2013.06 scor seminar istanbul - developing internal models
TRANSCRIPT
Developing Internal Models
SCORSolvency II Seminar
2
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
3
What is Solvency about?
risk
0
RoRAC
0
insurance
reinsurance
earn
ings
4
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
5
3 Pillars
quantitative qualitative transparency
6
What belongs to whom?
investments
assets liabilities
reserves
equity
belongs to the policyholders
belongs to the shareholders
7
What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
8
What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
9
What happens with it?
balance sheet1 Jan. 2013
P&L1 Jan. 2013 – 31 Dec. 2013
balance sheet31 Dec. 2013
10
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
11
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
12
RTC & SCR
RTC
simulated scenarios
RTC probability density
possible scenarios
possible portfoliosin 1 year
pandemics
stock markets
inflation
…
earthquakes
today in 1 year time
13
0.5% 99.5%
RTC & SCR
RTC
RTC probability density
best estimate
Value at Risk = VaR → SCR
14
RTC & SCR (SST)
RTC
1% 99%
Tail VaR = TVaR → SCR
best estimate
RTC probability density
Value at Risk = VaR → SCR
0.5% 99.5%
15
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
16
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
1717
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
18
Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
19
Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
20
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
21
Portfolio management
RTC
today in 1 year time
company today
22
Portfolio management
RTC
SCR
strategy A
strategy B
strategy C
company today
23
Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
24
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
25
Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
26
generalinsurance
Capital allocation
EC1EC2
EC3
EC1
EC2
EC3
lifeinsurance
investments
27
Capital allocation
EC1
EC2
EC3
AC1
AC2
AC3
AC1
AC2
AC3
diversifiedallocation
proportionalallocation
EC
company
28
proportional … expected shortfall
formula
fairness /
diversification /
simplicity /
communication /
ECEC
ECAC
jj
ii )(VaR XXXEAC ii
Capital allocation
29
Uses
Portfolio management Reinsurance optimization Capital allocation Pricing Underwriting limits Product development Mergers & acquisitions Incentive & remuneration policy …
30SCR
RTC
company today
add a policy
infinitesimal change of the portfolioRoRAC
Pricing
31
company today
RoRAC
portfolio today+
new policy
Pricing
32
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
33
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
34
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
35
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
36
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
37
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
38
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
39
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
40
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
41
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.
42
Procedural Framework
Tests
Draft report
Documentation analysis & interviews
Specifications
feedback
Final report
4343
Solvency II
Uses of an internal model
Components of an internal model
Validation of an internal model
Agenda
44
Trust is good... Modelling is better
45
Transmutation of Junk into AAA
46
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
48
A Model for Variable Income Risk
Value of the asset
Return of the asset
Wiener process ,~ln1
NSS
t
t
1t
t
SS
tS
49
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
50
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
51
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
52
RTC & SCR
RTC
simulated scenarios
RTCprobability
density
timetoday in 1 year
…
possible portfoliosin 1 year
earthquake
pandemia
yields
inflationMCV
MCV
53
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
54
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
55
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
56
Variance Reduction
? xfdxI
known~~ xfdxI
Ifdx
xfdxxfxfdxI~
~~
Monte Carlo
Monte Carlo
57
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
58
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• …
59
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
60
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
61
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