Solvency II –
Capital drivers &
reinsurance solutions
FIAR
May 22-26, 2011
Alexandra
Storr 2010 - Susanne Kaske-Taft
PAM 22 March
Capital drivers under Solvency II



Under Solvency I a lot of fundamentals
of the insurance business model have
been neglected in the regulatory regime
Under Solvency II the real risk
landscape of an insurance company
should be considered in the calculation
of the solvency capital requirements
Therefore the solvency capital
requirements under Solvency II are
influenced by a number of capital
drivers compared to Solvency I
Ability to
increase
capital
Availabke capital
Solvency II | Example: Capital drivers & reinsurance solutions
Unexpected
widening of
bond spreads
Embedded
options &
guarantees
Duration
mismatch
(ALM)
Frequency
Equity &
property price
risk
Exchange rate
mismatch
Insufficient
diversifcation
Required capital
Counterpartyd
efault risk
Highly volatile
peak risks
Volatility of
reserve
run-off
Summary
Solvency II & reinsurance
Examples:
Insufficient diversification
Transfer of peak risks
Natural catastrophe risk
Insurance Linked Securities
Large exposure to
increasing life spans
Longevity swap
Volatility of reserve run-off
Loss Portfolio Transfer & Adverse
Development Cover
Internal model
Examples:
… value the capital benefit
based on the model used
Partial internal model
… find the most efficient
reinsurance solution …
Standard Formula
Identify the individual
capital drivers …
Reinsurance is a powerful capital management tool under Solvency II
Solvency II | Example: Capital drivers & reinsurance solutions
Solvency II
Examples of Capital drivers and
Reinsurance solutions
Capital drivers
Reinsurance solutions P&C
Standard Formula
Partial Internal
Model
Internal Model
Insufficient diversification
(Structured) Quota share
High volatile peak risks
(Structured) Excess of Loss
Frequency
(Structured) Aggregate XL
Volatility of reserve run-off
(Structured) Quota share / LPT & ADC / Run off
Solvency II | Example: Capital drivers & reinsurance solutions
Insufficient
diversification and
quota share
Solvency II | Example: Capital drivers & reinsurance solutions
5
Capital driver under Solvency II–
Insufficient diversification

Insufficient diversification will lead to an increase in solvency
capital requirement compared to Solvency I

(Missing) diversification on the asset side will be a capital
driver, too

Better diversified insurers are able to deal with financial
consequences of risks relatively easier and therefore more
efficiently

Most affected:
Captives
 Monoliners
 Small local players
 Niche players

Solvency II | Example: Capital drivers & reinsurance solutions
P&C Quota Share
under Solvency II
Value proposition of a Quota Share
under Solvency II:
300
Gross situation:
250
BSCR (99.5 % VaR):
Loss
200

UW risk

Market risk
2.5 mio EUR

Credit risk
----------------
150
100
12.7 mio EUR
10.2 mio EUR
Reinsurance:
50
20 % Quota Share / 23 % Commission
0
Risk 1
Risk 2
Risk 3
Risk 4
…
Risk n
Net situation:
Insurer’s share (retention) ) 80 %
BSCR (99.5 % VaR)
Reinsurer’s share (cession) ) 20 %
•
UW risk
8.2 mio EUR
•
Market risk
2.1 mio EUR
•
Credit risk
0.3 mio EUR
The quota share reduces the Solvency Capital
Requirement (SCR) for the insurance risk under
Solvency II according to the proportion ceded to the
reinsurer
Solvency II | Example: Capital drivers & reinsurance solutions
10.6 mio EUR
= Capital relief of the 200-year event
= EUR 2.2 m
Example:
Highly volatile peak risk
and Excess of Loss covers
Solvency II | Example: Capital drivers & reinsurance solutions
8
Capital driver under Solvency II–
Highly volatile peak risk

Solvency II will require insurers
to back their book of business
with solvency capital that
reflects the economic risk

In contrast to Solvency I where
often only the premium volume
is decisive

Portfolios with the same
premium volume can have a
totally different capital
requirement

If one of the portfolios
(Portfolio B) contains high
volatile peak risks where the
resulting aggregate claims
distribution is more skewed to
the right than for a Portfolio A
of risks with low volatility
Probability
Probability
Claims amount
Portfolio A
contains only low
risks
Probability
Claims amount
Claims amount
Premium
volume
Portfolio A
VaR 99.5%
Premium
volume
Portfolio B
Portfolio B
contains only high
risks
VaR 99.5%
Probability
Probability
Claims amount
Solvency II | Example: Capital drivers & reinsurance solutions
Probability
Claims amount
Claims amount
P&C XL per risk
under Solvency II
Value proposition of an Excess of Loss
under Solvency II:
amount of losses
300
250
For a given safety level the ratio of net premiums
relative to required risk capital after reinsurance
will increase considerably with a XL treaty.
200
150
100
Risk mitigation
None
Quota share
(50 %)
50
Gross premium
0
1
2
3
4
5
6
number of losses
loss burden


