20140528 - ESGs (Czech Society of Actuaries) - Shaun Lazzari

© 2014 Deloitte MCS Limited. All rights reserved.

Testing and validating stochastic economic scenarios

Shaun Lazzari

29 May 2014


Agenda

• Using ESGs

‒ Purpose

‒ Process (providers, groups and business units)

‒ Solvency II requirements

• Formulating calibration assumptions

‒ Required assumptions

‒ Data challenges

‒ Potential solutions

• Validating scenario sets

‒ Aims

‒ Analyses

• Future challenges

2

© 2014 Deloitte MCS Limited. All rights reserved.3

Using ESGs


Using ESGsWhat do ESGs do?

• Generate many scenarios for future economic variables

• Asset classes:

‒ Nominal rates

‒ Real rates

‒ Inflation

‒ Equities

‒ Property

‒ Credit spreads / default probabilities

‒ Alternatives

‒ Exchange rates4

0 5 10 15 20 25 30 35

Time (y)


Using ESGsPurposes

• Two key types of ESG model:

• Application: Monte Carlo approach especially useful for valuation when liabilities

involve non-linear cashflows:

‒ Options/guarantees

‒ Path-dependence

‒ Management actions

5

• Market-consistent valuation (for reporting)

• HedgingRisk neutral

• Risk/return quantification

• Regulatory/economic capital calculation

• Investment strategy setting

• Pricing

Real world

(Deflator-based models incorporate features of both types of model)


Using ESGsStochastic modelling for valuation

Liability values found as expected value of discounted projected cashflows:

• Risk-neutral means no arbitrage opportunities:

‒ Expected PV of any investment strategy is equal to amount invested today

‒ In contrast to real-world simulation, where risk premiums may be used

6

ESG

Discount

factors

Other

outputs

Liability

info

Projected

cashflows

(Market)

value

average


Using ESGsMarket consistency

• Risk-neutral ESG models are calibrated to market data

• Calculated values of liabilities (which are complex financial contracts) can be

thought of as being a “market price”7

Calibration targets (market

prices)

Calibration

Model parameters

Scenario generation

Economic scenarios

Pricing

Scenario-calculated

prices

ES

G


Using ESGsProvision of scenarios: a typical process

8

ESG

provider

Group

office

Business

unit

• Software

• Calibrations

• Assumptions/insights

• Scenario files

• Software?

• Calibrations?

• Scenario files

• Business-unit specific

assumptions and file

requirements

• Company-specific

assumptions and file

requirements

Data

Data

Data


Using ESGsProvision of scenarios - challenges

• For example:

‒ Ownership of assumptions

‒ Adequate validation/challenge of assumptions

‒ Meeting ad-hoc requirements

• Often Business Units do not have access to software / provider contact

themselves, perhaps due to:

‒ Cost

‒ Resource/expertise requirements

• We are seeing reliance on third party providers and/or group centralisation

increasing over time

‒ For software and resources… but not assumptions!

• For CEE calibrations (e.g. Czech Koruna), lack of market data can make

calibration difficult

9


Using ESGsSolvency II

Article 126

“The use of a model or data obtained from a third-party shall not be considered to be a

justification for exemption from any of the requirements for the internal model set out in

Articles 120 to 125.”

• Use test

• Statistical quality standards

• Calibration standards

• Profit & loss attribution

• Validation

• Documentation

As an ESG provider, we find we get many more questions and challenges now

than we used to – this is good!

10


Formulating calibration assumptions


Formulating calibration assumptionsRequired assumptions

• Aim wherever possible to calibrate to today’s market price data

• Projected behaviour based upon these prices:

12

3

6

9

15

30

0%

20%

40%

60%

13

57

912

2030

Option term (y)Swap term (y)

Market implied vol (ATM)

40%-60%

20%-40%

0%-20%

Drift

• Linear payoffs – bonds, forward

contracts

Volatility, skew, autocorrelation etc.

• Non-linear payoffs - options +

other derivatives

0%

1%

2%

3%

4%

0 10 20 30 40

Sp

ot

Rate

Term (y)

Initial yield curve


Formulating calibration assumptionsRequired assumptions

• Ideally:

+ inter-asset class correlation assumptions!

