In the second stage of the vulnerabilty module development, the EDPs are translated to MDRs that express the expected damage as a percentage of the replacement value of the assets.

Figure 2 shows the vulnerability module derivation for a seismic model. First, a relationship between the earthquake intensities and the building performance has to be established. The building resistance increases with seismic demand until the building reaches its resistance capacity. Resistance then falls as damage occurs and the building degrades until it collapses. The graph represents the fragility of the building with resistance represented by distinct performance levels such as the initiation of cracking, the failure of some structural parts etc. The performance levels are then translated to loss damage, i.e. the cost of restoring the building to its initial condition (repair or complete replacement) expressed as a percentage of its replacement cost (MDR). Collapse translates to 100% MDR. Quantifying loss due to business interruption can be expressed as a percentage of total value through the assignation of downtime periods to building performance level. In turn these are expressed as a function of the initial earthquake intensities. A vulnerability function is derived for each building typology and these may be employed in the open modelling process.

**Figure 2: Assessment of building performance to damage ratios**

*Source: Aspen Re R&D*

### Dealing with opacity

Both the fragility estimation and the translation from EDP to MDR are carried out during the development phase of the models, and thus are still somewhat opaque. Only the overall vulnerability functions (i.e. the relationships between event intensities, expressed in terms of IMs and MDR) can be seen when using a model and often the documentation does not explicity describe details and assumptions used. A better understanding and better subsequent use of models requires comprehensive evaluation of the underlying IM and MDR methodologies.

### Hazard representation

The hazard representation within the vulnerability functions can have a strong impact on the final loss estimation. A variety of IMs can be used to describe the hazard at each exposure location, given an event. So different models for the same peril and region may use vulnerability functions with different IMs and the uncertainty in the loss calculation can be reduced through adoption of the most appropriate IMs.

For example, the range of IMs is very broad for seismic hazard. They vary from those that only consider acceleration on the ground (structural-independent IM) to those that are bound to the natural frequency of vibration of the structures (structural-dependent IM), representing the intensity experienced through the building which varies according to floor and building height). Structural dependent IMs have a greater correlation to structural performance than structural independent IMs and thus can reduce calculation uncertainty. Nevertheless, the former’s advantage is only relevant when the structural details (e.g. a building’s height - used as a proxy for estimating natural frequency of vibration of buildings) are known. If these exposure details are unavailable then use of such IMs can introduce randomness in the hazard representation and consequently errors to the loss calculation.

Figure 3 shows the different loss outcomes of four seismic events using structural dependent vulnerability functions derived from different building height assumptions. Losses, assuming mid, high and tall-rise buildings, are compared with those based on a low-rise building assumption. In Event 1, the loss from a tall-rise building is 80% greater than that of low-rise. This model is not appropriate to use where building heights are unknown; in this instance a model with structural-independent vulnerability functions would be more appropriate.

**Figure 3: Percentage loss change of modelled earthquake event losses using different building assumptions**

*Source: Aspen Re R&D*

### Devil is in the detail

Model users should be aware of the constraints and the sensitivities of the various model components – especially the vulnerability component. Model evaluation will consider incorporation, or otherwise, of engineering advances, the assumptions and their potential sources of uncertainty. Improvement has been made through the adoption of more recent engineering developments but exposure resolution and description quality are still likely to impose limitations. Newer, more advanced and precise models can be ‘data hungry’ and, moreover, may generate uncertain (and even unstable) loss calculations if the granularity of exposure quality is limited. Frequently, the (re)insurer still receives exposure data lacking in detail or already subject to classifications or translations that are not consistent with the modelling requirements.

Yet, advances in models make for a fundamental difference. Through greater knowledge and transparency, users can choose the right guidelines so that the available data is used in the best way.