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The Actuary The magazine of the Institute & Faculty of Actuaries
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Stress and scenario testing

Stress and scenario modelling is often portrayed as the poor relation to dynamic financial analysis (DFA) when modelling a company’s capital requirements in non-life insurance. In reality each approach plays an important role.
There are various situations when you would consider using stress and scenario tests as an alternative to DFA:
– When a particular business question requires a quick answer and a full-blown analysis of the company is not required.
– When you need an individual capital assessment (ICA) calculation with no DFA modelling.
– To fill in the gaps left by DFA models.
– To provide input into the design of DFA models with regard to causes and effects.
– To calibrate DFA models and to test their output.
In principle, there are three modelling approaches:
– Individual scenario modelling the modelling of specific events, eg pharmaceutical industry loss. Scenarios are modelled by the use of distributions, simulation, or point estimates. These scenarios can be considered in isolation or with their associated ‘ripple’ effects over time. The time horizon tends to be anywhere between one and five years.
– Direct modelling of a risk category, eg credit risk with the use of distributions, or the results from simulation.
– DFA models.
Stress and scenario testing in its broadest sense describes the first two forms of modelling, which are often as scientific in their approach as DFA models. A stress test does not imply a back-of-the-envelope estimate; it involves consideration of aspects such as distribution, simulation, model risk, and correlation. With stress and scenario testing, scenarios or risk categories are looked at separately and then aggregated, whereas with DFA with dependency modelling the risks are aggregated as the model builds up over time. One of the weaknesses of the stress-testing approach is that some of the causal relationships are lost for example, a large insurance loss leading to an increase in reinsurance recoveries. However, allowances for these casual relationships can be handled in other ways (for instance, the consideration of ‘ripple’ effects, or stress testing).

Risk categories
Consider the five risk categories of (i) insurance risk (underwriting and reserving risk), (ii) market risk, (iii) credit risk, (iv) liquidity risk, and (v) operational risk.
Insurance risk and market risk can be modelled relatively easily through the use of stochastic approaches. Stress and scenario testing would be more appropriate for credit, liquidity, and operational risk.
Credit risk can be modelled through simulation, taking into account the correlation of default between reinsurers. There is also value in considering the default of particular reinsurers to reflect their known risk characteristics. Liquidity risk, where a company does not have sufficient financial resources to meet its obligations as they fall due can be easily dealt with through scenarios using information on projected cashflows and estimates of the costs of realising assets or raising funds.

Operational risk
Operational risk losses are best treated through the use of scenarios, as future losses are a function of an organisation’s control and risk environment. It is helpful to split operational losses between high frequency/low severity and low frequency/high severity events. Losses relating to this first category may implicitly be present in other risk categories; for instance, insurance risk where the underwriter incorrectly uses a pricing tool. Once allowance has been made for the operational risk losses that are implicitly captured in the other risk categories, the remaining losses to model are typically the low frequency/high severity events. These can be modelled through detailed consideration of causes and effects and the losses emerging. Industry data and the use of an industry database can be very useful for benchmarking operational risk losses by category, but one has to recognise the limitations of external historical data because (i) other company operational risk losses were dependent on that company’s size, structure, and control framework and (ii) historical loss data can soon become outdated when changes take place within a company, especially in a period of developing governance and controls.

General considerations
It is worth mentioning some general points:
– Risk quantification needs to reflect the risks facing a company. Whether this is through DFA or stress and scenario modelling is secondary.
– How much capital is enough? What weight do you put on a one-year versus a three- to five-year view of risk, given the increasing uncertainty over time (and the annual repetition of the modelling exercise)?
– There is always uncertainty in the ‘best’ estimates of parameters, particularly if you are compounding many parameters over time and looking at the tails of distributions.
– Model risk is important. There are many different ways of forecasting results over time. A model may predict how reserves move from period to period, but how do you allow for the actual reserve decisions made by management under pressure to show good quarterly earnings statements?

Risk aggregation
One way of addressing risk aggregation with stress and scenario testing is by calculating capital within each of the risk categories separately and then aggregating the results with a correlation matrix. In the example in table 1:
– capital assuming all risks go ‘bad’ at the same time is _748m;
– capital assuming diversification benefits between risk categories is _484m; and
– capital assuming independence between the risks is _331m.
This exercise could be done for the next 12 months at the 99.5% confidence level and then repeated for other time periods, thus providing a range of capital figures for each of the risk categories. The selected capital level for each risk would then be based on the company’s economic capital definition and the risk dynamics over time. Individual and combinations of scenarios over three to five years could then be run to test the adequacy of the resulting capital.
It is difficult to predict 12 months in the insurance industry, let alone three to five years, and so a degree of pragmatism is helpful. A model is only a guide to capture the dynamics of a very complicated ‘real’ life process; ‘real’ life will not follow the model.

Note This article is based on the Stress Testing and Scenario Analysis Working Party paper and presentation at GIRO in Killarney, Ireland. The working party members were Philip Archer-Lock, Nigel Gillott, Natasha Regan, Richard Shaw, and Oliver Tang. Many thanks are due to them and earlier contributors to the paper who had to withdraw from the working party at one stage or another.

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