Brokers can help guide reinsurance purchasers through the maze of catastrophe models, says Oliver Peterken.

One of the most difficult decisions facing a reinsurance purchaser is how much catastrophe cover to buy. Despite having more sophisticated catastrophe models than ever before, many reinsurance buyers find it increasingly difficult to be confident they are making the best decisions. In this situation, though, the reinsurance broker can play an important role in helping reinsurance buyers get the best out of cat models.As cat models have become more complex, reinsurance decisions seem harder to make. Sometimes this can be due to unrealistic expectations of the accuracy of cat models, which after all can be no better than the science that underpins them. The role of a broker is to help the client understand the scientific basis of the various models and to implement a clear decision-making process, through knowing how accurate they can be and how best to use their results.

Provisional characterCat models have numerous sources of modeling error, ranging from imperfect event catalogues to the exposure data for an insurer understating its policy values. A cat model is never, going to be 'right'; the best that we can hope for is that over its evolution, a cat model becomes 'less wrong'. All models have a provisional character and recognising this is an important step in using them better.Studies of the use of complex models in other industries have shown that the desire for increasing accuracy drives us to demand greater complexity. In particular, complexity is often translated into higher resolution. This can be seen in the evolution of cat models from using wide area cresta zones to more detailed full zipcode modeling. Similarly, the scientific paradigms used to model the hazard itself have become more complex.The latest earthquake models use spectral displacement - an approach infinitely more complex than the early MMI models. In hurricane and windstorm modeling, there has been a progression from simpler parameterised statistical models which captured the outputs of a weather system (gust speed, duration, etc.) to numerical models which simulate the physics of a meteorological event (heat exchange, dry air stratospheric intrusion, etc.).A further area of increasing complexity is the measure of risk itself. In the early days of cat modeling, this measurement problem did not arise, as a deterministic approach was used. A past event was selected as the benchmark loss scenario and the insurer's current exposures were modeled to produce an 'as if' loss count.

Probabilistically speakingAs cat modeling developed, it took from earthquake engineering, and in particular the research done on siting nuclear plants in California, the concept of probabilistic modeling. This is the basis today of the most common output from a cat model - the loss exceedance curve. The use of a loss estimate for a given return period is nearly always used in deciding how much catastrophe reinsurance to buy.But this measure changes over time. A loss return period is the average number of years between the exceedance of a defined amount from all the events in the model. Thus it is sensitive to the probability attributed to each event and so changes over time as new events occur and as models evolve. When our historical record is short, such as for US east coast hurricanes (80 years) and European windstorm (200 years), return periods can change significantly. For example, 1990A (UK windstorm) was originally considered to be a 100 year event, then a 50 year loss, before dropping as low as 15 years and coming back up to 35 years. When faced with such changes, many users concluded that the models were wrong. Actually, these changes were a good sign as they showed the model evolving over time as new information became available. As complexity in terms of resolution increases, so it becomes harder to understand the scientific merits of a given model. Today, this has led many users to consider the results from alternative models. This increases considerably the number of issues a user must tackle in order to reach a rational decision: which model should be emphasised above the others, how should different results be interpreted, and how can a decision be reached based on multiple results? Every client's situation will be different, requiring a customised approach. As the number of complex models increases, so more complex decision methods are required.

Results driven What is often required is a clear decision process which takes the client from model results to reaching the best reinsurance purchasing decision for their company. Probably the single most important thing that can be done by all users of cat models is to decide how they will use the results of a cat model to reach a decision on reinsurance purchase. Maybe, they are very risk averse and will decide to always use the largest loss number at a given return period. Alternatively, they may feel that a certain model is more appropriate for their business in a certain territory and will rely on its results. Other users might be concerned at the risk of buying insufficient cover and add a safety margin to model results. The key is to recognise that a cat model is being used to make a decision and that no model possesses the ability to make a decision for you. How your broker helps you integrate decision-making with the modeling is a key factor in successful reinsurance buying.By Oliver PeterkenOliver Peterken is a Regional Director at Willis Re. Tel: +44 020 7488 8923; Email: oliver.peterken@willis.com ; Website: www.willisre.com