Practical Aspects of Stochastic Modeling.pptx

SoA Stochastic Modelingfor Leading Edge Actuaries 1

Stochastic Modeling forLeading Edge Actuaries

Overview of the Practical Aspects ofStochastic Modeling

Ron Harasym MBA, CFA, FSA, FCIAVice-President & Chief Risk Officer


Outline of Presentation

Stochastic Modeling Defined.

What Stochastic Modeling is and isn’t.

Advantages and Limitations of Stochastic Modeling.

When Stochastic Modeling is Preferred.

Key steps in Stochastic Modeling

Conditional Tail Expectation & Examples

Recommended Practices

Final Thoughts


Stochastic Modeling - Definition

Stochastic [Greek stokhastikos: from stokhasts, diviner, fromstokhazesthai, to guess at, from stokhos, aim, goal.]

A stochastic model by definition has at least one randomvariable and deals explicitly with time-variable interaction.

A stochastic simulation uses a statistical sampling of multiplereplicates, repeated simulations, of the same model.

Such simulations are also sometimes referred to as MonteCarlo simulations because of their use of random variables.


Stochastic Modeling - What it is

A stochastic model is an imitation of a real world system. Animprecise technique that provides statistical estimates and notexact results.

Stochastic modeling serves as a tool in a company’s riskmeasurement toolkit to provide assistance in: Valuation, Forecasting, Solvency Testing Financial Reporting Product Design & Pricing Risk Management

Simulations are used when the systems being modeled are toocomplex to be described by a set of mathematical equations forwhich a closed form analytic solution is readily attainable.

Part art, part science, part judgement, part common sense.


Stochastic Modeling - And What it isn’t

Not a magical solution! One needs to:

Perform reality checks Understand strengths & limitations of the model

Results are not always intuitively obvious!

Often requires a different way of looking at problems, issues,results, and potential solutions.

Greater exposure to model risk and operational risks.


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 outcomesarising from different actions/strategies before implementation.

Can attempt to better understand properties of real world systemssuch as policyholder behavior.

Quantification of the benefit from risk diversification.

Coherent articulation of risk profiles.

Potential reserve and regulatory capital relief.


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 a estimate. May create a false sense of confidence - a false sense of

precision let alone a false sense of accuracy. 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 more difficult. Garbage in, Garbage out!


Stochastic modeling is Preferred overDeterministic Modeling When:

Product or Line of Business has a “cliff” or “tail” risk profile.

Risks are dependent and/or there is path dependence.

When dealing with skewed and/or discontinuous distributions/costfunctions.

Outcomes are sensitive to initial conditions.

There is significant volatility in the underlying variables.

Volatility or skewness of underlying variables is likely to changeover time.

There are real economic incentives, such as reserve or capitalrelief, to perform stochastic modeling.


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

Output

HistoricalEconomic Data

HistoricalPolicyholder

DataRandom Number

Generator

EconomicScenario

Generator (ESG)

Stochastic ESGParameters &Assumptions

PolicyholderInput Data

EconomicScenarios

Data Validation&

ESG CalibrationRandomNumbers

StochasticAsset / Liability

Models

Liability DataValidation

Deterministic &Stochastic Liability

Assumptions

Deterministic &Stochastic Asset

Assumptions

Result Tabulation,Validation, & Review

ReportedFinancial Results,Risk Management

Measures


Where does one Start? Key Steps Are ...

Identify the key issues, objectives and potential roadblocksbefore considering ways of solving the problem.

Articulate the process / model in general terms beforeproceeding to the specific.

Develop the model: assumptions, input parameters, data,output.

Fit the model: gather and analyze data, estimate inputparameters

Implement the model.

Analyze and test sensitivity of the model results & loop back.

Communicate the results.


Points to Keep in Mind!

Stochastic modeling is an evolutionary / revolutionary concept.

There must be a constant feedback loop.

Learn to “walk” before you “run”.

Recognize that no one model fits all solutions.

Be careful of becoming “married to the method”, rather than theobjective.

Keep it simple, keep it practical, keep it understandable.

Keep performing validation and reality checks throughout allmodeling steps.

Strive towards the production of actionable information!


Conditional Tail Expectation

Conditional Tail Expectation (CTE) is a conditional expected valuebased on downside risk.

CTE can be defined as the average of outcomes that exceed aspecified percentile.

The CTE(Q%) is calculated as the arithmetic average of the worst(100-Q)% results of the stochastic simulation.

For example: CTE(75%) is the arithmetic average of the worst25% of the results of the stochastic simulation.

CTE is considered to be a more robust measure with greaterinformation content than percentiles.

The CTE measure can also be “modified”.


Random Number Generator

Objective: To produce random numbers between 0 and 1

Issues: The Random Number Generator (RNG) is a foundation building block Critical, but often ignored/forgotten about! Poor RNG can compromise all post modeling sophistication Numerous RNGs to choose from

Desirable Characteristics to check for: Robustness independent of the seed number Periodicity Fast, efficient, & effective algorithm Other statistical tests (an internet search will provide many)


Economic Scenario Generator

Objective: To produce capital market or economic scenarios

Components: Drift, Diffusion, Correlation, …

Issues: Is the focus on the mean, median, or tail events? What metric is of concern? Economic vs. Statistical model, Arbitrage-Free vs. Equilibrium What is our calibration benchmark? Numerous ESGs to choose from

Desirable Characteristics to check for: Integrated model (equity, interest rate, inflation, currency) Incorporates the principle of parsimony. Flexible. A component approach.


