Transcript Reinsurance Pricing

Reinsurance Pricing
Sean Russell
Occa Meeting
July 4, 2007
Overview

Basic Reinsurance Pricing Techniques
– Experience Rating
– Exposure Rating
– Modeling
Slide 2

Application of Actuarial Methods

Capital Allocation
Experience Rating

Individual Companies loss experience

Projection forward based on past experience
– Trending
– Layering
– Developing

Slide 3
Premium
Experience Rating
Simple Example
Reinsurance Layer $1 million excess of $1 million
Year
Subject Premium
2001
8,000,000
2002
11,000,000
2003
12,000,000
2004
13,000,000
2005
14,000,000
2006
15,000,000
Total
73,000,000
Brokers Burn
Total Losses in layer
Total subject premium
Rate
Slide 4
Loss Experience > 500,000
Year
Amount
2002
1,000,000
2002
800,000
2004
2,000,000
2005
1,400,000
2005
900,000
2006
1,100,000
1,500,000
73,000,000
2.1%
Experience Rating –
Trending/Developing
Trended losses (10% per year)
Year
2002
2002
2004
2005
2005
2006
Total
Amount
1,000,000
800,000
2,000,000
1,400,000
900,000
1,100,000
Trended Losses Losses to layer
1,610,510
610,510
1,288,408
288,408
2,662,000
1,000,000
1,694,000
694,000
1,089,000
89,000
1,210,000
210,000
2,891,918
Developed Losses
Loss Development factors to ultimate
Year
Factor
Trended losses
2001
1.1
2002
1.18
898,918
2003
1.26
2004
1.4
1,000,000
2005
2.2
783,000
2006
6
210,000
Slide 5
Developed losses
1,060,723
1,400,000
1,722,600
1,260,000
5,443,323
Experience Rating – On Level
On Level Premiums
Year
2001
2002
2003
2004
2005
2006
Total
On level Factor
1.8
1.5
1.1
1.05
0.95
0.9
Trended Devloped Losses
Burning Cost Rate
Slide 6
On level Premium
14,400,000
16,500,000
13,200,000
13,650,000
13,300,000
13,500,000
84,550,000
5,443,323
6.4%
Experience Rating Considerations
Slide 7

Lack of credible data

Weighting of individual years

Changes in Limit profiles

Changes in mix of business, classes of business

Legislative changes

New lines of business

Excess Leverage effect
Exposure Rating
Slide 8

What to do when there is very little individual
company data ?

Exposure rating Industry Burning cost

Exposure curves give distribution of loss relative to
the insured limit

With exposure data (limit profile) can then develop
expected losses

Loss ratio of portfolio is an important factor

Source of curves – ISO, internal data
Loss Modeling

Mathematical relationships which describe losses

Typical Reinsurance models
– Pareto distribution for Severity
– Poisson distribution for Frequency
– Log Normal distribution for Loss Ratio
Slide 9

Mean and Variance are important

Parameter Uncertainty

Simulation tools
Modeling

Loss Sensitive Features
– Sliding scale commissions
– Profit commissions
– No Claims Bonus
– Swing Rates
– Deficit Carryforwards

Slide 10
Payout Patterns/Discounting
Capital Allocation

Why we hold Capital
– Regulators
– Rating Agencies
– Risk

Risk  Volatility
Simplistic
Loading on
losses
Slide 11
Advanced
Loading on variance
of each deal
contribution to
portfolio of risk
Historical Results
Calendar Year Results 2002-2005
AXA RE
Caisse Centrale de Réassurance
Everest Reinsurance Company
General Reinsurance Corporation
Hannover Rückversicherung AG
PartnerRe SA
Toa Reinsurance Company of America
Transatlantic Reinsurance Company
Swiss Re Combined (gross)
Munich Combined
GEIS Combined
SCOR Combined
XL Re Combined
Total All Reinsurers
Casualty
Net Prem
533,556
123,975
220,794
229,382
211,983
184,994
94,531
112,676
541,000
612,782
614,650
227,154
195,956
4,110,825
Casualty Estimated
LR
Combined
91%
112%
82%
107%
86%
108%
142%
162%
105%
121%
93%
114%
85%
103%
96%
115%
86%
102%
100%
112%
82%
104%
103%
123%
71%
101%
96%
116%
May include primary business written in same legal entity. Includes treaty and facultative. “Combined” is sum of
all legal entities owned by the same group. Swiss Re premium is gross of internal quota shares.
Allocation of premium, losses, commisions to casualty (automobile,Liability) may not be accurate for multiline
treaties.
Slide 12
Combined ratio is estimated by adding average commission/brokerage for each company.
Conclusions
Slide 13

Reinsurance pricing applies similar actuarial
techniques as primary pricing

More reliance on statistical methods and
distributions due to smaller quantity of data

One step further removed from insured, data quality,
company knowledge critical