Stochastic Modeling Is on the Rise – Part 1
June  2014

Stochastic modeling is on the rise in the life insurance industry due to a coalescence of regulations on the horizon and an increasing demand for stochastic analysis in many internal modeling exercises. While regulatory developments across the globe certainly have played a part in this increased interest, there are plenty of other reasons why stochastic modeling proficiency is growing among both actuarial modelers and those who interpret stochastic results.

This topic continues to garner attention as the industry increasingly relies upon stochastic models to value its business, design its products, and manage its portfolios. It appears that stochastic models gradually are becoming the industry norm for internal metrics since deterministic models often cannot adequately quantify the risk profile of the industry’s increasingly complex business.

Stochastic Modeling Proliferation

As with many other industry trends, regulatory considerations will play a pivotal role in the increasing interest in stochastic modeling. Regulatory bodies in both the European Union (EU) and the United States continue to propose new stochastic modeling requirements, joining efforts from other nations worldwide. The EU is internally aligning its capital requirements under Solvency II, and the NAIC has introduced VM-20 to address life insurance statutory reserve requirements.

Each approach permits the use of internal stochastic models. VM-20 calls for stochastic modeling of economic risks, but does not require stochastic modeling of mortality risk (however, a company may elect to do so). Each of these regulations, when fully implemented, will significantly expand the use and importance of stochastic models.

Leaving aside these looming regulatory changes, however, companies are discovering stochastic models’ value to an organization’s cash flow projections and risk management activities. Insurers are expanding their use of internal stochastic models as available tools and computing power make this modeling more feasible.

Companies are implementing stochastic models not only to determine economic capital, but also to use in product development areas. In reinsurance units, non-proportional reinsurance programs such as stop-loss and catastrophic coverages may necessitate stochastic modeling for both pricing and valuation.

Need for Continued Research

Given these and other reasons for the ongoing proliferation of stochastic models, the life insurance industry still has room to expand its stochastic modeling knowledge and techniques. While the stochastic modeling of market and credit risks is fairly well established, stochastic modeling of mortality is not as fully developed. In fact, most published research regarding stochastic mortality modeling either has been across general population segments where there are no underwriting selection effects or has been conducted on longevity risks covering pensioners or annuitants.

Both of these approaches pose challenges. Research on general populations, pensioners and annuitants does not carry over well to the stochastic modeling requirements of fully underwritten life insurance. These insured populations have distinctly different mortality characteristics that require partitioning by product, underwriting class, distribution channel, policy issue year and policy duration.

Similar to deterministic modeling, such partitioning should consider the level of credibility within the partitioned segments when determining stochastic distribution metrics such as means and variances. Adjoining segments may need to be combined when segmented credibility is low.

Another consideration that affects fully underwritten portfolios is policyholder lapsation. For example, lapse rates are typically very high at the end of level period for term life insurance products. These rates are difficult to model because they depend upon a number of factors, most of which are highly dependent upon post-level period premium increases and the insured’s health status. This is typically not a concern when stochastically modeling general population segments or annuitants.

A good introductory resource addressing stochastic mortality for underwritten life portfolios is a document produced by Ernst & Young LLP entitled “Stochastic Analysis of Long-Term Multiple-Decrement Contracts” published by the Society of Actuaries in 2008. This report evaluates stochastic modeling of life insurance nonmarket risks (i.e., mortality and lapse). It lays out the primary issues and describes potential modeling solutions.

However, it also recognizes the need for an increased understanding of the sensitivities associated with stochastic mortality model design. Suggested areas of research are selection of stochastic variable probability distributions, stochastic variable correlations, and other relatively unchartered terrain for fully underwritten life insurance.

Figure 1 – Uses of Internal Stochastic Models
Tail Risk Analysis
Hedging Strategies
Product Pricing and Design
Business Mix Optimization
Risk-Adjusted M&A Pricing
Evaluation of Reinsurance Programs
Risk Structure Optimization
Calculation of Diversification Effects
Corporate Strategy Development
Risk -Adjusted Performance Measurements and Targets
Management Compensation Strategy
Satisfying Parent Company Requirments

The benefits of incorporating stochastic modeling enterprisewide expand well beyond simply preparing for possible regulatory changes. Though we mention a dozen in this list, we easily could have included many more.


The benefits of stochastic modeling cannot be overstated. We have touched on only a few of these benefits but certainly could have extended the discussion into various areas of pricing, valuation and stakeholder interest.

Last but not least, ratings agencies have been increasingly supportive of the improved risk management metrics derived from stochastic modeling, making it even more vital that companies continue to develop their internal stochastic models to keep pace with what is rapidly becoming an industrywide best practice.

Having set the stage as to the “whys” of stochastic modeling our next article will discuss some of the “hows,” presenting a practical example of designing a stochastic model of death benefits on fully underwritten life insurance.