Transcript CIA Pension Seminar

CIA Annual Meeting
Assemblée annuelle de l’ICA
June 29 & 30, 2006  Les 29 et 30 juin 2006
Ottawa, Ontario
INSURANCE PRICING HOT TOPICS
CIA Annual Meeting  Assemblée annuelle de l’ICA
INSURANCE PRICING HOT TOPICS
Session IND – 4
June 29 – 30, 2006
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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
CIA Annual Meeting  Assemblée annuelle de l’ICA
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
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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!
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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!
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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!
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
Example of a Fitting a Risk-Return Relationship
18%
16%
Fit through the primary index
Effective Annual Return
14%
12%
10%
8%
Indicies
6%
Risk-Return Frontier
4%
Adjusted Indices
2%
0%
0%
5%
10%
15%
20%
Standard Deviation (annualized)
Stochastic Modeling
Ron Harasym FSA, FCIA
25%
30%
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
Percentage Error from Base under Various Scenario Sets
25%
20%
Note: Assume 10,000 scenarios
produce the correct result. I
i.e. Base = 1-10000 scenario set.
15%
% Error
10%
5%
0%
-5%
-10%
-15%
Scenario Set
CTE(95)
Stochastic Modeling
CTE(80)
CTE(60)
Ron Harasym FSA, FCIA
CTE(0)
9001 - 10000
8001 - 9000
7001 - 8000
6001 - 7000
5001 - 6000
4001 - 5000
3001 - 4000
2001 - 3000
1001 - 2000
1 - 1000
1 - 10000
-20%
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
Percentage Error from Base under Various Representative Scenario Sets
25%
20%
Note: Assume 10,000 scenarios
produce the correct result. i.e.
Base = 1-10000 scenario set.
15%
% Error
10%
5%
0%
-5%
-10%
-15%
Scenario Set
CTE(95)
Stochastic Modeling
CTE(80)
CTE(60)
Ron Harasym FSA, FCIA
CTE(0)
Rep 100
Rep 125
Rep 200
Rep 250
Rep 400
Rep 500
Rep 625
Rep 1000
Rep 1250
Rep 2000
Rep 2500
Rep 5000
1 - 10000
-20%
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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.
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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!
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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?
Stochastic Modeling
Ron Harasym FSA, FCIA
CIA Annual Meeting  Assemblée annuelle de l’ICA
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?
Stochastic Modeling
Ron Harasym FSA, FCIA