The document provides an overview of stochastic modeling in the financial reporting world. It discusses (1) the definition and purpose of stochastic modeling, including its use for product design, forecasting, and risk management; (2) a generic modeling framework that involves economic scenario generation, random number generation, and stochastic modeling of assets and liabilities; and (3) an example of stochastic modeling of a guaranteed minimum income benefit rider to calculate reserve and capital requirements under different economic scenarios.

1. 1
Stochastic Modeling
In The Financial Reporting World
Ron Harasym
AVP Financial Risk Management
TS 68
Society of Actuaries
2003 Washington DC Spring Meeting
2
Presentation Outline
I. Overview of Stochastic Modeling
II. A Generic Modeling Framework
III. Random Number Generation
IV. Economic Scenario Generation
V. Stochastic Modeling of a GMIB Rider
VI. Model Results & Sensitivity Testing
VII. Reserve & Capital Relief
VIII. Final Thoughts

2. 2
3
I. Overview of Stochastic Modeling
4
Stochastic Modeling - Definition
• Stochastic [Greek stokhastikos, from stokhasts, diviner, from
stokhazesthai, to guess at, from stokhos, aim, goal.]
• A stochastic model by definition has at least one random variabl e
and deals explicitly with time-variable interaction.
• A stochastic simulation uses a statistical sampling of multiple
replicates, repeated simulations, of the same model.
• Such simulations are also sometimes referred to as Monte Carlo
simulations because of their use of random variables.

3. 3
5
Stochastic Modeling - What it is
• A stochastic model is an imitation of a real world system. An
imprecise technique and that provides only statistical estimates
and not exact results.
• Stochastic modeling serves as a tool in a company’s risk
measurement toolkit to provide assistance in:
• Product Design & Pricing
• Forecasting
• Financial Reporting
• Risk Management
• Simulations are used when the systems being modeled are too
complex to be described by a set of mathematical equations for
which a closed form analytic solution is readily attainable.
• Part art, part science, part judgement, part common sense.
6
Stochastic Modeling - And What it isn’t
• Not a magical solution!
• Need to perform reality checks.
• Need to understand model limitations.

4. 4
7
Advantages of Stochastic Modeling
• Systems with long time frames can be studied in compressed time.
• Able to assist in decision making and to quantify future outcomes
arising from different actions/strategies before implementation.
• Can attempt to better understand properties of real world systems
such as policyholder behavior.
• Potential reserve and regulatory capital relief.
• Pick-up on diversification benefits.
• You can watch your company fail over and over again!
8
Limitations of Stochastic Modeling
• Requires a considerable investment of time and expertise.
• Technically challenging, computationally demanding.
• Reliance on a few “good” people.
• For any given set of inputs, each scenario gives only estimates of
the model’s outputs.
• May create a false sense of confidence - a false sense of precision.
• Relies heavily on data inputs and the identification of variable
interactions.
• It is not possible to include all future events in a model.
• Results may be difficult to interpret.
• Effective communication of results may be even harder.
• Garbage in, Garbage out!

5. 5
9
Stochastic Modeling is Preferred over
Deterministic Modeling When:
• Risks are dependent.
• When dealing with skewed and/or discontinuous
distributions/cost functions.
• There is significant volatility in the underlying variables.
• Outcomes are sensitive to initial conditions.
• There is path dependence.
• Volatility or skewness of underlying variables is likely to change
over time.
• There are real economic incentives, such as reserve or capital
relief, to perform stochastic modeling.
10
II. A Generic Modeling Framework

