CIA Annual Meeting Assemblée annuelle de l’ICA

CIA Annual MeetingAssemblée annuelle de l’ICA

June 29 & 30, 2006 Ÿ Les 29 et 30 juin 2006Ottawa, Ontario

INSURANCE PRICING HOT TOPICS

CIA Annual Meeting Ÿ Assemblée annuelle de l’ICA

INSURANCE PRICING HOT TOPICS

Session IND – 4

June 29 – 30, 2006

Ron Harasym FSA, FCIA

Agenda: Stochastic Modeling Fundamentals: Stochastic Modeling Defined

What Stochastic Modeling It Is and Isn’t

Advantages & Limitations of Stochastic Modeling

When Stochastic Modeling is Preferred

Key steps in Stochastic Modeling

Points to Keep in Mind

Other Issues to Wrestle With

Final Thoughts & Where We Are Going

Stochastic Modeling Ron Harasym FSA, FCIA


Stochastic Modeling Defined: 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 variable 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.



Stochastic Modeling – What it is! A stochastic model is an imitation of a real world system balancing

precision and accuracy.

A technique that provides statistical estimates and not necessarily exact results.

Stochastic modeling serves as a tool in a company’s risk measurement toolkit.

Pricing & Product Design, Valuation, Capital & Solvency Testing, Forecasting, Risk Management

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



Stochastic Modeling – What it isn’t! Not a magical solution! One needs to:

Continually 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 risk.



Advantages of Stochastic Modeling: Systems with long time frames can be studied in compressed time.

Able to assist in decision making before implementation.

Can attempt to better understand properties of real world systems such 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, may create a false sense of confidence - a false sense of precision let alone accuracy.

Each scenario gives only a estimate. Results rely heavily on data inputs and the identification of variable interactions.

Results may be difficult to interpret. Effective communication of results may be even more difficult.

Garbage in, Garbage out!



When Stochastic Modeling is Preferred: When the interactions being modeled are too complex for which a

closed form analytic solution is readily attainable.

When dealing with risk that is skewed, discontinuous, dependent, path dependent, or of a cliff / tail profile.

Outcomes are sensitive to initial conditions.

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.



Key Steps in Stochastic Modeling: Identify the key issues, objectives, and potential roadblocks before

considering ways of solving the problem.

Articulate the process / model in general terms before proceeding to the specific.

Develop, Fit, and Implement the model.

Analyze and test the sensitivity of the model results. Constantly keep looping back through the process.

Communicate the results.

All in all, a dynamic, fluid, and constantly evolving process!



Points to Ponder in Stochastic Modeling:

Example #1: Calibration of Economic Scenario Generators The issue is the adjustment of model parameters calibrated to historical

data in order to better reflect future realities.

Example #2: Model Risk & Exposure to Sampling Error

The issue is how does one recognize and deal with the convergence of simulation results.



Example #1: Calibration of Economic Scenario Generators Objective:

To produce capital market or economic scenarios

Questions to ask:

Is the focus on the mean, median, or tail events?

Economic vs. Statistical model, Arbitrage-Free vs. Equilibrium model

Calibration

Desirable Characteristics to check for:

Incorporates the principle of parsimony

Flexible & Integrated. A component approach.



Other Considerations: Stability of the components over time

Drift Stability versus Diffusion Stability

Calibration

Historical data period versus forecast horizon

Frequency of recalibration

Data sources – Caveat Emptor!

Approaches to fitting the data & Risk-Return relationship

False sense of precision and subjectivity – Caveat Venditor!





Example of a Fitting a Risk-Return Relationship

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

0% 5% 10% 15% 20% 25% 30%

Standard Deviation (annualized)

Eff

ect

ive

An

nu

al R

etu

rn

Indicies

Risk-Return Frontier

Adjusted Indices

Fit through the primary index

Example #2: Model Risk & Exposure to Sampling Error A significant risk inherent in stochastic modeling is the exposure to

sampling error.

The CIA 2002 Task Force report on the modeling of segregated fund liabilities indicates (section 2.1.2):

"Note that it is the model which must pass the calibration tests, not the actual scenarios used for valuation. It is important to emphasize that a calibrated model used with parameters estimated from data series different from the prescribed dataset (i.e., different market and/or historical period) will produce scenarios that may or may not meet the calibration criteria."

Thus, the calibration requirement applies to the model and not to the scenarios used for valuation.





Percentage Error from Base under Various Scenario Sets

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%1

- 10

000

1 -

1000

1001

- 2

000

2001

- 3

000

3001

- 4

000

4001

- 5

000

5001

- 6

000

6001

- 7

000

7001

- 8

000

8001

- 9

000

9001

- 1

0000

Scenario Set

% E

rro

r

CTE(95) CTE(80) CTE(60) CTE(0)

Note: Assume 10,000 scenarios produce the correct result. Ii.e. Base = 1-10000 scenario set.

One Possible Solution: Use of Representative Scenarios Stochastic modeling is computationally intensive.

Variance reduction techniques, converge on the mean of the distribution efficiently, but compromise the distribution of the risk factors in the process.

The information content of the “tail” may no longer be credible.

Article in the July 2002 NAAJ, written by Yvonne Chueh, details the use of representative scenario techniques for interest rate sampling.

2003 CIA Stochastic Symposium article, Efficient Stochastic Modeling Utilizing Representative Scenarios: Application to Equity Risks, written by Alastair Longley-Cook, details use for equity scenario sampling.





Percentage Error from Base under Various Representative Scenario Sets

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%1

- 10

000

Rep

500

0

Rep

250

0

Rep

200

0

Rep

125

0

Rep

100

0

Rep

625

Rep

500

Rep

400

Rep

250

Rep

200

Rep

125

Rep

100

Scenario Set

% E

rro

r

CTE(95) CTE(80) CTE(60) CTE(0)

Note: Assume 10,000 scenarios produce the correct result. i.e. Base = 1-10000 scenario set.

Advantages of Representative Scenarios: Allows for a reduction in scenario sample size while preserving the

probability distribution.

May reduce, but does not eliminate, sampling error.

Scenario reduction algorithms can be independent of the form of the scenario generator and the asset/liability models.

Assists in sensitivity testing.

A quick way of estimating tail risk when pressed for time.



Limitations of Representative Scenarios: Some algorithms involve the estimation of the present value or future

value of a stream of cash flows.

May result in different representative scenario sets for different products – limits direct comparison of results.

When a metric is developed to measure similarity or dissimilarity between scenario paths, the continuity property is desirable.

The continuity means that if two paths are close in the domain of a function, the corresponding function outputs will be similar.

The condition is difficult to verify or satisfy due to its mathematical complexity.

In some case, sampling errors could be just too significant to provide a reasonable replication of the true distribution.



Points to Keep in Mind: Learn to “walk” before you “run”.

Recognize that no one model fits all solutions.

Be careful of becoming “emotionally married to the method” as losing cognitive awareness of 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!



Other Issues to Wrestle With: Some model set-ups generate more volatility in results than others.

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 deal with sampling error?

How do we model policyholder behaviour?

How do we incorporate hedging in the model?



Final Thoughts & Where We Are Going: Will stochastic modeling change the way we conduct business?

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

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

Even closer to home, how will stochastic modeling impact the educational experience and skill requirements of current and future actuaries?



Documents

CIA Annual Meeting Assemblée annuelle de l’ICA