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1
Analyzing Tail Risk: Scenario Generation and Selection
Tony Dardis
June 11 2009
Agenda
+ Tail risk case study: 2008+ Lessons learned?+ General tips and techniques for good scenario generation
2
Tail risk case study: 2008
Global Interest Rates: Gov. Bond Yields
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-2.00
-1.00
0.00
1.00
2.00
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4.00
5.00
GBP USD EUR JPY
10
ye
ar S
pot
Rat
es
-G
ove
rnm
en
t B
ond
s
End Sep 2008
End Dec 2008
Changes
-3.00
-2.00
-1.00
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GBP USD EUR JPY
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ye
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ove
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ond
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End Sep 2008
End Dec 2008
Changes
Global Interest Rates
5
+ Globally, risk-free yield curves fell significantly in the fourth quarter of 2008.
+ This increased the cost of insurer’s long-term investment guarantees
+ This impact was felt in every major life insurance market
+ 10-yr swap spreads in major developed economies have recently been negative
+ This is unprecedented
Global Equity Markets
6
-60%
-50%
-40%
-30%
-20%
-10%
0%
GBP USD EUR JPY
Equi
ty m
arke
t re
turn
(Yea
r 20
08)
Global Equity Markets
7
+ 2008 global equity market returns were close to or worse than typical 99.5% equity stress test assumptions– Virtually no diversification benefit between major global equity markets
– Impact on insurance company capital was universal, but particularly marked in countries with significant unhedged equity exposures such as Canada and Japan
– Equity falls also resulted in reductions in the present value of future asset-related fees
+ e.g. for unit-linked or VA business
+ Realised equity volatility was also at very high levels– e.g. realised daily S&P 500 volatility between October 1st and November 25th was
in excess of 80%pa, which included several daily returns of ~10% magnitude
– VA delta hedging programs do not work well in these conditions. This impact was clearly apparent in US Q4 earnings reports
USD Credit Spreads: Historical Perspective
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0
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Cre
dit S
prea
d (b
ps)
US 30 year maturity AAA credit spreads
US 30 year maturity BBB credit spreads
Credit spreads
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+ Long-term investment-grade credit spreads in 2008 were at extreme levels from historical perspective– AAA spreads at unprecedented levels
– BBB spreads were last at these levels in 1932
+ This generated mark-to-market losses well beyond typically assumed 99.5% stress tests
+ Again, this impact was global and negative for insurance groups
1-month Option-Implied Equity Vols: Historical Perspective
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0
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2009
Europe
UK
US
Japan
Dotted line atend-Dec2008
Options
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+ Long-term option-implied volatilities for long-term interest rates more than doubled during 2008 in several major economies
+ Long-term option-implied equity volatilities proportionally increased by over 50%
+ Yet again, this was universally negative for the global insurance sector from a market risk-based perspective
+ Yet again, the experienced changes likely exceeded firms’ 99.5% stress test capital assessments
Global Financial Market Conditions
12
+ At the start of the year, the 2008 market experience would have looked like a ‘perfect storm’ extreme global stress test that was beyond 99.5% confidence levels– Significant falls in long-term interest rates
– Equity market falls at 99.5% stress test levels
+ Virtually no diversification benefit across equity markets
– Unprecedented increases in credit spreads
– Doubling of long-term option-implied equity and long-term interest rate volatilities
+ This naturally had a significant negative impact on market risk-based assessments of 2008 profits and ongoing capital adequacy
+ It has prompted firms to re-consider....– their business models with relation to how they write and price long-term
investment guarantees, and how they manage the resultant market risk exposures
– how they are modeling financial market risk – the concept of “model risk”
+ It has also prompted policymakers to consider re-defining market-based, risk-based measures of profitability and capital requirements
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100
Percentiles 5% to 1%
Percentiles 25% to 5%
Percentiles 50% to 25%
Percentiles 75% to 50%
Percentiles 95% to 75%
Percentiles 99% to 95%
Legend
0%
2%
4%
6%
8%
10%
12%
14%
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18%
20%
1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100
Percentiles 5% to 1%
Percentiles 25% to 5%
Percentiles 50% to 25%
Percentiles 75% to 50%
Percentiles 95% to 75%
Percentiles 99% to 95%
Legend
Where did your models fall?: example RW calibration at end-June 08
13
3-month rate10-yr spot rate
Lessons learned?
Lessons learned?
