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2013.06 SCOR Seminar Istanbul - Developing Internal Models
Transcript of 2013.06 SCOR Seminar Istanbul - Developing Internal Models
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Developing Internal Models
SCORSolvency II Seminar
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What is Solvency about?
risk
earn
ings
2
1
0
2 destroys value
1 adds value
2 adds value
1 destroys value
RoRAC
1
2
0
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What is Solvency about?
risk
0
RoRAC
0
insurance
reinsurance
earn
ings
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Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
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3 Pillars
quantitative qualitative transparency
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What belongs to whom?
investments
assets liabilities
reserves
equity
belongs to the policyholders
belongs to the shareholders
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What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
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What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
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What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
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How much is left after one year?
today in 1 year time
equi
ty
pandemics
stock markets
inflation
possible scenarios
…0earthquakes
possible portfoliosin 1 year
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capitalSCR
free surplus
Economic Balance Sheet
investments
reserves
RTC
RTC = Risk Taking Capital= economic value of the company= assets – reserves
• assetsmarket consistent / mark-to-market
• reservesbest estimate + risk margin / mark-to-model
SCR = Solvency Capital Requirement= risk adjusted capital = risk statistic of the RTC
free surplus ≥ 0RTC ≥ SCR
assets liabilities
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RTC & SCR
RTC
simulated scenarios
RTC probability density
possible scenarios
possible portfoliosin 1 year
pandemics
stock markets
inflation
…
earthquakes
today in 1 year time
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0.5% 99.5%
RTC & SCR
RTC
RTC probability density
best estimate
Value at Risk = VaR → SCR
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RTC & SCR (SST)
RTC
1% 99%
Tail VaR = TVaR → SCR
best estimate
RTC probability density
Value at Risk = VaR → SCR
0.5% 99.5%
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Differences S II & SST
S II SSTstart 2017 ? 2006 - 2008required capital VaR(99.5%) → SCR TVaR(99%) → SCRrisk horizon 1 year 1 year
insurance risk
market risk
credit risk
operational risk
deterministic scenarios
internal model ? % market players 50% market players
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Standard Models
Reserves
Different models depending on data availability / quality line of business / market processes / claims mgmt … actuarial judgment
→ 1st moment of a distribution
standard reserving model
Capital
Different models depending on data availability / quality line of business / market processes / products … actuarial judgment
→ nth moment of a distribution
standard solvency model
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Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
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Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
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Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
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liability
fire
earthquake
reinsurance
indiv. life
…motor
group life
gov. bonds
corp. bonds
stocks
derivatives100%
100%
100%
strategy A
strategy B
strategy C
portfolio today
Portfolio management
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Portfolio management
RTC
today in 1 year time
company today
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Portfolio management
RTC
SCR
strategy A
strategy B
strategy C
company today
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Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
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Reinsurance optimization
0
20
40
60
80
100
120
0 200 400 600 800 1000
Economic Capital
Net
Ret
urn
rete
ntio
nce
ssio
nre
tent
ion
cess
ion
rete
ntio
n
excessof loss
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Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
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generalinsurance
Capital allocation
EC1EC2
EC3
EC1
EC2
EC3
lifeinsurance
investments
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Capital allocation
EC1
EC2
EC3
AC1
AC2
AC3
AC1
AC2
AC3
diversifiedallocation
proportionalallocation
EC
company
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proportional … expected shortfall
formula
fairness /
diversification /
simplicity /
communication /
ECEC
ECAC
jj
ii )(VaR XXXEAC ii
Capital allocation
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Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
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30SCR
RTC
company today
add a policy
infinitesimal change of the portfolioRoRAC
Pricing
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company today
RoRAC
portfolio today+
new policy
Pricing
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Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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Components of the SCR
500
400
300
200
100
300
200
50
100
50
400
600
0 100 200 300 400 500 600 700 800 900 1000
reserves
life
P&C
earthquake
reinsurance
market
credit
diversification
operational
risk margin
SCR
RTC
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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Model Risk
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Aug‐yy May‐yy Jan‐yy Oct‐yy Jul‐yy Apr‐yy Jan‐yy Oct‐yy Jul‐yy Apr‐yy
MXN / USD0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
‐0.50 ‐0.40 ‐0.30 ‐0.20 ‐0.10 0.00 0.10 0.20
log‐return MXN / USD
modelo
2 / dof = 0.6
normal Models
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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Deterministic Stress Scenarios
0.01%
0.10%
1.00%
10.00%
100.00%
100'000'000 150'000'000 200'000'000 250'000'000 300'000'000
prob
abili
ty
RBC t=1
RBC distributionRBC shiftedmeanVaRtVaR
occurrence probability distribution w/o scenarios
RTC shift
xRTCPpxRTCP s
S
ss
0
0
distribution w/ scenarios
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Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
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Methodological Framework
Risk categoriesreserves riskattritional losseslarge claimscatastrophe riskbiometric riskoptions & guaranteeseconomic scenariosfixed income riskvariable income riskexotic financial instrumentscredit riskoperational riskMonte Carlo convergencedependenciesCRTIstress scenariosparameter riskrisk marginliquidity
Model componentsmethodologydataparameterscalculationsplatformgovernanceuse test
Validation proceduresagreed upon proceduresmarket benchmarksmethodology assessmentsimplementation testssource codes checksplausibilisationsreconciliationsinput testssensitivity analysisbacktestingemulationsprocess walkthroughs
e.g.