6. 6
11
Is There Really A Starting and Ending Point? … No!
Output
Historical
Economic Data
Historical
Policyholder
Data
RandomNumber
Generator
Economic
Scenario
Generator (ESG)
StochasticESG
Parameters &
Assumptions
Policyholder
Input Data
Economic
Scenarios
Data Validation
&
ESG Calibration
Random
Numbers
Stochastic
Asset / Liability
Models
Liability Data
Validation
Deterministic &
StochasticLiability
Assumptions
Deterministic &
Stochastic Asset
Assumptions
Result Tabulation,
Validation, & Review
Reported
Financial Results,
RiskManagement
Measures
12
Where does one Start? Key Steps Are ...
• Identify the key objectives and potential roadblocks before
considering ways of solving the problem.
• Identify key issues and potential road blocks.
• Describe the process/model in general terms before proceeding to
the specific.
• Develop the model: assumptions, input parameters, data, output.
• Fit the model: gather and analyze data, estimate input
parameters
• Implement the model.
• Analyze and test sensitivity of the model results.
• Communicate the results.

7. 7
13
Points to Keep in Mind.
• Stochastic modeling is an evolutionary process.
• Learn to “walk” before you “run”.
• Recognize that no one model fits all solutions.
• Be careful of becoming married to the method, rather than the
objective.
• Keep it simple, keep it practical, keep it understandable.
• Keep performing validation and reality checks throughout all
modeling steps.
• Strive towards the production of actionable information.
14
III. Random Number Generation

8. 8
15
Random Number Generator (RNG)
• Objective:
• To produce random numbers between 0 and 1
• Issues:
• The RNG is a foundation building block
• Critical, but often ignored/forgotten about!
• Poor RNG can compromise all post modeling sophistication.
• Many RNGs to choose from.
• Desirable Characteristics to check for:
• Robustness independent of the seed number
• Periodicity
• Independence
• Fast, efficient, & effective algorithm
• Other statistical tests
16
IV. Economic Scenario Generation

9. 9
17
Economic Scenario Generator
• Objective:
• To produce capital market or economic scenarios
• Issues:
• Outputs determined by end requirements.
• Economic vs. Statistical model
• Arbitrage-Free vs. Equilibrium
• Calibration.
• Is the focus on the mean, median, or tail events?
• Many Economic Scenario Generators to choose from.
• Desirable Characteristics to check for:
• Integrated model (equity, interest rate, inflation, currency)
• Incorporates the principle of parsimony.
• Flexible. A component approach with variable modes.
18
VI: Stochastic Modeling of a GMIB Rider

10. 10
19
A Practical Example
• Product:
• Guaranteed Minimum Income Benefit Rider
• Objective:
• Produce Measures for Financial Reporting
• Calculate Total Balance Sheet Requirement (TBSR)
• Calculate Reserve & Capital Requirements
• Nature of the Situation:
• GMIB Guaranteed Account Value of $1.4B
• Market Account Value of $1.0B
• 5% Roll-up rate per annum
• Conservative interest and mortality assumptions in pricing
20
Economic Scenario Generation
• Economic Scenario Generator:
• Equity returns modeled using RSLN2 model
• Fixed income returns modeled using Cox-Ingersol-Ross model
• Calibration Method:
• Maximum Likelihood Estimation
• Calibration Issues:
• Data is limited and often inconsistent/incorrect.
• Insufficient effort is often not given to data validation.
• Requires complex methods
• Historical data period vs. forecast horizon
• Frequency of re-calibration
• Simulation:
• 1000 scenarios, monthly frequency, 35 year projection horizon

11. 11
21
VII. Model Results & Sensitivity Testing
22
Conditional Tail Expectation: CTE(%)
• CTE is a conditional expected value based on downside risk.
• CTE can be defined as the average of outcomes that exceed a
specified percentile.
• The CTE(Q%) is calculated as the weighted-average of the worst
(100-Q)% results of the stochastic simulation.
• CTE is considered to be a more robust measure than percentiles.

