The multi-period explosion

Suppliers of asset and liability modelling software are using grid computing to help life companies cope with the increasing burdens put on them by regulators and rating agencies

Life companies are being urged to get a better measure of their balance sheets and risks. Regulators want them to calculate their reserves and capital on a more realistic basis, while rating agencies look askance at companies that do not model and hedge the risks of the guarantees and options they sell in their policies. Meanwhile, the bear market in stocks, falling interest rates and sharper competition has forced companies to realise that they cannot continue managing their portfolios on traditional assumptions about the value of guarantees and options in the policies on their books, nor about the premium rates they can charge, or returns they can expect on assets.

Regulators, through Solvency II in Europe and the National Association of Insurance Commissioners' Risk-Based Capital (RBC) C-3 Phase II in the US, are insisting that insurance companies now calculate reserves and capital using stochastic modelling: projecting the value of their assets and liabilities forward in time under a number of different possible economic scenarios.

It is a logical requirement given the nature of the guarantees and options commonly embedded in policies, as well as the derivatives used to hedge assets, and the limits of the closed-form methods to capture the full extent of their risks.

But this also presents a considerable technological challenge. Modelling the behaviour of highly complex products, both assets and liabilities, and their interactions over long periods - often 20-40 years - under thousands of scenarios, and valuing them periodically to check reserves, can stretch the capabilities of even the most advanced forms of computing. Suppliers of asset and liability modelling software are upgrading their technology to cope with the new demands, taking advantage of modern 'grid' high-performance computer architectures. Meanwhile, a number of companies still prefer to build their own systems, convinced that they can tame the technological challenge by carefully targeting their software to their individual requirements.

Life companies - and their regulators - didn't really think of using stochastic modelling for their with-profits funds until recently. In the past, the discretionary actions that management could take in reducing bonuses or increasing charges could largely compensate for changes in economic conditions, says Mike Kipling, director and chief actuary at Phoenix Life Group, part of Resolution Life Group. "It wasn't until interest rates came down in the late 1990s that it became clear there were some options embedded in policies of such magnitude relative to the likely returns on assets in the future, that they could potentially override the discretionary actions of management," he says. Regulators wanted to bring this under control, but a tightening of the formula for traditional statutory reporting would have constrained the flexibility of management to respond to market conditions. The result in the UK is the 'realistic balance sheet', which requires the stochastic modelling of any sort of guarantee or option. Similar demands are being made of life companies across Europe and the US through Solvency II and RBC C-3 Phase II.

Model behaviour

For a company to calculate a realistic balance sheet - and hence the reserves it requires to cover its liabilities - it must be able to model all its assets and liabilities and to project their evolution over time to some point in the future: to year-end, or when policies run off, or even 40 years in the future. To do this, a company must first build a model of all its existing products that incorporates all their characteristics and features, including any guarantees or options such as bonuses or early cash-in. Then it has to do the same for all the assets it holds to cover its liabilities. The company must project the evolution of these liabilities and assets under a number of scenarios - typically 3,000-5,000 - with varied assumptions about economic conditions such as the movement of interest rates, the volatility of equity returns, etc.

Then there is the interaction between the assets and liabilities. "Many products sold by insurers around the world provide policyholders with returns that depend on the performance of the assets and, as in the case of embedded options, both assets and liabilities need to be modelled together to properly understand the possible financial outcomes from a portfolio of these products," says Mark Schneider, managing principal of Tillinghast Software Solutions, the actuarial software arm of global consultancy Towers Perrin, and developer of the MoSes stochastic modelling system.

Adding to the difficulty is the nature and complexity of some of the products life companies have on their books, says Kipling. Unlike banks, which won't sell a product unless they have first figured out how to model and price it, life companies spent years selling products designed to catch the customer's eye rather than make the modeller's life easy. Companies weren't hindered in their designs by the need to mark products to market; accounting practices were simpler then, and the notions of realistic balance sheets or risk-based capital had yet to surface. So life companies have ended up with portfolios full of path-dependent options and other awkward embedded instruments that can only be handled with stochastic modelling. "Banks are valuing things for which they already have pricing models, whereas we are valuing things for which there never were proper pricing models," says Kipling.

But that's not the end of it. While economic conditions unfold and markets rise and fall, management doesn't just sit on the sidelines. Companies can increase or decrease bonuses or premiums, or take other actions in response to market conditions. "A company's models now have another level of complexity, because they have to reflect how management will behave when there are market shocks," says Richard Baddon, partner at global consultancy Deloitte & Touche, which supplies the Prophet asset and liability modelling system. Systems must allow companies to set business rules that reflect their likely decisions in response to economic and market events - decisions that in the UK will follow the principles and practices of financial management (PPFM) that the Financial Services Authority has required life companies to define.

