Zurich solvency II conference dec 2012

Stochastic Scenario CreationInfoline Zurich13 December 2012

Servaas Houben

1

Agenda

Solvency II Capital requirementRisk identificationData selection and limitationsCalibrationAggregation and dependenciesValidation

2

Infoline 13 December 2012 Zurich

Agenda



3

Capital requirement under SII

4


VaR limitations - subaddivity

5


Risk 1Probability Loss

0.03 1 mln

0.97 0

95% VaR 0

Risk 2Probability Loss

0.03 1 mln

0.97 0

95% VaR 0

Risk 1 and 2

Probability Loss

One event 0.0582 1 mln

Two events 0.0009 2 mln

95% VaR 1 mln

QuizData:• Monthly capital return index S&P 500 returns from Dec

1927-Feb 2011• Dec 1927 index value 17.66, Feb 2011 1,327.22• Total number of 998 monthly returns

6


Question:When excluding 10 highest monthly returns (setting them to 0%) what would be the index value as at Feb 2011?

Answers

<250

250-500

500-750

750-1000

>1000

Results• Set highest 10 values to 0: 172.80 (-87%)• Set lowest 10 values to 0: 15,330.78 (+1.050%)

0

200

400

600

800

1,000

1,200

1,400

1,600

1927

1934

1941

1948

1955

1962

1969

1976

1983

1990

1997

2004

All inclusive

Top 10 excluded

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1927

1935

1943

1951

1959

1967

1975

1983

1991

1999

2007

All inclusive

Bottom 10 excluded

7


“Risk mitigation” through dividends

8

-

1.000

2.000

3.000

4.000

5.000

6.000

Valu

e to

tal r

etur

n

Date

S&P500 Total return

total return index

without top 10

Overall scenario creation process

Data• Regime shifts?• Proxy data• Stale prices• Volatility

clustering

Calibration• Stationarity?• Body and tail

calibration• Sensitivity

testing measures

Dependencies• Body and tail

dependencies• PSD condition• Trade-off data

and economic rationale

Validation of scenarios• Sampling error• Flooring of risk

drivers• Rare event

distortion

9


Agenda


10


Risk identification

• Identification of quantifiable risks • Mapping of individual risks to homogeneous risk

groups▫ Diversification▫ Reporting

• Trade-off granularity and practical implementation

• Risk universe stores information

11


Agenda


12


Data selection• Empirical data:▫ Market risks

• Non empirical data/expert judgment:▫ Operational risks ▫ Non market risks Life and non-life risks

13


Nominal yield curves

Risk Management Hedging uses assets quoted on OISPricing (Guarantees) Funding for hedging based on OISProvisioning Solvency II based on LIBOR & UFR

– One-off surplus (based on current market environment)– Hedging efficiency and provisioning risk due to LIBOR-OIS basis

EUR 24 August 2012

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

1 11 21 31Term (Years)

EUR / 24 August 2012 / Spot / Annual

Market LIBORMarket OISSolvency II Risk Free

Source: Bloomberg

14


Liquidity and Matching premium adjustments

15

050

100150200250300350400450500

LQP

in b

asis

poi

nts

Date

LQP development over time

USD

GBP

EUR

(100)

(50)

-

50

100

150

200

250

300

350

400

MP

in b

p

Date

MP development

UK

US

EUR


Source: Itraxx

Agenda


16


Historical data collection

17


0

200

400

600

800

1.000

1.200

1.400

1.600

1.800

1928 1938 1948 1958 1968 1978 1988 1998 2008

Inde

x va

lue

Date

S&P 500

capital returnindex

Data amendments• Select indices deemed most appropriate• Apply transformation to data to check if data is

stationary

18


-30%

-20%

-10%

0%

10%

20%

30%

40%

1928 1938 1948 1958 1968 1978 1988 1998 2008

Inde

x va

lue

Date

S&P 500 return

Calibration

• Determine sample stats• Distribution fitting: ▫ Fit to different distributions▫ Individual country fitting/clustering

• Fit testing:▫ Kolmogorov-Smirnov goodness of fit

test▫ Anderson Darling▫ Sense test: 0.5% and 0.05%

percentiles▫ Plot sample data and fitted

distributions

19


Agenda


20


Case study - diversification

• Measurement of strength and direction of relationship 2 risk drivers:

21

-100,00%-80,00%-60,00%-40,00%-20,00%

0,00%20,00%40,00%60,00%80,00%

-4,000% -3,000% -2,000% -1,000% 0,000% 1,000% 2,000% 3,000% 4,000%

TWD

equ

ity

UK property

Property Monthly Total Return UK vs TWD equity return, Feb 1991 - Feb 2011


Produce correlated risk drivers

22

Uncorrelated risk drivers Correlated risk drivers


Scenario production

• Apply correlated random numbers to calibrated distributions

• Apply restrictions to certain risk drivers▫ Interest rates▫ Credit spreads▫ Volatilities

23


Agenda


24


Validation

25

Risk drivers

• Key statistics• Mean/median• Standard deviation• Skewness• Kurtosis

• Key percentiles• 1 in 200 capital

requirement

Dependencies

• Complications for risk drivers portraying tail behaviour


References & contact details• CEIOPS, Task Force Report on the Liquidity premium, 1 March 2010

• Cooke, Houben, Varnell, Dependencies and aggregation, AENORM August 2012

• Shaw, Smith, Spivak, Measurement and Modelling of Dependencies in Economic

Capital, 10 May 2012

• Taleb, Fooled by Randomness – the hidden role of chance in life and in the markets,

2001

• Taleb, The Black Swan – the impact of highly improbable, 2007

• Vose, Fitting distributions to data – and why you are probably doing it wrong, 15

February 2010

• Email: [email protected]• Blog: http://actuaryabroad.wordpress.com

26

About me

Servaas Houben heads the risk scenario

generation team at Prudential, London. He

studied econometrics in the Netherlands and

worked in life insurance for the first four

years of his career. Following this, he worked

in Dublin and London. Besides actuarial,

Servaas completed the CFA and FRM

qualifications, and regularly writes on his

blog, for CFA digest and Dutch actuarial

magazines.

27

Appendix - Correlated random numbers• Start with correlation matrix C• Find lower lower triangle matrix L such that

LTL = C• C needs to be positive semi definite (positive

eigenvalues)

28

1 0.7 0.70.7 1 0.70.7 0.7 1

C =

1 0 00.7 0.714 00.7 0.294 0.651

L =


Appendix - From uncorrelated to correlated random seed

• Z = uncorrelated random number stream• X = correlated random number stream• X = L * Z

• =퐿 0 0퐿 퐿 0퐿 퐿 퐿

푍푍푍

• X=푍

퐿 ∗ 푍 + 퐿 ∗ 푍퐿 ∗ 푍 + 퐿 ∗ 푍 + 퐿 ∗ 푍

=푋푋푋

29


Zurich solvency II conference dec 2012

Documents

Transcript of Zurich solvency II conference dec 2012