+ Areas that you may wish to revisit in our models– Equity fat tails and skew
– Lack of diversification in market downturns
– Credit risk
– Risks left behind by a delta hedge
+ Other aspects– Senior management buy-in of models
– Use of the American Academy scenarios
Equity fat tails and skew
16
0.0%
0.1%
0.2%
0.3%
0.4%
0.5%
0.6%
0.7%
0.8%
0.9%
1.0%
-30% -25% -20% -15% -10%Excess log-return
Fre
qu
ency
Historic (20th Century)
Stochastic Vol Model
Normal Distribution
Lack of diversification in market downturns
+ Bivariate Lognormal + Stochastic Volatility
17
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
-50% -40% -30% -20% -10% 0%
Excess log-return (Asset 1)
Ex
ce
ss
log
-re
turn
(A
ss
et
2)
0.1% percentile
1% percentile
= 0.64
-50%
-45%
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
-50% -40% -30% -20% -10% 0%
Excess log-return (Asset 1)
Ex
ce
ss
log
-re
turn
(A
ss
et
2)
0.1% percentile
1% percentile
= 0.64
Credit risk
18
What needs to be captured in a credit model?+ A good credit risk model should be arbitrage-free, fully integrated
with the other financial market risks that are being modeled (thus correlated with equities and interest rates), and provide a framework to describe:
– issuer rating changes & defaults (spread to cover default risk)
– “credit risk premium” (additional spread to compensate for uncertain return)
+ Starting point: real-world credit transition matrix– Assuming a Markov process, enables us to readily determine survival
probabilities over the years and hence spreads (by bond rating and maturity) to cover default risk (“break-even spread”)
+ Moving to risk-neutral– In practice, actual spreads are larger than break-even - the credit risk premium
– The credit risk premium clearly is not something that is constant over time
+ Stochastic spreads– Transition matrix (and hence rating changes/defaults) can be modeled as a
stochastic process
– Credit risk premium can be modeled as a stochastic process19
Risks left behind by a delta hedge
+ Prior to the events of 2008, many companies did not fully understand what a delta hedging strategy was leaving on the table
+ RW modeling of a delta hedge creates very demanding ESG requirements:
Real-World Scenarios– Equity scenarios need to consistently model the risk factors that matter to the
performance of a hedging strategy:+ Variations in short-term underlying equity volatility (Gamma)+ Variations in option-implied equity volatility (Vega)
– The experience of Q4 2008 highlights how significant these risks can be for delta-hedging strategies
– Real-world scenarios need to be capable of capturing these risks to provide robust assessment of the risks left behind
Market-Consistent Scenarios– May require ‘inner’ simulations for projection of future hedge positions
– These scenarios need to be consistent with the corresponding ‘outer’ simulation+ Interest rates, option-implied volatilities+ Need automated calibration processes 20
Delta-Hedging and Gamma Losses in Recent Market Environment
21
Real-world projection of option-implied volatility: Vega Risk
22
+ Joint modeling of underlying real-world equity returns and real-world stochastic evolutions of the option-implied equity volatility surface is important for delta-hedging risk assessment
0.25 0.
5
0.75
1
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Maturity
Strike
Model Volality Surface
0%
5%
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25%
0% 4% 8% 12% 16% 20% 24% 28% 32% 36% 40% 44% 48% 52% 56% 60%
Prob
abili
ty D
ensi
ty
Implied Volatility
US
UK
Japan
Germany
France
35.00%-40.00%
30.00%-35.00%
25.00%-30.00%
20.00%-25.00%
15.00%-20.00%
10.00%-15.00%
5.00%-10.00%
0.00%-5.00%
Other aspects: senior management buy-in of models+ Natural reluctance to accept the results from models that are
contrary to experience and intuition– Often an obstacle to getting senior management buy-in to a model
– There may be transition aspects to consider (e.g., how to manage a big one-off impact on capital)
+ Senior management often don’t understand enough about models– Need to have an understanding of the questions that the model is trying to answer
– Need to have a deep understanding of the complexities of the underlying products that the company is issuing
– Need to understand model limitations
+ Judgment will always be required, e.g., assumptions setting– Senior management needs to be able to give input to this process
Other aspects: use of the Academy’s scenarios?+ The AAA scenario sets provide an ‘entry-level’ stochastic economic
scenario capability for VA statutory reserves and capital– Never intended to be used for complex asset-liability profiles
– Clearly documented in the VA CARVM and C3 Phase II Practice Notes that the scenario sets will not be appropriate where a dynamic hedging strategy is in place
– Not designed for uses outside of meeting the statutory requirements
+ A number of important risk factors are not modeled...– Credit
– FX rates
– Option implied volatilities
+ ... And there are also a number of technical limitations– No integration of equity and interest rate scenarios
– Correlation matrix between modeled indices is assumed constant
– Technical modeling limitations of equity and yield curve scenarios
+ Equity tail under-stated+ No arbitrage-free interest rate yield curve modeling
General tips and techniques for good scenario generation
General tips and techniques for good scenario generation (1)+ Integrated Approach – Consistent with good ERM,
scenario generation should model all risks within a single framework and recognize the interrelationships between risks
+ Flexibility - A more complex model isn’t necessarily a better model– It depends on the application. A consistent framework is needed that can be
applied across an organization, but you need flexibility and options to meet the requirements of the specific application (e.g., the modeling choices you make for daily hedging will be different to what you use for reserving)
– Also touches on “model risk” – depending on the application you may not want to rely on just one model (e.g., hedging)
General tips and techniques for good scenario generation (2)+ Transparency - A model is not a good model if it’s a
“black box”+ Dynamic assumptions – Many models fell down in 2008
because assumptions/correlations were static– Models generally overstated the level of diversification benefit that would be
available – in distressed markets, correlations approach 1.
General tips and techniques for good scenario generation (3)+ How much is enough? – A decision has to made as to
how many scenarios are enough– Depends on the application, and the company’s asset/liability profile
– AAA’s Modeling Efficiency Work Group – has identified many different potential techniques for building more “efficient” models, including usage of scenario reduction techniques
– Need to look at the actual metric you are calculating (not just at the scenarios) –calculate the standard error of that metric and identify the limiting point