Solvency II in Europe and Internal Risk Modelling N. Savelli -

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Solvency II in Europe and
Internal Risk Modelling
N. Savelli -
nino.savelli@unicatt.it
Catholic University of Milan
Member IAA Solvency Sub-Committee
Concurrent Session:
”Update on a Global Risk Based
Capital Standard”
Agenda
 The new Solvency Regimes adopted by
some European Supervisory Authorities
 Solvency II Project: the state-of-art
 Some Results of capital requirements by
a Risk-Theory Simulation Model
 Final comments
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The new Solvency Regimes
adopted by some European
Supervisory Authorities
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The FSA approach
 Financial Services Authority (FSA) – UK:
ECR (Enhanced Capital Requirement): is calculated using a
standardized formula with different charges (in %) on assets (for
asset risk), on liabilities (for reserving risk) and on premiums (for
pure underwriting risk).
ICA (Individual Capital Assessment): Insurers are additionally
required to develop their own view on their capital requirements
using simple Stress & Scenario testing or Internal Models.
Time horizon = 1 year
confidence level = 99.5% .
These ICA results are submitted and discussed with regulator, and an
individual capital requirement then is agreed.
These tests are currently “soft”. They should become “hard” in
the near future.
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The FSA Approach: the structure of ECR
Total Capital Requirement (TCR) = AC + RC + UC
 AC = Asset charge = by applying factors to various categories of assets
(Form 13 – FSA Returns) where more risky assets are attracting higher
factors. Further, they include credit risks such as reinsurance recoverables.
 RC = Reserve charge = by applying factors to the net of reinsurance
reserves for each class of business (for a total of 24 classes of business: 8
LoB for each of direct&facultative, proportional treaty and non-proportional
treaty). Reserves include outstanding claims, IBNR, unearned premium
reserve (undiscounted and excluding equalisation reserves)
 UC = Underwriting charge = by applying factors to the net premium for
each class of business (the same 24 classes of business are used as for
Reserve Charge).
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 8 Lines of Business:
- Accident & Health,
- Transport
- Motor
- Property
- Aviation
- Liability
- Marine
- Miscellaneous
& Pecuniary loss
 3 different reinsurance covers:
Direct & Facult. / Proportional Treaty / Non-Proportional Treaty
 8 overall sets of risk factors:
Timescale:
T=1 and T=5 years
Probability Capital Requirement to be insufficient:
1/40=2.5%
1/100=1%
1/200=0.5%
1/500=0.2%
 Data available: for all major UK insurers and for many of the
smaller insurers (Lloyd’s not included) 1985-2001 fin. years.
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Optimised RISK FACTORS based on
ALL INSURERS
(T=1 year and PoF=1%)
Optimised RISK FACTORS based on
ALL INSURERS
(T=1 year and PoF=0.5%)


Asset Factors
- Debt securities approved
3.4%
- Land & Buildings:
7.4%
- Equities: insurance dependents
0%
- Equities: group&non-ins. dependents: 7.4%
- Equities: other
15.5%

Reserve Factors
Property:
9.7% 12.1% 12.1%
Liability:
14.2% 14.2% 14.2%


Asset Factors
- Debt securities approved
- Land & Buildings:
- Equities: insurance dependents
- Equities: group&non-ins. dependents
- Equities: other
Reserve Factors
Property:
8.0% 10.5% 10.5%
Liability:
12.1% 12.1% 12.1%
2.8%
6.1%
0%
6.1%
12.8%
(Dir./Prop./Non-Prop.)
(Dir./Prop./Non-Prop.)
Underwriting Factors
Property:
8.6% 19.1% 45.3%
(Dir./Prop./Non-Prop.)
Liability:
12.4% 12.4% 12.4%
(Dir./Prop./Non-Prop.)
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
(Dir./Prop./Non-Prop)
(Dir./Prop./Non-Prop)
Underwriting Factors
Property:
10.2% 23.1% 53.6% (Dir./Prop./Non-Prop)
Liability:
13.9% 13.9% 13,9% (Dir./Prop./Non-Prop)
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
The above results have been optimised
using All Insurers in the market (a larger
weight is placed on the larger insurers)

