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The Actuary The magazine of the Institute & Faculty of Actuaries
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Practical stochastic modelling!

The term ‘stochastic modelling’ is becoming increasingly used by actuaries. What does it mean to you? The most common interpretations of a stochastic model tend to be:
– something that allows for uncertainty of future outcome;
– a very complicated calculation engine with lots of technical maths involved;
– something that has to be run several hundred or thousand times, can take days to run and requires several ‘top of the range’ computers; or
– an interesting model that unfortunately may not bear much resemblance to the ‘real world’.
Of course, all of the above (and more) might be relevant descriptions of a stochastic model, depending on how it has been designed.
Given the direction of accounting standards and regulation and the increased focus on capital, within a very short time period life insurance actuaries will need to build, apply, and interpret stochastic models for many jobs; these will include the determination of realistic balance sheet liabilities for regulatory reporting, calculations required under international accounting standards and internal value management, risk management, and management reporting. In preparation, many life insurers have started to building or to extend their modelling capabilities to meet these future demands. However, a model that is suitable for one of these purposes will not necessarily be suitable for all, unless designed with sufficient flexibility.
The more technical aspects of a stochastic project (in particular, the economic scenario generator model) tend to be those at the forefront of an actuary’s thinking. In practice, while these can indeed be challenging, it is the more practical problems that often require the most thought and resource. It is often assumed that many of these practical problems are easy to solve unfortunately the opposite can be the case, leaving the actuary with a number of challenging obstacles to overcome to meet required delivery dates.

A dynamic corporate model
Before considering the practical aspects of stochastic modelling, it is perhaps worth defining our purpose. Stochastic refers to the nature of uncertainty of particular variables (normally economic assumptions, but sometimes other variables such as lapse rates). The term ‘stochastic modelling’ can mislead to a certain extent. A better description might be ‘dynamic corporate modelling’ as, in practice, the project will be focused on delivering a model that fully reflects the interactions within the company of assets, liabilities, and various decision rules.
Building this dynamic corporate structure is where most of the work lies for actuaries. The stochastic nature, provided through the selection of an appropriate scenario generator, should be relatively quick to implement provided that the model is sufficiently well planned.

Main practical problems
The most significant practical problems tend to fall under one of the following headings, listed below in the order that they typically arise within the project.
1 Scope, timetable, and team
2 Systems, data, and support
3 Specification and decision rules
4 Stochastic assumptions
5 Adapting to unexpected issues
6 Testing and reasonableness
7 Interpretation, explanation, and reporting
We look at the first three of these problems in this article, and will cover the remaining four in the second part of this series.

Scope, timetable, and team
Many areas of a life insurer’s business would benefit from some form of stochastic model. One of the first challenges will be to define, agree, and communicate the scope of the development. Knowing what you intend to deliver and the scope of the project may seem obvious, but failing to do this in the race to start the model build can be a killer. From experience, putting in place a strong project management team and structure will be at least as important as having the appropriate technical actuarial input. If you shortcut this stage, you could be eliminating your chance of success right from the start.
The key questions to consider will be:
– what is the purpose of the model?;
– what existing systems/processes should be re-used?;
– what accuracy is required?;
– which parts of the business should be modelled?;
– what are the essential deliverables? and how important are the others?;
– how much flexibility is there on resources, budget, and timetable?
It can be tempting at this stage to overpromise this should be avoided at all cost. Even with perfect planning, unexpected problems are likely to arise. Such is the current pace of regulatory and accounting change that a multi-phase approach to the project is likely to be attractive, with each phase delivering a different component and subsequent phases building on each other.
Appointing an actuarial project manager with hands-on experience and awareness of the pitfalls greatly increases the likelihood of successfully delivering on time and within budget.
Finally, looking for ways of simplifying your solution from the start and continuing to ask critical questions throughout is vital. Many pragmatic and cost effective solutions are likely to be available: these will be particularly appealing for organisations with limited resources, restricted timetables, or smaller blocks of business. Examples include the use of approximation techniques to support future decisions within the model, or the use of ‘closed-form’ option pricing methods to avoid the need for nested stochastic projections.

Systems, data, and support
Early on in your project, the state of the existing systems, data, and processes will need to be assessed. A careful and unbiased assessment must be made about what can be reused to save costs, while not letting this reuse overly constrain the performance of the new model. This assessment will be wide ranging and, for many insurers, will include decisions on using new software for the model. Having access to experienced and impartial people who have already been through this process can be useful.
The choice of system will need to take account of a number of factors including:
– existing functionality;
– known future software enhancements and their integration with current versions;
– availability of experienced users with the relevant skills;
– the long-term software strategy and hardware requirements.
As none of these factors is likely to remain fixed over time, the decision can be a complex one.
Deciding how the model will be built is important. A modular approach tends to work well, enabling additional functionality to be added during a later phase of development (see figure 1).
On the data side, the main challenge is to achieve a sufficiently small representative set of model points to keep run times manageable. In addition to the standard grouping packages (many of which come with the modelling software), variance reduction techniques are available to reduce the number of scenarios required and hence reduce run times. Aside from these scientific approaches, a number of more practical techniques can offer substantial performance improvements. For example, a small proportion of grouped policies (by model point count) may represent a very high proportion of the business (by value).

Specification and decision rules
Once the scope of the model has been agreed, the specification can be prepared. For individual asset and liability calculations this is relatively straightforward, particularly where reliable existing internal documentation exists. It is the programming of corporate interactions and management discretionary decisions that will require more thought. This is possibly the most time-consuming albeit fascinating aspect of the project, and can be very productive if approached with clear objectives.
To succeed you will need to codify and document the management philosophy and actions that would be taken in all future scenarios. This will be a time-consuming exercise for management. Certain scenarios may not have been considered from all possible angles before, particularly for insurers still adapting to complicated financing arrangements or demutualisation schemes. There is an obvious and crucial overlap here with the development of the firm’s principles and practices of financial management (PPFM).
For regulatory calculations, accurately judging management reactions in the extreme scenarios is important. Capital requirements will be based on the distribution tails, whereas they are arguably slightly less important for fair value calculations, where they will be given a low probability weight. Therefore, the degree of detail and realism of the model will depend on its purpose.
Given the likely pressures on timetable and resources, there may be a temptation to avoid spending too much time on less familiar parts of the model build, such as tax. The risk here is that the model is over-engineered in certain areas and too crude in others.
Overall, a pragmatic approach to this phase will help to speed up your project. This is particularly appropriate where management policy is as yet undefined. A sensible approach can be implemented in these situations, with the model results being used to enable management to determine or refine an appropriate strategy. Over time this can become one of the key uses of the dynamic corporate model.
You have now scoped the project, specified the detailed requirements of the model, and (with management support) defined the PPFM. In the next part we will look at the stochastic generator, building, and testing the model, and how to report from it.

Jargon buster
Closed-form option pricing
Option valuation methods which use formulaic solutions, Black Scholes being the best known. Closed-form option pricing is easier to do than stochastic modelling, but has several limitations, particularly in valuing long-term insurance liabilities
Nested stochastic projections
Projections where each scenario requires a stochastic calculation within itself. Such approaches cause problems with computing power and memory (hence the attractiveness of closed-form solutions)
Principles and practices of financial management (PPFM)
A statement of how matters such as investment mix, bonuses, new business will be managed; introduced by the FSA in Consultation Paper 167 (see p6)

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