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The Actuary The magazine of the Institute & Faculty of Actuaries
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Cat. modelling: Not so sudden impact

Catastrophe modelling companies build models to assess the potential for large losses before they occur. A catastrophe model’s principal purpose is to anticipate the likelihood and severity of events so that companies (and governments) can appropriately prepare for their financial impact. A catastrophic event could cover anything from an earthquake or hurricane to terrorism and crop failure. A catastrophe model is made up of several modules:

The hazard module
The hazard module looks at the physical characteristics of potential disasters and their frequency. To capture the wide range of potential events that can affect insured property, an event catalogue is built. Statistical and physical models are used to simulate a large catalogue of events, for example 10,000 scenario years of earthquake experience. The 10,000 scenario years should be thought of as 10,000 potential realisations of what could happen in the year 2010, not simulations until the year 12010.

The vulnerability module
The vulnerability module assesses the vulnerability (or damageability) of buildings and their contents when subjected to disasters. This is done through the use of vulnerability functions, which relate the intensity of a particular event to the building’s mean damage ratio (the ratio of the cost of repairing a building to the cost of rebuilding it).

The financial or loss module
The financial or loss module finds the corresponding loss by computing the product of the building’s replacement value and its damage ratio. To expand on the last two modules, we introduce the concept of a distribution around the damage ratio. Seemingly identical buildings can experience different levels of damage following the same intensity event. This can be due to small differences in construction or the effect of debris.

To illustrate this, imagine a scenario where one house experiences no debris impact during a storm and the neighbouring house of identical construction is hit by a piece of debris that breaks a window and, as a result, the roof blows off. To capture this variability of damage, we look at a distribution of possible values. The mean of this distribution is known as the mean damage ratio.

When this damage ratio distribution is multiplied by the replacement value of the building, we can obtain the loss distribution showing the potential losses arising out of a single event. It should be noted that the idea is the same across different perils and, as an example, earthquakes could be used instead of hurricanes.

Now that we have the distribution of loss from a single building, we can compute the combined loss distribution of all buildings through convolution. Convolution is a means of computing all possible combinations of X + Y and their associated probabilities, given the probability distributions of X and Y separately. After convolving the n distributions for the n locations affected by an event, we have the policy loss distribution for all locations within a particular policy. At this point, policy terms can be applied.

I will use an example from the Lloyd’s market. In Lloyd’s, excess policies can be found where the cedant takes a line on a layer. For example, a Lloyd’s syndicate may take a 5% line on a $15m xs $10m layer. This means the syndicate is liable for 5% of the loss from $10m to $25m (ie. $750,000). Such terms are applied to the loss distribution above and the distribution is adjusted appropriately to determine the loss to the syndicate.

In summary, the hazard module gives us a way of assessing how much a specific region is at risk to a certain peril. The vulnerability and financial modules allow us to compute the loss due to damage from these perils. Combining the results gives a reasonably accurate assessment of the losses that are likely to occur in a given region. So while we may not be able to avert disasters, we can at least prepare for their financial impact.
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Shane Latchman works as a client services associate with the catastrophe modelling company AIR Worldwide Limited