e.g.
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Procedural Framework
Tests
Draft report
Documentation analysis & interviews
Specifications
feedback
Final report
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4343
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
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Trust is good... Modelling is better
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Transmutation of Junk into AAA
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There’s more to Solvency II than just satisfying the regulator
It is an opportunity to optimize your reinsurance
But only with an internal model
Conclusions
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A Model for Variable Income Risk
Value of the asset
Return of the asset
Wiener process ,~ln1
NSS
t
t
1t
t
SS
tS
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A Model for Variable Income
Value of the asset
Return of the asset
Wiener process
Deterministic stress scenarios
,~ln1
NSS
t
t
1t
t
SS
tS
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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Life Options & Guarantees
fix interest rate
yield curve
stochastic yield curve
stochastic cash flow
rDEXE rDXS
rDX
rDEX rDXE
cash flowdepends on interest rates
MCV
cash flow
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RTC & SCR
RTC
simulated scenarios
RTCprobability
density
timetoday in 1 year
…
possible portfoliosin 1 year
earthquake
pandemia
yields
inflationMCV
MCV
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Replicating Portfolios
Life insurance options & guarantees intimately weave market and insurance risk together SCR = RBC statistic over (real world) economic scenarios RBC = average over (risk neutral) economic scenarios Monte Carlo of Monte Carlo
Standard solution: replicating portfolio = RBC closed form estimate approximation of an approximation
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Replication Quality in the Bulk
-20'000'000'000
-10'000'000'000
0
10'000'000'000
20'000'000'000
0 25'000'000'000 50'000'000'000 75'000'000'000
resi
dual
replicated BELre
sidu
alreplicated BEL
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Replicating Portfolios
Life insurance options & guarantees intimately weave market and insurance risk together SCR = RBC statistic over (real world) economic scenarios RBC = average over (risk neutral) economic scenarios Monte Carlo of Monte Carlo
Standard solution: replicating portfolio = RBC closed form estimate approximation of an approximation
Other solution = Monte Carlo of Monte Carlo with variance reduction
techniques
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Variance Reduction
? xfdxI
known~~ xfdxI
Ifdx
xfdxxfxfdxI~
~~
Monte Carlo
Monte Carlo
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Major Risk Models
Insurance risk
General insurance
Reserves
Underwriting
Attritionallosses
Large claims
Catastrophic losses
Life insurance
Biometry
Options & guarantees
Market risk
Fixed income
Variable income
Exotic instrumentsCredit risk
Operational risk
Aggregation
Convergence
Dependences
CRTIs
Meta-risks
Economic scenarios
Stress scenarios
Parameters
Risk margin
Liquidity
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riesg
o 2
riesgo 1
best estimate
50% confidence level
70% confidence level
90% confidence level
Dependences
Kobe EQ• property• burglary• Barings Bank
September 11• aviation• property• BI• life• market• …
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0
5'000
10'000
15'000
20'000
0 5'000 10'000 15'000 20'000
riesg
o lo
gnor
mal
riesgo Pareto
0
5'000
10'000
15'000
20'000
0 5'000 10'000 15'000 20'000
riesg
o lo
gnor
mal
riesgo Pareto
cópulade Clayton
Dependences
cópulaindependiente
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0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
GAUSS
0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
CLAYTON
Use copulas, but with a realistic tail dependence
Dependences
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Economy’s Complex Phenomenology
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.0 0.2 0.4 0.6 0.8 1.0ta
il de
pend
ence
limit process variable ε
observaciones
escenarios0%
20%
40%
60%
80%
100%
0% 20% 40% 60% 80% 100%
log
retu
rn E
Q (U
SD) r
ank
log return EQ (EUR) rank
observacionesescenarios
uvP |lim0