1

Financial Model Risks

Tony Dardis

June 26 2009

Agenda

+ How well did your financial model do in 2008?+ Lessons learned?+ General tips and techniques for good scenario generation

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How well did your financial model do in 2008?

Global Interest Rates: Gov. Bond Yields

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-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

GBP USD EUR J PY

10 y

ear

Spot

Rat

es

-Gov

ern

ment Bon

ds

End Sep 2008

End Dec 2008

Changes

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

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5.00

GBP USD EUR J PY

30 y

ear

Spot

Rat

es

-Gov

ern

ment Bon

ds

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%

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-10%

0%

GBP USD EUR JPY

Equi

ty m

arke

t re

turn

(Yea

r 20

08)

Global Equity Markets

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+ 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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dit S

prea

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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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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

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+ 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

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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

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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

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3-month rate10-yr spot rate

Lessons learned?

Lessons learned?

+ Areas that you may wish to revisit in your 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

Equity fat tails and skew

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0.0%

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-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

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-50%

-45%

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Excess log-return (Asset 1)E

xc

es

s lo

g-r

etu

rn (

As

se

t 2

)

0.1% percentile

1% percentile

= 0.64

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Excess log-return (Asset 1)

Ex

ce

ss

log

-re

turn

(A

ss

et

2)

0.1% percentile

1% percentile

= 0.64

Credit risk

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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 process

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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

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Delta-Hedging and Gamma Losses in Recent Market Environment

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Real-world projection of option-implied volatility: Vega Risk

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+ 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

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Maturity

Strike

Model Volality Surface

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Proba

bility

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Implied Volatility

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UK

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Germany

France

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Maturity

Strike

Model Volality Surface

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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

General tips and techniques for good financial risk modeling

General tips and techniques for good financial risk modeling (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 financial risk modeling (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 financial risk modeling (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

– American Academy of Actuaries’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