Then in order to fit the factors to smaller
Insurers, the optimisation has been also
based on:
- All Insurers except the largest 10
- All Insurers with net premium in 2001
below 10 million (GBP)

Higher measures are clearly obtained for
smaller Insurers (e.g. small Insurers often
show a greater degree of volatility than
large insurers)

For T=1 and PoF = 0.5% the results show
a capital requirement equal to 50-60% of
net premiums.
For T=1 and PoF = 1,0% the results show
a capital requirement equal to 40-50% of
net premiums.
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Total Capital Requirements implied by
each of the three optimisation methods
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The PV approach
 Pensioen Verzekeringskamer (PV) – Netherlands:
Financial Assessment Framework (it will be gradually
implemented until 2008)
This system consists of 2 tests:
- FIRST TEST: reported liabilities > actual value of liabilities
where “actual” liabilities = PV expected cash flow + risk margin.
Furthermore, insurers are required to extend this test to show that in
1-year time, with 99.5% confidence level:
actual value of resources > actual value of liabilities
(assuming no new business)
- SECOND TEST (continuity test): it concerns long-term survival of
the insurer. It is performed over a 3-5 years time horizon and new
business and proposed policy are considered.
For both tests, a choice of methods is available, ranging from
simplified versions with input by regulators to internal Models.
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The SFOPI approach
 Swiss Federal Office of Private Insurance (SFOPI)
– Switzerland:
Swiss Solvency Test (currently under consultation but due for
implementation in 2006)
Insurers are required to show that they hold sufficient capital to the
extent that in an unlikely negative scenario (e.g. 1%), assets
and liabilities can be transferred to a third party.
The regulator will provide a standard model for insurance, market
and credit risk, which insurers can deviate from previous
authorization of the regulator.
Alternatively, insurers can use internal models, if they can prove that
their model reflects risks more appropriately.
Assets and liabilities must be reported at their market-consistent
value.
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Solvency II Project:
the state-of-art
(Pillar I Non-Life Working Group:
Solvency II – Issues paper, February 2005)
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The Solvency II structure
Who is involved in Solvency II project:
 Insurance Commission (IC): European Commission’s regulatory and
legislative policy body ultimately responsible for drafting the new
directives. IC members are appointed from the insurance supervisory
authorities of the 25 member states;
 Committee of European Insurance and Occupational Pension
Supervisors (CEIOPS): advisory body within the European
Commission who advices the IC on technical aspects of Solvency II.
It is composed by high-level representatives of the (insurance and
pension) EU supervisory authorities
Timetable:
 by December 2005: it is expected a proposal for framework
directive key principles
 by December 2009: measures implementation.
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 Pillar I: it focuses on quantitative aspects of solvency,
mainly calculating the capital requirement (MCR and
SCR)
 Pillar II: it is mainly concerned with qualitative
measures regarding the Supervisory review
 Pillar III: concerns disclosure requirements. The aim is
to reinforce market discipline and risk-based supervision
(Note: many European insurers are not listed and then at the moment are
not subject to a very high degree of public disclosure).
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Risks and Capital Measures
under Pillar I
 In Pillar I are contained all the components of the
“Insurance Risk” that can be measured
quantitatively:
- underwriting risk (pricing risk and reserving risk)
- market risk
- credit risk,
- liquidity risk
- operational risk
 Total Balance-Sheet approach: target capital and
technical provisions to be covered by high quality assets
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 Two capital measures likely to be introduced:
- MCR (Minimum Capital Requirement)
- SCR (Solvency Capital Requirement or Target Capital)
and an Early Warning indicator (set above SCR and
calibrated over a longer time horizon, likely to be used for
supervisory intervention level)
 The EU Insurance Commission would like to keep a
simple formula for MCR as it is now for Solvency I
(roughly the maximum between 16%-18% of net
premiums and 23-26% of net claims amount). It should
include an absolute floor expressed in euros.
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 A capital below MCR represents an unacceptable risk
for policyholders and then immediate supervisory
action is required
 Alternative options for determining MCR are:
- extending present Solvency I formula to capture
asset risks;
- using SCR as a reference;
- establishing a simple risk margin over and above
liabilities
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 As to SCR, it should reflect the level of capital that an insurer would
