1

Stochastic Modeling In The Financial Reporting World

Ron HarasymAVP Financial Risk Management

TS 68Society 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

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 Carlosimulations because of their use of random variables.

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 estimatesand 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

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 variableinteractions.

• 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

9

Stochastic Modeling is Preferred overDeterministic 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

11

Is There Really A Starting and Ending Point? … No!

Output

HistoricalEconomic Data

HistoricalPolicyholder

Data

Random NumberGenerator

EconomicScenario

Generator (ESG)

Stochastic ESGParameters &Assumptions

PolicyholderInput Data

EconomicScenarios

Data Validation&

ESG Calibration

RandomNumbers

StochasticAsset / Liability

Models

Liability DataValidation

Deterministic &Stochastic Liability

Assumptions

Deterministic &Stochastic Asset

Assumptions

Result Tabulation,Validation, & Review

ReportedFinancial Results,Risk Management

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 tothe 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

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

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

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

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

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

23

Stochastic Simulation Results:

• Recall• GMIB Guaranteed Account Value of $1.4B• Market Account Value of $1.0B

CTE GMIB ($millions)

95% $204.390% $177.2

80% $145.875% $133.970% $123.865% $114.960% $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

25

Present Value vs. Average Interest Rate per Scenario Scatter PlotStochastic 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

Ave

rag

e In

tere

st R

ate

ove

r P

roje

ctio

n H

ori

zon

2%

4%

6%

8%

10%

12%

26

Present Value vs. Average Equity Return per Scenario Scatter PlotStochastic 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

Ave

rag

e E

qu

ity

Ret

urn

ove

r P

roje

ctio

n H

ori

zon

14

27

Sensitivity Testing

• Quantifies the impact of an immediate change in an assumption orvariable.

• 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

Bas

e C

ase

Rid

er C

har

ge

-10

bp

s

Cu

rren

t P

rici

ng

Sp

read

-10

bp

s

Pre

-An

n M

ort

Dec

r10

%

Pos

t-A

nn M

ort

Dec

r10

%

Lap

se R

ate

x2

Lap

se R

ate

x0.5

Ann

uitiz

atio

n R

ate

x2

Ann

uitiz

aion

Rat

ex0

.5

CTE(95%)

CTE(90%)

CTE(80%)

CTE(70%)

CTE(60%)

CTE(0%)

BaseCase

15

29

GMIB CTE Measures: Investment Assumption Sensitivity Testing

$0

$50

$100

$150

$200

$250

$300

Bas

e C

ase

Equ

ity R

etur

n =

10%

Equ

ity R

etur

n =

9%

Equ

ity R

etur

n =

7%

Equ

ity R

etur

n =

6%

LT Y

ield

= 8

%

LT Y

ield

= 7

%

LT Y

ield

= 5

%

LT Y

ield

= 4

%

CTE(95%)

CTE(90%)

CTE(80%)

CTE(70%)

CTE(60%)

CTE(0%)

BaseCase

30

VIII. Reserve & Capital Relief

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

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

35

Thank-you for attending!