1. 2007 Annual Meeting ● Assemblée annuelle 2007 Vancouver
Canadian
Institute of
Actuaries
L’Institut canadien
des
actuaires
2007 Annual Meeting ● Assemblée annuelle 2007
Vancouver

2. Stochastic Scenario Development for Inexperienced Users
IP-41 Stochastic Modeling for Insurance Products
Stochastic Scenario Development for Inexperienced Users
Julia Wirch-Viinikka
Investment Products Pricing
Assemblée annuelle 2007
2007 Annual Meeting

3. Stochastic Tools Objectives and Constraints Scenario Generators
Start Simple:
Fixed Income Scenarios
Equity Scenarios
Picking a model:
Key Considerations
Calibration
What can go wrong?
Assemblée annuelle 2007
2007 Annual Meeting

4. Is stochastic modeling going to give you a better answer?
What is your objective?
Appropriate Pricing (Products/Derivs)
Variability and Risk Management
Duration, Convexity, Hedging
Aggregation across products
Reserve and capital calculation (tail results)
What are your constraints?
Time, computation power
Analysis of results
Expertise
What will you do with the results?
Assemblée annuelle 2007
2007 Annual Meeting

5. When is Stochastic Important?
Models are dependent on
Highly variable random variables
Complex correlations/ dependency structures
Models are highly sensitive to assumptions and RVs
Asymmetry of Results
Optionality / one extreme tail
Low Frequency, High Severity
Fat tailed distribution
Systematic/Non-diversifiable Risk
Assemblée annuelle 2007
2007 Annual Meeting

6. P’s and Q’s: Stochastic Etiquette
P: Real World Probability
Often based on economic theories and statistical data
Historical data provides long-term averages
Full distribution of possible outcomes
Used for cash flow projection, tail events
Q: Risk Neutral Probability
Replicates current market prices & implied volatilities
No Arbitrage “free lunch”
Only the mean has significance
Used to price financial instruments, where investors hedge risk and require no risk premium
Assemblée annuelle 2007
2007 Annual Meeting

7. RN vs RW? Tail risk: Average cost: EXAMPLES:
Use real-world valuation to measure tail risk
Average cost:
Use “real world” inputs when you are willing to accept the “average” result with a high amount of variability
Use risk neutral when you want results (e.g. a price or a profit measure) which you can be very confident can be realized (through hedging)
EXAMPLES:
Hedging (Financial Engineering)
Market-consistent pricing - RN
Risk Management, Valuation and Pricing (Actuarial Modeling)
Tail exposures – RW
Volatility - RW
Averages – RW/RN
Static Hedging - RN
Dynamic Hedging – RW/RN
Assemblée annuelle 2007
2007 Annual Meeting

8. Traditional Actuarial Stochastics
Wilkie (Cascade Structure)
Factor Models
More recent addition:
RSLN-2:
Assemblée annuelle 2007
2007 Annual Meeting
REGIME 1
Low Volatility s1
High Mean m1
Correlation r1
Introduced by J D Hamilton in 1989.
Increasing popularity in econometrics.
Another actuarial version – G Harris, ASTIN 29; quarterly multivariate model.
Semi-markov versions also exist
REGIME 2
High Volatility s2
Low Mean m2
High Correlation r2

9. Interest Rate Models Yield Curve General Characteristics
Spot / Yield / Forward curves
Starting yield curve
How many key rates do you need?
How to fill in the rest of the yield curve?
General Characteristics
Initial yield curve should match actual
Mean Reversion (to a non-fixed target rate)
Long Periods of Relative Stability
Range of Shapes (Normal, Inverted, Humped)
Correlation between maturities and with Inflation
Non-negative
No exploding rates
Assemblée annuelle 2007
2007 Annual Meeting

10. A Few Models Assemblée annuelle 2007 2007 Annual Meeting
Mean Reversion
DRIFT: (Long-term mean – Current rate) dt
Hull & White (Vasicek with time dep params):
dr=theta(a(t)-r)dt+v(t)dz
Non-Negative
RANDOM TERM: volatility * sqrt(current rate) dz
CIR: dr=theta(a-r)dt+v sqrt(r) dz
As interest rates go toward zero, the random term diminishes and the interest rate is pulled up toward the long term average
Easier Calibration
BDT: mean reverting with lognormal distribution (mutually dependent mean reversion and volatility terms):
d(ln r)=(a(t)+(v’(t)/v(t))ln r)dt + v(t) dz
Black-Karasinski: Lognormal – indep parameters (like BDT)
HJM: generalization - any volatility function
Easier to parameterize when vol is indep of the forward rate
Market Models
More flexible: separation of risk between volatility and correlation
Assemblée annuelle 2007
2007 Annual Meeting

11. Yield Curve vs. Equity Are they related? However…
Direct relation shows zero correlation
However…
Bond Funds and Equity Indices show 30%-60% correlation
Duration analysis can explain 90%+ of bond fund returns:
an( int – int-1) = Bond Fund Return (t-1,t)
Assemblée annuelle 2007
2007 Annual Meeting

12. What to watch out for: Random Number Generators:
Are they really random? Do they generate enough variables before repeating?
Do you have Enough Scenarios?
Representative Sampling
Variance Reduction Techniques only helps you get a quicker estimate of the mean.
Test robustness on much larger sample size
Especially important for tail measures
Are your Parameters Right?
Validation and Recalibration
Assemblée annuelle 2007
2007 Annual Meeting

13. Enough Scenarios? Convergence / Sampling error
Variance Reduction Techniques may help
Many techniques work for averages not tails
Assemblée annuelle 2007
2007 Annual Meeting

14. Histograms & Box Plots Stochastic Results Assemblée annuelle 2007
2007 Annual Meeting
Stochastic Results +
Maximum
75th Percentile
Median
25th Percentile
Minimum
Outliers

15. The Small Print
Model risk: the possibility of loss or error resulting from the use of models.
Model misspecification
Assumption misspecification
Inappropriate use or application
Inadequate testing, validation, and documentation
Lack of knowledge or understanding, user and/or management
Error and negligence
Beware: Often there is a false sense of precision
Assemblée annuelle 2007
2007 Annual Meeting

16. Assemblée annuelle 2007
2007 Annual Meeting
Questions?