CIA Annual Meeting Assemblée annuelle de l’ICA

1. CIA Annual MeetingAssemblée annuelle de l’ICA June 29 & 30, 2006 Ÿ Les 29 et 30 juin 2006 Ottawa, Ontario INSURANCE PRICING HOT TOPICS

2. CIA Annual Meeting ŸAssemblée annuelle de l’ICA INSURANCE PRICING HOT TOPICS Session IND – 4 June 29 – 30, 2006 Ron Harasym FSA, FCIA

3. 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 CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

4. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

5. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

6. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

7. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

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, 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! CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

9. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

10. 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! CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

11. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

12. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

13. 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! CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

14. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

15. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

16. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

17. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

18. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

19. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

20. 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. CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

21. 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! CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

22. 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? CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA

23. 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? CIA Annual Meeting ŸAssemblée annuelle de l’ICA Stochastic Modeling Ron Harasym FSA, FCIA