need to operate with a “rather” low probability of failure for a fixed
time horizon. In principle it should be calculated on a going-concern
basis.
 This low level has not yet been defined, but at the moment the low
probability might be 0.5% for 1 year time span.
 The Risk Measure has not yet been defined, but VaR or TVaR are
good candidates (the choice will be likely linked to the desired safety
level and the actual capital ratios of the market).
On this matter, IAA has suggested TVaR as a more appropriate
risk measure for insurers.
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Standard Formula vs Internal Model
for calculating SCR
 The approach for calculating SCR:
- Standard Formula: it should be technically feasible for all firms,
but clearly no standard formula would be able to capture the
complete risk profile of the company.
Two main methodologies:
a) Factor-Based Capital Models
b) Scenario-Based Approaches.
They could be combined in the SCR standard formula.
- Internal Model: likely Solvency II will allow partial models
initially (FSA and PV allow the use of internal models for their own
new solvency regime, and SFOPI permits its use as approved
alternative tool only).
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Standard Formula
 Factor-Based Approach: formulaic relationship
between risk measures and capital requirements. The
parameters in any formula can be either identical for all
firms or tailored to reflect individual aspects, or a
combination. The RBC in US and the Swiss Solvency Test
adopt a personalised factor-based model.
 Criticism:
-
weak ability to capture interaction of risks
opacity
lack of dynamism
low predictive power
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 Scenario-Based Approach:
- it can be used to analyse the impact of adverse scenarios on
the firm, defined for each category of risk (underwriting, market,
credit, etc. …).
- Static or Dynamic scenarios (in the latter case, the assumption of
management’s inertia is relaxed).
 Scenarios may be used to model extreme events where the
factor-based approach may fail because these events may be either
absent from the data or may have to be smoothed out in the
calibration process;
 e.g. in the SST a separate treatment for catastrophic underwriting
risk is made by scenarios capturing the impact of extreme events.
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 In principle, a third approach might be the Probabilistic
Approach (usually via Monte Carlo simulation), but it
requires intensive use of data and computing power and
therefore it is not useful for a standard formula.
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Internal Model
 Internal Models : they can be used to represent the
business of an individual firm much more closely than the
standard formula, with capital requirements more
significantly aligned to the effective risk of the
company.
 Internal Model could also be used as an effective
risk management tool within the firm, and then it
would be desirable to encourage firms to move from the
standard formula to internal models through capital or
other incentives.
 Internal models may also be a relevant tool for the capital
requirements at the group level.
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 Firms would only seek approval of internal models if
they lead to a reduction in capital requirements compared
with the standard formula
 The model’s approval process will require considerable
effort and expertise from the supervisor
 Internal Models can be highly sensitive to the
underlying assumptions and parameters: sensitivity
testing as part of the validation process needed
 Cherry-picking risk: firms should not have the option
of switching back to the standard formula simply because
this leads to a minor capital requirement
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 Potentially, internal models might be used only for
some risks (or for the main lines of business) whilst the
standardised formula is used for the remaining (e.g.
operational risk, where less data are available)
 Anyhow, partial use of internal models would be a
temporary solution (to avoid cherry-picking again)
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Some Results from a
Risk-Theory Simulation Model
see paper by Rytgaard & Savelli
”Risk-Based Capital requirements for property and liability insurers according
to different reinsurance strategies and the effect on profitability”,
(presented at XXXV ASTIN Colloquium 2004 in Bergen)
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General framework
of the model
General Insurance
Casualty and Property (separately)
T=3 years
Compound Mixed Poisson Process
Neg. Binomial distrib.for non-CAT claims
Poisson
distrib. for
CAT claims
 Claim Size
: LogNormal distrib. for non-CAT claims
Pareto
distrib. for
CAT claims
 Dynamic Ins. Portfolio : Volume of premiums increases annually
according to real growth and claim
inflation
 Reinsurance strategy : Traditional Quota Share, Surplus, XL
(and CAT XL only for Property)
 Investment Return
: Stochastic (AR model), only 1 asset category
 Monte Carlo approach: 400.000 simulations
 Risks not considered
: Reserving, Credit and Operational Risks