Calibration of theEconomic Scenario Generator

Stability of the components over time Drift Stability versus Diffusion Stability versus Correlation Stability

Frequency of recalibration Historical data period versus forecast horizon

Selection of lead index Selection of starting regime if using a multiple regime model

Foreign exchange Issues Data sources and Caveat Emptor Approaches to fitting the data Risk-Return relationship False sense of precision and subjectivity


Example: Variable Annuity GMIB Rider

Product: Guaranteed Minimum Income Benefit Rider

Objective: Produce Measures for Financial Reporting Calculate Reserve & Capital Requirements

Nature of the Situation: Case #1: MV = $1.00B, GV = $1.40B (in-the-money) Case #2: MV = $2.75B, GV = $2.75B (at-the-money)

Mixture of policyholders 5% Roll-up rate per annum Conservative interest and mortality assumptions at time of product

pricing


Economic Scenario Generation

Economic Scenario Generator: Equity returns modeled using RSLN2 model Fixed Income returns modeled using Cox-Ingersol-Ross model Correlated Equity & Fixed Income Returns

Calibration Method: Maximum Likelihood Estimation

Calibration Issues: Data is limited and often inconsistent/incorrect. Insufficient effort is often given to data validation. Requires complex methods Historical data period versus forecast horizon Frequency of recalibration

Simulation: 1000 scenarios, monthly frequency,

30 year projection horizon


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%

Case #1:MV = $1.0B, GV = $1.4B (in-the-money)


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



CTE Percentile100% -$481.9 -$481.995% -$247.9 -$164.090% -$187.6 -$97.585% -$151.4 -$64.280% -$126.7 -$42.275% -$107.3 -$18.370% -$90.6 $1.765% -$76.4 $15.160% -$64.3 $24.355% -$54.0 $32.850% -$45.0 $38.045% -$37.2 $44.640% -$30.1 $50.135% -$23.8 $54.030% -$18.1 $56.925% -$13.0 $60.120% -$8.3 $65.215% -$3.8 $70.810% $0.5 $76.25% $4.8 $88.30% $9.7 $137.6

CTE & Percentiles: GMIB Case #2

Stochastic Simulation Results

Present Value of GMIB Rider Cash Flows

Assumptions:

Expected equity return = 8% per annumExpected long term interest yield = 6%Number of Scenarios = 1,000

Expected Value or Average

Median or 50th Percentile

Maximum Value

MaximumValue

MinimumValue


PV of GMIB Rider Cash Flows: Distribution of Stochastic Results

0%

5%

10%

15%

20%

25%

30%

35%

-$500 -$450 -$400 -$350 -$300 -$250 -$200 -$150 -$100 -$50 $0 $50 $100 $150

Prob

abilit

y

CTE(0%)

50th Percentile

Assume Reserve isset at CTE(70%)CTE(95%)

Capital

$0

Reserve

Total Gross CalculatedRequirement

Maximum

CTE & Percentiles: GMIB Case #2


Sensitivity/Stress Testing

Quantifies the impact of an immediate change in anassumption or variable.

Useful for validation of the model with respect to individualassumptions

Also a check on the modeled variable interactions

Allows one to identify and thereby direct more effort on keyassumptions or variables.


GMIB CTE Measures: Liability Assumption Sensitivity Testing

$0

$50

$100

$150

$200

$250

$300 B

ase

Cas

e

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

%

Po

st-A

nn

Mo

rt D

ecr

10%

Lap

se R

ate

x2

Lap

se R

ate

x0.5

An

nu

itiz

atio

n R

ate

x2

An

nu

itiz

aio

n R

ate

x0.5

CTE(95%)

CTE(90%)

CTE(80%)

CTE(70%)

CTE(60%)

CTE(0%)

BaseCase



GMIB CTE Measures: Investment Assumption Sensitivity Testing

$0

$50

$100

$150

$200

$250

$300 B

ase

Cas

e

Eq

uit

y R

etu

rn =

10%

Eq

uit

y R

etu

rn =

9%

Eq

uit

y R

etu

rn =

7%

Eq

uit

y R

etu

rn =

6%

LT

Yie

ld =

8%

LT

Yie

ld =

7%

LT

Yie

ld =

5%

LT

Yie

ld =

4%

CTE(95%)

CTE(90%)

CTE(80%)

CTE(70%)

CTE(60%)

CTE(0%)

BaseCase



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.

Focus on accuracy first, precision second.

Add complexity on a cost/benefit basis.

Don’t ignore data validation and model validation procedures.

Continually perform reality checks.

Constantly loop back through the process.


Other Issues to Wrestle With:

Some model set-ups generate more volatility in results thanothers. How do we choose between them?

How do we perform calibration and parameter estimation?

How do we capture the correlations between markets.

How many scenarios do we use?

How do we model policyholder behaviour?

How do we incorporate hedging in the model?


Finally, Where Are We Going … ???

Will stochastic modeling change the way the insurance industryconducts business?

What will be the impact of the recent acceptance/application ofstochastic modeling within the next 1, 5, 10+ years?

How will stochastic modeling alter/impact pricing, productdevelopment, and valuation / risk management practices &procedures?

Even closer to home, how will stochastic modeling impact theeducational experience and skill requirements of current andfuture actuaries?


Wrap-Up

Questions & Answers!

Practical Aspects of Stochastic Modeling.pptx

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