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© 2014 Deloitte MCS Limited. All rights reserved.
Testing and validating stochastic economic scenarios
Shaun Lazzari
29 May 2014
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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)
© 2014 Deloitte MCS Limited. All rights reserved.
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)
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.11
Formulating calibration assumptions
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptionsSolutions
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
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptionsSolutions
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptionsExample – Czech/CEE equity
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!
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptionsExample – Czech/CEE equity
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
© 2014 Deloitte MCS Limited. All rights reserved.
Formulating calibration assumptionsExample – Czech/CEE equity
• 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
© 2014 Deloitte MCS Limited. All rights reserved.23
Validating scenario sets
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario setsAnalyses – market consistency
Compare market prices against those found through pricing using scenarios:
26
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario setsAnalyses – market consistency
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
© 2014 Deloitte MCS Limited. All rights reserved.
Validating scenario setsAnalyses – market consistency
• 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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.35
Future challenges
© 2014 Deloitte MCS Limited. All rights reserved.
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
© 2014 Deloitte MCS Limited. All rights reserved.
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.
© 2014 Deloitte MCS Limited. All rights reserved.
Future challengesLonger term
• 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).
© 2014 Deloitte MCS Limited. All rights reserved.
Future challengesLonger term
• 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
© 2014 Deloitte MCS Limited. All rights reserved.
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