Company
Lines of Business
Time Horizon
Total Claim amount
Number of Claims
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:
:
:
:
:
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The Risk-Reserve process (Ut)
~
U
t





Ut
Bt
Xt
Et
BRE
=
=
=
=
=
~ ~
 (1  j ) U
t
t 1
~
~ RE
~
RE
 ( B  X  E )  ( B  X  C RE )  (1  j )1/ 2
t
t
t
t
t
t
t
~
 j  LR
 TX  DV
t
t 1
t
t


Risk Reserve at the end of year t 
Gross premiums in year t

Aggregate claims amount

Actual total expenses of year t

Premiums ceded to reinsurers


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XRE
CRE
j
LR
TXt
DVt
=
=
=
=
=
=
Solvency II in Europe and IRM
Claims amount recovered by reins
Reinsurance Commissions
Investment return (annual rate)
Loss Reserve amount
Taxation amount
Dividends of the year
27
Total Claims Amount (Xt)
~
kl , t
~
k cat , t
l 1 k 1
k 1
L
~
~
~
X t   Z l ,k ,t   Wk ,t
non-CAT claims
CAT claims
(for Property only)
 kl,t = non-CAT Claim Number of year t (for the line l)
is assumed to be Negative Binomial distributed (i.e. Poisson
distribution with a stochastic parameter n*q, where q is a
multiplicative random structure variable with mean 1 and distributed
as a Gamma(h,h) - only short-term fluctuations and no systematic
changes are assumed).
The expected number of claims is increasing with the real rate of
growth:
nt=n0*(1+g)t
 kCAT,t = CAT Claim Number of year t (affecting only property lines)
is assumed to be Poisson distributed. The Poisson parameter is kept
constant over the chosen time horizon
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 Zl,k,t = non-CAT claim Size for the k-th non-CAT claim
of year t (for the line l):
is assumed to be LogNormal distributed, with values
increasing annually according to the deterministic claim
inflation (i) only.
 Wk,t = CAT claim Size for the k-th CAT claim of year t
(affecting only property lines):
is assumed to be Pareto distributed, with values
increasing every year according to the joint
(deterministic) effect of real growth (g) and claim
inflation (i) rates.
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 For each line, non-CAT claim size random variables Z are
here assumed to be i.i.d.;
 In case of a CAT claim, the CAT claim sizes affecting
each line are clearly not independent
 Here random variables Xt are assumed time
independent. In reality, however, long-term cycles are
present and therefore auto-correlation might be
significant (especially for medium/long-term analyses).
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General assumptions

Real growth rate (g): 5% (for every line)

Claims inflation rate (i):
 Liability
5%
 Property
2%

Loss reserve ratio (LR/B):
 Liability
120%
 Property
30%

Expenses loading coefficient (c): 25%

Risk loading coefficient (λ):
1  tx   E ( X~ )  E ( ~j )  LR  b  X~ 
Motor Liability:
λ = 2.1 %
Commercial Liability:
λ = 14.7 %
Property (Homeowners, Agriculture, Commercial): λ = 17.5 %
(having fixed b=35%)

Investment return process (j): expected rate 4% and std 2% (approx.)