12. 12
23
Stochastic Simulation Results:
• Recall
• GMIB Guaranteed Account Value of $1.4B
• Market Account Value of $1.0B
CTE GMIB ($millions)
95% $204.3
90% $177.2
80% $145.8
75% $133.9
70% $123.8
65% $114.9
60% $106.9
0% $43.4
24
(Negative) PV of GMIB Cash Flow by CTE
$0
$50
$100
$150
$200
$250
$300
$350
$400
$450
0% 20% 40% 60% 80% 100%
Conditional Tail Expectation ( % )
Base Case
Equity Return = 6%
Lapse Rate x0.5
PV of GMIB Cash Flow by Percentile
-$300
-$250
-$200
-$150
-$100
-$50
$0
$50
0% 20% 40% 60% 80% 100%
Percentile (%)
Base Case
Equity Return = 6%
Lapse Rate x0.5

13. 13
25
Present Value vs. Average Interest Rate per Scenario Scatter Plot
Stochastic Base Case: Target Equity Return = 8%, Target Interest Rate = 6%
2%
4%
6%
8%
10%
12%
-$300 -$250 -$200 -$150 -$100 -$50 $0 $50 $100
AverageInterestRateoverProjectionHorizon
2%
4%
6%
8%
10%
12%
26
Present Value vs. Average Equity Return per Scenario Scatter Plot
Stochastic Base Case: Target Equity Return = 8%, Target Interest Rate = 6%
-5%
0%
5%
10%
15%
20%
25%
-$300 -$250 -$200 -$150 -$100 -$50 $0 $50 $100
AverageEquityReturnoverProjectionHorizon

14. 14
27
Sensitivity Testing
• Quantifies the impact of an immediate change in an assumption or
variable.
• Useful for validation of the model. A check on the modeled variable
interactions
• Allows one to identify and there by direct more effort on key
assumptions or variables.
• GMIB Observations:
• Results are highly sensitive to the lapse and annuitization
assumptions.
• Results are moderately sensitive to the interest rate and the
equity return assumptions.
28
GMIB CTE Measures: Liability Assumption Sensitivity Testing
$0
$50
$100
$150
$200
$250
$300
BaseCase
RiderCharge-10bps
CurrentPricing
Spread-10bps
Pre-AnnMortDecr
10%
Post-AnnMortDecr
10%
LapseRatex2
LapseRatex0.5
AnnuitizationRatex2
AnnuitizaionRate
x0.5
CTE(95%)
CTE(90%)
CTE(80%)
CTE(70%)
CTE(60%)
CTE(0%)
Base
Case

15. 15
29
GMIB CTE Measures: Investment Assumption Sensitivity Testing
$0
$50
$100
$150
$200
$250
$300
BaseCase
EquityReturn=10%
EquityReturn=9%
EquityReturn=7%
EquityReturn=6%
LTYield=8%
LTYield=7%
LTYield=5%
LTYield=4%
CTE(95%)
CTE(90%)
CTE(80%)
CTE(70%)
CTE(60%)
CTE(0%)
Base
Case
30
VIII. Reserve & Capital Relief

16. 16
31
Why Perform Stochastic Modelling?
• AAA capital recommendations and MMMM promote the use of
stochastic approaches.
• Proposed changes to US GAAP reserving for GMDB and GMIB
benefits also promote the use stochastic approaches.
• Canadian MCCSR requirements favor the use of stochastic
approaches.
32
IX. Final Comments & Other Issues

17. 17
33
Recommended Practices
• Keep focused on the business objectives.
• No one model fits all. Best to understand fundamentals.
• Cultivate “best practices”. Keep it simple and practical.
• Don’t use a sledgehammer to crack a walnut.
• Focus on accuracy first, precision second.
• Add complexity on a cost/benefit basis.
• Perform reality checks.
• Don’t ignore model and data validation procedures.
• Avoid the creation of “black boxes”.
• Constantly loop back through the process.
34
Other Issues to Wrestle With
• Some models generate more volatility in results than others. How
do we choose between them?
• How do we perform calibration and parameter estimation?
• How do we model fixed-income returns.
• How do we capture the correlations between markets.
• How many scenarios do we use?
• How do we model policyholder behavior?
• How do we incorporate hedging in the model?

18. 18
35
Thank-you for attending!