for Large Losses
Fictitious Example for Green Card XL Reinsurance
• Reinsurance for 3 layers:
1. Layer: 200.000 EUR xs 200.000 EUR
2. Layer: 600.000 EUR xs 400.000 EUR
3. Layer: unlimited xs 1.000.000 EUR.
• Data:
new contract period: 2009
same portfolio for 10 years
loss history for the years 1999 – 2008:
complete list of all losses above 100.000 EUR.
What is the price for reinsurance?
Problem: We do not know the future losses.
5

Simple Stochastic Model for Large Losses
• 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 (200.000 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

Loss Amount in EUR
Simple Stochastic Model for Large Losses
Fictive Loss History (above 100.000 EUR in 1999-2008)
1.200.000
1.000.000
800.000
600.000
400.000
200.000
0
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Accident Year
7

Number
Simple Stochastic Model for Large Losses
All Loss Amounts above 200.000 EUR, ordered
51
41
31
21
11
1
0 200.000 400.000 600.000 800.000 1.000.000 1.200.000
Loss Amount in EUR
8

Cumulative Probability
Simple Stochastic Model for Large Losses
Empiric Severity Curve
100%
80%
60%
40%
20%
0%
0 400.000 800.000 1.200.000 1.600.000
Loss Amount in EUR
9

Cumulative Probability
Simple Stochastic Model for Large Losses
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%
0 400.000 800.000 1.200.000 1.600.000
Loss Amount in EUR
10

Number of Large Losses
Simple Stochastic Model for Large Losses
Number of Losses above 200.000 EUR per Year
10
8
6
4
History
Average 5,4
2
0
1998 2000 2002 2004 2006 2008 2010
Accident Year
11

Simple Stochastic Model for Large Losses
We have estimated the parameters of a
frequency-severity-model:
1. Model threshold: 200.000 EUR
2. Frequency:
average 5,4 losses (above 200.000 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

1
Overview of the Pricing Process for Green Card XL
2
Simple Stochastic Model for Large Losses
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

Cumulative Probability
Calculation of the Price for XL Reinsurance
Expected Loss to each Layer = Area * Frequency 5,4
100%
80%
60%
40%
20%
0%
0 400.000 800.000 1.200.000 1.600.000
Loss Amount in EUR
14

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 500.000 EUR or less.
1. Layer 0,2 xs 0,2
2. Layer 0,6 xs 0,4
3. Layer unlimited xs 1
0%
0 500.000 1.000.000 1.500.000 2.000.000
Loss Amount in EUR
15

Costs in EUR
Calculation of the Price for XL Reinsurance
1. layer: “working layer”,
mainly driven by expected loss.
Expected Costs per Layer
600.000
3. layer: rarely hit, small expected loss
mainly driven by cost of capital.
400.000
200.000
Cost of Capital
Internal Expenses
Brokerage
Expected Loss
0
0,2 xs 0,2 0,6 xs 0,4 unlimited xs 1
Layer
16

1
Overview of the Pricing Process for Green Card XL
2
Simple Stochastic Model for Large Losses
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

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

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

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

1
Overview of the Pricing Process for Green Card XL
2
Simple Stochastic Model for Large Losses
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

Hvala na pažnji!
-
Thank you for your
attention!
Dr. Torsten FISCHER
Phone: +49-221-2928-1452
TFischer@scor.com
Domenico SEMERARO
Phone: +49-221-2928-1304
DSemeraro@scor.com
Pricing of Green Card XL Reinsurance - Sarajevo
September 1st, 2009