Taxation flat rate (tx):
Dividends flat rate (div):
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35%
20%
gross profit of the year
net profit of the year
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Liability multi-line insurer
(most relevant input parameters)
LoB 1
Motor
LoB 2
Commercial
TOTAL
18.000
2.000
20.000
Variance structure variable
0,02
0.03
Skewness structure variable
+ 0.28
+ 0.35
Initial expected claim size (Eur)
6.000
16.000
7
16
Initial Risk Premium (mill Eur)
108,0
32,0
140,0
Initial Gross Premiums (mill Eur)
147,0
48,9
196,0
Initial expected number of claims
Variability coefficient of claim size
7.000
NOTE: Parameters as Var(q), E(Z) and CV(Z) are derived from the IAA-SWP Report (2004)
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Property Multi-line Insurer
(most relevant input parameters)
LoB 1
Homeowners
200.000
200.000
LoB 2
Agriculture
40.000
400.000
LoB 3
Commercial
20.000
1.200.000
Exp. loss frequency per risk losses
8.0 %
16.0 %
8.0 %
Initial expected number of claims
Variance structure variable q
Skewness structure variable q
Initial expected claim size (EUR)
Variability coefficient of claim size
6.000
0,04
+ 0.40
8.000
4
2.000
0.04
+ 0.40
12.000
8
2.000
0.04
+ 0.40
24.000
12
10.000
80,0
128,0
48,0
256,0
1
Initial Number of policies
Sum Insured per policy (EUR)
Catatrophe PML (mill EUR)
Exp. n. of catastrophe claims
TOTAL
260.000
12.000
Catastr. claims – Pareto param
1.2
Cumulation factor
0.5
Initial Risk Premium (mill EUR)
- hereof single risk losses
- hereof cat losses
Initial Gross Premiums (mill EUR)
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49,3
44,7
4,6
77,2
27,5
20,6
7,0
43,2
Solvency II in Europe and IRM
43,2
40,4
2,7
67,6
120,0
105,7
14,3
188,0
33
Simulation steps
1.
2.
3.
4.
Start simulations with u0=0
Calculate risk measure rbc for a time horizon T=1,2,3
(gross and net of reinsurance)
Use u0=rbc(TVaR; 99%,T=1) as initial capital ratio
Compute expected RoE
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Alternative Reinsurance Strategies
At the moment we consider the only reinsurance
strategies available on the market, which are:
Liability Multil. Insurer
1. No reinsurance
2. Q/S 10% with commission 25% (cRE=c)
Property Multil. Insurer
1. No reinsurance
2. Q/S 40% with commission 27% (cRE=c+2%) and Cat
XL protecting retention
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Results of 400.000 simulations
No reinsurance (Strategy 1)
Risk
Measures
(% Total Gross
Premiums at T=0)
Liability
Multi-line Insurer
Property
Multi-line Insurer
T=1
T=2
T=3
T=1
T=2
T=3
99.0 %
19.9
25.1
27.4
125.8
149.6
159.3
99.5 %
26.6
32.9
37.2
152.7
175.4
186.4
99.9 %
55.0
75.0
77.9
204.4
226.1
252.6
99.0 %
33.4
41.3
46.0
161.4
184.7
200.3
99.5 %
44.0
54.3
60.4
184.2
209.0
230.0
99.9 %
85.7
94.7
96.6
235.7
263.2
313.6
rbc (VaR)
rbc (TVaR)
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Results of 400.000 simulations
With reinsurance (Strategy 2)
Risk
Measures
(% Total Gross
Premiums at T=0)
Liability
Multi-line Insurer
(QS 10%)
Property
Multi-line Insurer
(QS 40% + CAT XL)
T=1
T=2
T=3
T=1
T=2
T=3
99.0 %
17.9
22.6
24.7
10.5
12.9
14.5
99.5 %
24.0
29.6
33.5
12.5
15.4
17.7
99.9 %
49.5
67.5
70.1
17.4
22.4
25.7
99.0 %
30.0
37.2
41.4
13.6
16.9
19.3
99.5 %
39.6
48.8
