2007 Annual Meeting ● Assemblée annuelle 2007 Vancouver Canadian Institute of Actuaries L’Institut canadien des actuaires 2007 Annual Meeting ● Assemblée annuelle 2007 Vancouver

IP-41 Stochastic Modeling for Insurance Products Assemblée annuelle 2007 2007 Annual Meeting IP-41 Stochastic Modeling for Insurance Products

That which is static and repetitive is boring That which is static and repetitive is boring. That which is dynamic and random is confusing. In between lies art. John A. Locke Assemblée annuelle 2007 2007 Annual Meeting

What is Stochastic Modeling? A process whereby different scenarios are generated by a random process and used in a model to approximate real world results Assemblée annuelle 2007 2007 Annual Meeting

What is Stochastic Modeling? A process whereby different scenarios are generated by a random process and used in a model to approximate real world results Deterministic scenario testing on steroids!!! Assemblée annuelle 2007 2007 Annual Meeting

Why Stochastic Modeling? It enables the user to see model results under a wide variety of scenarios intended to reflect real life It shows the distribution of possible outcomes including extreme results. Analysis of individual scenarios can provide insights into the interaction of the product with real world processes. It allows analysis into the impact of risk mitigation and diversification strategies. Assemblée annuelle 2007 2007 Annual Meeting

Why Stochastic Modeling? Financial markets are inherently volatile and do not move in a straight line. True cost of some product design features can only be determined using stochastic models Insured’s don’t always lapse and die when they are supposed to. Assemblée annuelle 2007 2007 Annual Meeting

When to Use Stochastic Modeling? Stochastic modeling is a powerful tool to use when the random variable Is inherently volatile,and Has a large range of possible outcomes, Assemblée annuelle 2007 2007 Annual Meeting

When to Use Stochastic Modeling? Stochastic modeling is a powerful tool to use when the random variable Is inherently volatile, and Has a large range of possible outcomes, But The random variable must have a material impact on the model results to be worth the effort Assemblée annuelle 2007 2007 Annual Meeting

When to Use Stochastic Modeling? Stochastic modeling is a powerful tool to use when the random variable Is inherently volatile, and Has a large range of possible outcomes, But The random variable must have a material impact on the model results to be worth the effort And A simpler closed form solution isn’t available Assemblée annuelle 2007 2007 Annual Meeting

Common Uses of Stochastic Modeling in Insurance Pricing of Financial Instruments Extensive use in capital markets/seg funds Limited use in life insurance products Determination of cost of interest rate guarantees for deterministic pricing Aggregate Stop Loss Reinsurance Assemblée annuelle 2007 2007 Annual Meeting

Common Uses of Stochastic Modeling in Insurance CALM Valuation CLIFR to provide guidance on interest rate calibration in 2007 Economic Capital Extended beyond economic parameters to include mortality, morbidity and lapse MCCSR is moving to a economic capital approach for many risks Assemblée annuelle 2007 2007 Annual Meeting

Possible Uses of Stochastic Modeling in Insurance Impact of Investment Strategies Equities versus Fixed Income Cost of Policyholder Guarantees Long Term Guaranteed Premiums Interest Rate Floors Retention Limits Assemblée annuelle 2007 2007 Annual Meeting

Possible Uses of Stochastic Modeling in Insurance Policyholder Distribution Demographics UL Funding Patterns Policyholder Behaviour Lapses, Deaths, Premium Persistency Assemblée annuelle 2007 2007 Annual Meeting

Challenges Significant Overhead Initial set up can be extensive Model Research Model Parameterization Design Run times can be long Don’t want to have to redo Volumes of Data Assemblée annuelle 2007 2007 Annual Meeting

Challenges Appropriateness of assumptions Is history a good predictor of future? TSX returned 9.86% from 1956-2005 Inflation outlook lower than historical average Dividend yields have dropped Does answer change depending on projection period? Is historical frequency of the high and low interest rates correct? Have macro-economic factors changed? What time frame is appropriate? Assemblée annuelle 2007 2007 Annual Meeting

Challenges Appropriateness of model Are scenarios reasonable in relation to history? Do they produce a distribution of results similar to history? Do they produce patterns similar to history? Assemblée annuelle 2007 2007 Annual Meeting

Challenges Presentation of Results What information is important? Mean or Median of results? Distribution of results? Percentile or CTE? Periodic volatility? Specific scenario results? Assemblée annuelle 2007 2007 Annual Meeting

Conclusion Stochastic modeling is an activity involving significant investment in education, resources and computer time The results are only as good as the inputs used “Art” may be involved Benefits can be significant Assemblée annuelle 2007 2007 Annual Meeting