The Intelligent Quarterly from the publishers of The Insurance Insider

Winter 2011 / 2012

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Over the past 20 years, the use of natural catastrophe (cat) models has become an important commodity for the insurance community, both for the assessment of a portfolio of insurance exposure and for single risks.

Probabilistic cat models can generate loss exceedance frequency curves and annual expected losses for an entire risk or a layer of the risk. Model outputs can also represent scenario losses, which are used as inputs in many capital models (Solvency II, rating agency, internal enterprise risk management (ERM) models and so on).

As the usefulness of cat models has increased, so has the reliance on them. This has reached a level where any significant change in a model can lead to great discomfort for a (re)insurance company or indeed the industry as a whole - particularly if that model dominates the market. Recent model updates have incorporated significant changes in their view of risk. Any change in the view of risk at a constant risk appetite can impact the capital and reinsurance needs, business mix and ultimately the profitability of a (re)insurance company. This means that significant model revisions can have a broad and long-term impact.

In addition to recent model updates, events over the past 12 months have shown that models are often not capable of capturing all aspects of the risk event, as the scale of many of these events (for example, in Australia, New Zealand, Japan and the US) was unexpected.

Modelling companies are keen to advocate a prudential use of cat models and to emphasise the subjective nature and limitations of modelling. Some even support a multi-model approach to cope with uncertainty. This is a healthy development as it puts the role of cat models in the right position in the context of underwriting and ERM. It also reminds us that "unknown unknowns" remain a component of the business and hence models will always remain "uncertain", regardless of how much they are improved (see graph). Click to enlarge

It seems cynical to blame uncertainty of cat models, as it is inevitable that the results of a model describing something that is unsure will itself be uncertain.

Where do the variations in model results come from? Changes in model results can stem from changing assumptions in one of the main components of a cat model, namely the quantification of the natural hazard (where, how strong, how often), the vulnerability (what damage at which physical intensity), exposures (where, how much) and the effect of insurance conditions such as deductibles and loss limits.

The complications from understanding changes of the resulting loss curves comes if more than one of the main model components changes and model transparency is insufficient to distinguish and quantify the different but overlapping effects.

Coping with uncertainty

So model uncertainty is a certainty. But how can we cope with it? Advocates of the multi-model approach would argue that several expert opinions are often better than a single expert opinion. In addition, the effects of a single model change are dampened, and therefore blended model results should be more stable over time. But the multi-model approach requires greater effort and higher costs.

A more cost-effective approach might be to build up in-house modelling expertise. This may sound expensive, but it does not have to be. A simple deterministic scenario loss model is a good start as it can be built around a low-cost Excel-based solution. This will help individual companies to better understand cat models in general and learn how to ask the right questions. In addition, those who have been involved in building even the most basic scenario loss models are likely to have a healthy dose of scepticism towards probabilistic cat models and will use them with caution.

A conservative approach in handling model uncertainty is to add a safety margin to compensate for the "unknown unknowns". As with the New Zealand and Japan earthquakes of this year - where the influence of un-modelled perils such as liquefaction, aftershocks and tsunami proved so devastating - models often miss sometimes large portions of the overall loss. Every major event in the recent past had its black swan(s), which by definition are not included in the model.

However, by far the most sustainable approach to tackle model uncertainty is to increase data availability. It will not bring about an immediate cure as it cannot be achieved overnight, but it will bring long-term stability, as more data will help improve the fundamentals of any cat model.

More is better

One can argue that on the hazard side there is already a lot of public research data available. After all, most nations have a national weather and/or seismological service. Together with academic research institutions they produce vast amounts of base data to be mined when constructing the hazard module of a probabilistic cat model.

On the other hand, the availability of data to quantify the damageability or vulnerability of insured values as well as the effect of insurance conditions is scarcer. This situation is presumably one reason why the vulnerability module of any commercial cat model is kept opaque. It is the "dark heart" of cat models, to quote a vendor model executive.

This limited knowledge of vulnerability can be improved because the data needed to quantify vulnerability already exists in almost every insurance company's claims and policy systems.

To illustrate the point, imagine that an independent data collector has systematically collected industry losses and corresponding exposure data (sums insured) on a granular level (say per county) for every major hurricane over the last 50 years. There would be a huge pool of data to base robust vulnerability functions upon and model differences and changes would presumably be much smaller than observed today. Click to enlarge

Perils systematically collects company loss and sums insured data and makes aggregated and anonymised market data available to the industry. This is greatly enhancing the transparency of cat risk in Europe and assists in building more stable and more realistic cat models.

The graph above plots the losses in percentage of sums insured against gust values. The analysis stems from Windstorm Xynthia (Feb 2010) for residential business in Germany with the underlying data available in a Cresta zone and property line of business resolution. The data has been collected directly from insurance companies.

Over time, gathering new, independent and high-quality industry data will significantly increase the knowledge of exposure, insurance conditions and vulnerability. This will enhance transparency and bring more stability to the underlying assumptions for the generation of loss distributions.

Luzi Hitz is CEO of Perils; Eduard Held is head of Sales & Products for Perils