13

Nominal rates

• Initial yield curve

• Swaption prices/implied vols

Real rates/inflation

• Initial yield curve

• Volatility & mean reversion levels

Equities & other indices

• Option prices/implied vols

• Forward dividends

• Dividend volatility & mean reversion

Credit

• Initial credit spread curves

• Spread volatility

FX

• FX option prices/implied vols


Formulating calibration assumptionsData challenges

Ideally, we would calibrate using targets solely sourced from market prices. In

practice, many reasons why not possible:

14

• Swaption prices based on swap rates – inconsistency if using government curveNominal rates

• Few economies issue inflation-linked bonds

• Derivatives on these bonds are even rarerReal rates

• Insurers generally interested in long term implied volatilities – very scarce data

• For property etc., no liquid derivative marketsEquities & other indices

• Data very fragmented as multiple issuers – some indices do exist for major economies

• Few derivativesCredit

• Few liquid cross-asset class derivativesCorrelations


Formulating calibration assumptionsImportant features of an assumption-setting approach

The issues described have long existed and many workarounds can be used. In

a Solvency II world, these must be well-justified!

• Informed by relevant data

• Limited and well-validated use of expert judgement

• Stability over time

15


Formulating calibration assumptionsSolutions

1 – Use of historic data

• Common approach for several targets

‒ Volatility – property, inflation, credit…

‒ Correlations

• Note implied volatility ≠ volatility

‒ Bias

‒ Observed volatility says nothing about forward-looking term structure, skew

16

0

20

40

60

80

1990 1993 1995 1998 2001 2004 2006 2009 2012

IV /

vh

isto

ric

vo

l(%

)

Time

VIX implied

60D vol

Average 3.5%

difference



2 – Use of proxy data series

• Asset class may be approximated by a related, more established class for which

data exists

• Substitute assumption should be well-validated:

‒ Statistically

‒ Analysis of underlying

drivers

• May seek to make appropriate adjustments to proxy data

17

1998 2001 2004 2007 2009 2012

CECE CTX



3 – Third party guidance

• Calibration assumptions are, ultimately, prices of simple financial contracts

‒ Request quotes from banks – they are the market makers!

‒ Seek assistance from data provider

‒ Inspect regulatory returns

• With Solvency II, insurer still required to take ownership of assumptions

18


Formulating calibration assumptionsExample – Czech/CEE equity

• Only short-term options traded for CECE

‒ Would like a full surface

• Could we use a major EUR index like the Eurostoxx or DAX as a proxy?

Historic behaviour:

19

1998 2001 2004 2007 2009 2012

CECE

Eurostoxx 50

DAX



Historic volatility:

Short term ATM implied volatilities:

20

CECE Eurostoxx 50 DAX

27.2% 23.1% 24.44%

0

5

10

15

20

25

30

May-14 Oct-15 Feb-17 Jun-18

AT

M I

V (

%)

Expiry date

CECE

DAX

Eurostoxx 50

Unusual downward slope!



Higher moments:

21

Den

sit

y

Historic log returns (annualised)

CECE

Eurostoxx 50

CECE Eurostoxx 50

Skewness -0.7 -0.8

Kurtosis 6.2 5.9



• Lot of choice as to how incorporate these observations into assumptions

‒ But this analysis provides us with evidence to back-up approach

• Approach should be robust – i.e. stable over time

22

Calibration assumptions

Short-term market data

Difference in historical

volatilitySimilar higher

moments, hence skew


Validating scenario sets


Validating scenario setsAims

• Having made a set of scenarios, must adequately validate them

• Seek to verify:

• Ideally in as automated and judgement-free way as possible

24

Arbitrage-freeness

Market consistency / fit

to calibration targets

Model stabilityCompatibility with cashflow

model


Validating scenario setsAnalyses – no arbitrage/leakage

Test both raw outputs and more complex (dynamic?) strategies:

• Means of quantifying error:

‒ Maximal error

‒ Confidence intervals

‒ Terminal leakage

25

0.8

0.9

1

1.1

1.2

0 10 20 30 40

Time (y)

Govt. CMI Term 15

0.8

0.9

1

1.1

1.2

0 10 20 30 40

Time (y)

Equity TRI

Undervaluation of guarantees


Validating scenario setsAnalyses – market consistency

Compare market prices against those found through pricing using scenarios:

26



Compare market prices against those found through pricing using scenarios:

27

0%

1%

2%

3%

4%

5%

0 5 10 15 20 25 30 35 40

Sp

ot

rate

Term (y)

Average deflator

Yield curve

95% confidence interval



• Monte Carlo prices are an average

→ can use similar pass/fail criteria used for no-arbitrage tests

• Can break down error into two parts:

• Significance of sampling error best quantified through comparing prices, not vols

etc.

28

Fitting errorSampling

error

Market consistency

error

Targets - Fitted Fitted - Generated


Validating scenario setsAnalyses – convergence

• Are we convinced enough simulations have been used?