54.3
15.9
19.9
22.5
99.9 %
77.1
85.2
86.9
22.7
27.4
30.8
rbc (VaR)
rbc (TVaR)
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Alternative Reinsurance Strategies
(Liability Multiline Insurer)
Now we assume that the following reinsurance strategies
are available on the market:
1.
No reinsurance
2.
Q/S 10% with commission 25% (cRE=c)
3.
Q/S 20% with commission 25% (cRE=c)
4.
Unlim. xs 730.000 @ 7.57%
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Alternative Reinsurance Strategies
(Property Multiline Insurer)
1.
No reinsurance
2.
Q/S 40% with commission 27% (cRE=c+2%) and Cat XL
protecting retention
3.
Surplus treaty after € 300.000 (i.e. retention = 100% for
househ., 75% for agric. and 25% for comm.) with commission
26% (cRE=c+1%) and Cat XL protecting retention. This coverage
corresponds approx. to cede the same amount of premiums as
QS 40%.
4.
Risk XL € 840.000 xs 360.000 @ 7.51% and Cat XL protecting
retention
5.
Cat XL only (XL 369,9 mill xs 14,1 mill - RoL 6.27%)
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rbc(TVaR 99%)
according to different retentions
T = 1 year
Liability
Property
Strategy 1
50%
50%
Strategy 1
40%
oo
30%
RBC
RBC
40%
20%
Strategy 2
10%
30%
20%
o
10%
Strategy 2
0%
0%
0%
20%
40%
60%
80%
100%
0%
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XL
40%
60%
80%
100%
Ceded premiums
Ceded premiums
QS
20%
QS & Cat XL
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Surplus & Cat XL
Risk and Cat XL
40
Liability Multi-line insurer – Results (400.000 simul.)
u0 = rbc (TVaR - 99%, T=1)
Reinsurance
strategy
1. No reinsurance
2. Net of QS 10%
3. Net of QS 20%
4. Net of risk XL
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T=1
T=2
T=3
rbc (TVaR - 99%)
33.4
41.8
46.9
Exp. RoE (%)
19.32
40.88 (in [0;2])
65.00 (in [0;3])
rbc (TVaR - 99%)
30.1
37.6
42.2
Exp. RoE (%)
19.33
40.89
65.00
rbc (TVaR - 99%)
26.7
33.4
37. 6
Exp. RoE (%)
19.32
40.88
65.00
rbc (TVaR - 99%)
23.5
30.9
36.4
Exp. RoE (%)
12.75
26.81
42.49
Solvency II in Europe and IRM
41
Property Multi-line insurer - Results (400.000 simul.)
u0 = rbc (TVaR - 99%, T=1)
Reinsurance
strategy
1. No reinsurance
2. Net of QS 40%
3. Net of Surplus
4. Net of risk XL
5. Net of CAT XL
N. Savelli
T=1
T=2
T=3
rbc (TVaR - 99%)
161.4
187.3
205.3
Exp. RoE (%)
7.45
15.28
23.76
rbc (TVaR - 99%)
13.7
17.1
19.5
Exp. RoE (%)
18.08
37.71
59.13
rbc (TVaR - 99%)
19.3
25.5
30.1
Exp. RoE (%)
7.52
15.64
24.48
rbc (TVaR - 99%)
26.7
36.6
44.6
Exp. RoE (%)
0.92
1.72
2.53
rbc (TVaR - 99%)
24.2
31.1
36.3
Exp. RoE (%)
12.79
26.61
41.69
Solvency II in Europe and IRM
42
Final Comments
Prominent role of Internal Modelling in the future
Quantitative Tools are strongly necessary for this task (with
special reference to extreme events and dependencies)
Nowadays the minimum EU solvency ratio for a P&C Insurers is
roughly 16-20% of net premiums, and the results of many
studies show how the minimum capital ratio should be
significantly increased (at least 35-40% of premiums)
Attention must be paid to excessive capital requirements
with undesirable effects on a higher cost of capital for the
insurance market
N. Savelli
Solvency II in Europe and IRM
43
Questions
and
Comments ?
N. Savelli
Solvency II in Europe and IRM
44
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