2013.06 scor seminar istanbul - developing internal models

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

47

Frank Cuypers

+41 (41) 725 32 94

frank.cuypers@prs-zug.com

Speaker’s Coordinates

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