• In more volatile environments, more scenarios required

29

10%

15%

20%

25%

0 1,000 2,000 3,000 4,000 5,000

10

x1

0 s

wa

pti

on

Im

pli

ed

vo

l

# simulations

Simulations

Model


Validating scenario setsAnalyses – out of sample testing

• Wish to verify model is not over-fitted, but instead has some predictive power

‒ If it doesn’t, ESG is pointless!

Do not always have excess data available, but sometimes we do!

30

10%

15%

20%

0 5 10 15

Imp

lied

vo

lati

lity

Term (y)

Simulated Market Fitting

o Bond prices

o Swaption cube points

o Interest rate caps

o Intermediate points on

implied vol term structure


Validating scenario setsAnalyses – distributional features

• Out-of-sample contracts most likely to be mispriced if output distributions are “not

sensible”

• Extreme distributions may also impact ALM model compatibility

• Additionally, consider changes in distributional statistics over time – are these

consistent with changes in calibration assumptions?

31

-80% -60% -40% -20% 0% 20% 40% 60% 80%

Log-return

SVJD

Black-Scholes


Validating scenario setsAnalyses – distributional features

• Out-of-sample contracts most likely to be mispriced if output distributions are “not

sensible”

• Extreme distributions may also impact ALM model compatibility

• Additionally, consider changes in distributional statistics over time – are these

consistent with changes in calibration assumptions?

• Aside: have seen other European regulators asking firms to test multiple models

32

-4%

0%

4%

8%

12%

16%

20%

24%

28%

0 5 10 15 20 25 30 35 40

Sp

ot

rate

Time (y)

Hull-White

-4%

0%

4%

8%

12%

16%

20%

24%

28%

0 5 10 15 20 25 30 35 40

Sp

ot

rate

Time (y)

LMM

-4%

0%

4%

8%

12%

16%

20%

24%

28%

0 5 10 15 20 25 30 35 40

Sp

ot

rate

Time (y)

LMM-DDSV


Validating scenario setsAnalyses – calibration stability

• For a given model, finding optimal parameter set is a hard problem

1) Test optimisation routine

‒ Generate targets from the model

‒ Fit to these targets – should be able to achieve exact fit, and ideally same parameters as

used to generate targets

2) Test goodness-of-fit over time

‒ Fit to historic targets

‒ Asses fit in range of market conditions, and stability over time

3) Test parameter stability

‒ Make small adjustments to initial guess – should have small impact on outcome

33


Validating scenario setsDoing all this analysis

• Some of this is one-off work (validating optimisation routine etc.)

• Model is not particularly firm-specific – provider may be best to validate

‒ Firm need only demonstrate evidence and understanding

• If Business Unit is reliant on Group for scenarios, must seek to request sufficient

information to calibrate

‒ e.g. to accurately price swaption, many outputs required

• Much of regular validation process can be automated

34


Future challenges


Future challengesImmediate issues

• ESGs models have reached a mature stage where most calibration targets can

be achieved:

‒ Initial yield curves

‒ Option surfaces

‒ Volatility cubes

• Some advances can still be made with regards to credit modelling

• Automation an area of focus as volume of ESG file required increases

‒ Quicker delivery

‒ Sensitivities

‒ Nested stochastic etc.

36


Future challengesLonger term

• Emerging standards, including Solvency II and IFRS, continue to emphasize

market consistency - generally a good thing.

• Insurance definition is based on classical option pricing theory (replicating

portfolios); many assumptions:

• Limitations highlighted post-2008!37

Forbidden

• Bid-ask spreads

• Market impact of trades

• Information asymmetries

• Taxes

• Solvency capital requirements and

costs of holding these.

• Collateral posting requirements

• Risk of default on derivatives

• Illiquidity premiums or other non-cash-

flow valuation effects

Required

• Investment and unlimited borrowing at a

single risk free rate.

• Unlimited and infinitely-divisible supply of

underlying assets.

• Continuous-time trading (24/7)

• Buying and selling with no impact on the

market price.

• Consensus on possible price moves in

the underlying asset.



• Banks have adopted adjustments to counter weaknesses in theory:

• These innovations may hit insurers first via IFRS rather than Solvency II

38

Credit valuation

adjustment

CVA

Debit valuation

adjustment

DVA

Funding valuation

adjustment

FVA

Allowance for possible default by

derivative counterparties

Reduce stated liabilities with an

allowance for own default.

Allowance for funding of derivative

position (borrowing over the risk free

rate, stock lending, collateral posting).



• Real-world modelling has itself advanced greatly in recent years due to

Solvency II

‒ Diverged from risk-neutral approach

• Incorporating these “real-world” features into market-consistent modelling will

bring these two types of modelling closer together

• Working towards a Grand Unified Model!

39


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Documents

20140528 - ESGs (Czech Society of Actuaries) - Shaun Lazzari