Meanwhile, policyholders might also react to changing market circumstances, and modelling systems should allow for this. "The system needs information on what policyholders will do as the economic environment changes, what will cause them to cash in their policies, or put more money in or take up other options they might have," says Gary Finkelstein, leader of the risk management practice in London for global consultancy Milliman, which supplies the MG-Alfa and MG-Hedge asset and liability modelling and exposure hedging software.

This all adds up to an enormous modelling task, which stretches the capabilities of even today's high-performance computers. UK life company Friends Provident has two million policies for which it runs 5,000 scenarios covering a period of 40 years for its realistic balance sheet calculations. To make the task more manageable, it aggregates these policies into 10,000 entities that it models using Life DFA, the stochastic modelling module of Deloitte & Touche's Prophet system. The company programs in management decision rules based on its PPFM, although it does not do the same for policyholders, believing their behaviour is less deterministic, says Nick Meyers, stochastic modelling manager at Friends Provident. The company also uses stochastic modelling for business planning and capital assessment. With the latter, the company looks at the extreme results of the scenario simulations rather than the average that is used for realistic balance calculations.

Like Deloitte & Touche's Prophet and Life DFA module, Tillinghast's MoSes and Milliman's MG-Alfa and MG-Hedge are able to use sets of interlinked computers to speed up calculations. This grid computing approach breaks up calculations into sub-components and farms them out across networks of processors. Stochastic modelling is ideally suited to grid computing, consisting as it does of large numbers of individual component tasks - the scenario simulations - that can be separated and performed in parallel. Many life companies are now setting up grids suitable for other purposes besides asset and liability modelling.

Norwich Union Life, which also uses Prophet, is able to employ the company's grid - around 100 PC servers in a special data centre - for its stochastic modelling. It runs its models regularly: two to three times a week for pricing calculations when developing new products, says Rob Kerry, head of capital management planning and strategy at Norwich Union Life, part of the Aviva Group. Currently, it performs full valuations of its portfolios three times a year: the stochastic modelling element running over a weekend, although the full task - gathering and checking all the data and the results - takes around three weeks.

Multiple scenarios

In addition to the technical complexity of models and the computer power required to run them, Kerry believes stochastic modelling of assets and liabilities presents a further challenge: communicating the results to senior managers more used to traditional approaches. Previously, companies might have used a 'central scenario', a best guess of how economic conditions will unfold over a number of years. Stochastic modelling, with its multiple scenarios, doesn't come up with a single answer for the future. "With stochastic modelling, there is no one view of what the future might hold," says Kerry. "We are dealing with long-term products, so it's about setting rules for how we will act under various circumstances, thinking through the impact on (our portfolios) and our customers."

Although Deloitte & Touche, Milliman and Tillinghast's stochastic modelling software is now widely used, some life companies still prefer to build their own applications. Phoenix uses a third-party economic scenario generator from Edinburgh-based risk consultancy Barrie and Hibbert, but has developed its own modelling system. Kipling says third-party systems tend to be expensive and need considerable customisation to fit an individual company's business practices. They also tend to include more techniques and functionality than any one company is likely to use because they are trying to meet a wide range of needs. "We don't want a lot of the functionality, and our experience is that these models can get over-complex and can have quite an overhead when you want to make changes to them," he says.

Phoenix began building its own stochastic modeller around 18 months ago, and is happy with the outcome. The software, written in Visual Basic and running on several 3Ghz Pentium processor-based PCs, is able to model the key aspects of the future cashflows of all the company's major policies. "It has got reasonably efficient run times compared with some of the bigger systems that put the data through lots of routines we don't require. Our system does just what we want it to do and no more," says Kipling. Having built and documented it, the company also finds it easy to amend to changing requirements. "And our auditors are happy to accept the results coming out of it," he adds.

According to the software suppliers, most life companies are still getting to grips with the stochastic modelling of their assets and liabilities, with all their embedded optionality, taking into account the interactions between the assets and liabilities, the effect of asset hedges and the consequences of management and policyholder actions. The next challenge is to follow Friends Provident and start doing nested stochastic modelling to value portfolios at each year-end in order to calculate reserves and capital at each step along the 40-year scenarios.

The first level stochastic modelling run will tell a company whether it is holding enough capital to pay off policyholders, including bonuses, when all the policies run off under the various economic scenarios. What it doesn't reveal is what the capital requirement might be at each step along the way. So if the stock market crashes and equity returns are down for three or four years, a company might need to hold extra capital during that period to meet regulatory requirements, even though the stock market will probably right itself and the capital the company holds will be sufficient to meet its liabilities in the long run.

To calculate this periodic capital requirement, companies must value their portfolios at these time points using stochastic methods to accurately calculate the value of the options and other instruments in the portfolios. This means a whole other layer of scenario simulations: say, 3,000 valuations for 40 yearly time steps for each of the 3,000 economic scenarios. The computational task is enormous, but software suppliers have been upgrading their applications to cope with it, and companies will have to make use of extensive computing grids to achieve reasonable run times.