reinsurance cover
not covered
An XL reinsurance treaty reduces not only the
absolute variability of the reinsured’s retained
losses but also their relative variability.
The premium ceded to the reinsurer is in
relative terms considerably smaller compared to
the reduction of required capital through a nonproportional reinsurance treaty.
Solvency II | Example: Capital drivers & reinsurance solutions
WXL
7.000.000
7.000.000
7.000.000
R/I premium
-
3.500.000
1.260.000
Net premium
7.000.000
3.500.000
5.740.000
12.300.000
6.150.000
3.500.000
57 %
57 %
164 %
Capital requirement
Net premium /
Capital requirements
Indicator: Recognition as reinsurance
Capital requirements net
Premium & Reserves net

Capital requirements gross
Premium & Reserves gross
3.500 .000
12.300 .000

5.740 .000
= 0.28 < 0.82
7.000 .000
Example:
Frequency risk and
Aggregate-XL
Solvency II | Example: Capital drivers & reinsurance solutions
11
Capital driver under Solvency II–
Exposure to frequency risk
12%
10%
8%
6%
4%
Often, there is no protection against
frequency risk below the deductible
(missing horizontal protection)
30
28
26
24
22
20
18
16
14
12
Number of losses

The aggregate claim is the result of the combination of
the distribution of the claims amount (severity) and of the
distribution of the claims frequency

The more dangerous the claims frequency for any given
severity, the more capital required to back the portfolio

Solvency II | Example: Capital drivers & reinsurance solutions
8
This in turn is the result of the
combination of the distribution of the
claims amount (severity) and of the
distribution of the claims frequency
0%
10

2%
6
Within Solvency II, the required solvency
capital is determined by the distribution
of the overall aggregate annual loss
Portfolio B
14%
A growing risk-taking ability often
implies a growing deductible for the CXL
programme which exposes the insurer
to frequency risk below the deductible

Portfolio A
4

Probability
2

Primary insurers are normally well
protected against losses from a severity
perspective (vertical protection) through
the core Catastrophe Excess of Loss
(CXL) programme
0

Portfolio B requires more capital than Portfolio A
P&C Aggregate XL
under Solvency II
Value proposition of a Structured Stop Loss &
Aggregate XL & under Solvency II:
Loss ratio per
year / %
Term limit 400 mio EUR
200
150
100
200
mio
EUR
140%
200
mio
EUR
200
mio
EUR
Insurance risk:


150 %
160 %

Level of the capital relief determined by the
design of the cover and the additional
structural elements
Especially if the structured elements influence
the risk mitigation
or
utilize the diversification in time or over lines
of business
Qualitative aspects:
0
Year 1
Year 2
Year 3
Solvency II | Example: Capital drivers & reinsurance solutions

Multi-year covers are providing certainty
regarding price and capacity for a specified
future periods

This could be used as a qualitative argument
for the regulator (Pillar 2)
Example:
Volatility of reserve run-off
and LPT & ADC
Solvency II | Example: Capital drivers & reinsurance solutions
14
Capital driver under Solvency II–
Volatility of reserve run-off

While the final payments to a
policyholder or a beneficiary will not yet
be precisely known, the run-off
contributes to the absolute volatility of
an insurer’s result

This implies that the client will need,
from an economic perspective, risk
capital in order to support the run-off of
a portfolio of liabilities

The inclusion of the volatility of reserve
run-off may decrease or (more likely)
increase the capital requirement
1. Timing risk
Total claims
amount to be
paid
Expected
payout
pattern
Slow er
payout
pattern
Faster payout
pattern
0
1
2
3
4
5
6
Time
2. Reserving Risk
Claims incurred
(one AY)
Reserved
100% estimate
at end AY
Paid
1
Solvency II | Example: Capital drivers & reinsurance solutions
2
3
4
5
Time
Loss Portfolio Transfer (LPT) &
Adverse Development Cover (ADC)
under Solvency II
Claims
Expected
claims
(Claims
provision on
balance sheet)
“Loss Portfolio
Transfer”
premium
(Net present
value of claims
provision)
Run-Off solution
Reserve risk (a)
“Adverse
Development”
Cover (a)
Timing risk (b)
“Loss Portfolio
Transfer”
Cover
(b+c)
Investment risk (c)
Value proposition of a LPT/ADC under
Solvency II:
Insurance risk:

LPT removes the timing risk

ADC removes the reserving risk
=> both consequently remove the
necessity to set aside regulatory capital
Market risk:

Time
Remarks:

Normally the capital relief from transferring the LPT part
will be lower than the relief achieved by reinsuring
adverse claims (ADC)

So far in some European countries the LPT is not
recognized as reinsurance
Solvency II | Example: Capital drivers & reinsurance solutions
Reduction of market risk due to the
reduction of investments
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Solvency II | Example: Capital drivers & reinsurance solutions