The industry increasingly relies on catastrophe models for crucial information, but what limitations do they have? asks Dr Steve Smith

For a property catastrophe insurer or reinsurer, accurately measuring the risk of an individual client or the whole portfolio of business is an important activity since this impacts the prices charged and the capital held.

Insurers and reinsurers typically do not develop their own models, preferring to purchase commercially available models, usually from one (or more) of the three major model vendors: Applied Insurance Research (AIR), EQECAT (a subsidiary of the ABS Group) and Risk Management Solutions (RMS). Since modeling catastrophes is extremely complicated, developing a comprehensive model in-house is expensive and based on a more limited database. From a market point of view it also means there is no common language.

All of the commercial models, with one small exception, can be described in one word - statistical.

The mechanics of a cat model can conceptually be broken down into four components:

- Event generation - here a single peril, such as a single hurricane or earthquake, is simulated;

- Hazard modeling - given the single simulated peril, the hazard from that peril is calculated (eg for a hurricane, the wind-field at ground level is calculated);

- Damage modeling - given the hazard, the actual damage suffered by the exposed building(s) is calculated; and

- Financial calculation - this component translates the building(s) damage into a ground up loss and, ultimately after applying re/insurance contracts, the insured loss.

This process is repeated a very large number of times to develop a full distribution of insured losses. The actual "very large number" is chosen to ensure that the statistics of the insured loss distribution are stable (see figure 1).

Event generation

In general, all current cat models generate events in a similar way. This process is used for tropical cyclones, windstorms, tornado outbreaks, flood events and earthquakes. They gather historical event data - for hurricanes this is typically the historical database of hurricane tracks since 1851 (the HURDAT database), for earthquakes this consists of the map of earthquake faults. They parameterise historical events - ie given the set of historical data, the data is analysed to determine how an event can best be described numerically. For example, some of the parameters used to define a hurricane are its track, central pressure and radius of maximum winds.

Cat models also generate probability density functions (PDFs - the set of individual outcome probabilities) of historical event parameters. Once the events can be numerically described, a PDF is built from the historical data for each parameter. Finally, all cat models sample PDFs to generate a synthetic event - a random number generator is used to pull a single parameter from each PDF. The simulated event is then built from the randomly derived individual parameters.

Given a hazard (windspeed, ground shaking), the damage produced by this hazard on a building must be determined. Using insurance claims data and engineering studies, damage curves are generated which relate the amount of damage suffered by a building of a certain type to the magnitude of the hazard affecting that building. Furthermore, the damage curves are modified by various building attributes such as cladding, building code, enforcement and so on.

Cat modelLing challenges

Historical event data - As noted, the event generation component of a cat model relies heavily on historical data. However, the historical data may not be representative of the current or future state of the particular event.

For example, the basic dataset for Atlantic hurricanes is the HURDAT database administered by NOAA. This data stretches back to 1851. However, much of the data pre-1900 is based on the reconstruction of storms using data from newspaper reports of landfall and from data in ships' logs. Necessarily, this data only captures storms that were actually observed - storms that passed out to sea without encountering either ships or land are unlikely to be in the database. The data informing the cat models is then incomplete.

In much the same way as the early parts of the HURDAT database, from 1950 to the widespread introduction of weather radar in the US, tornadoes were only recorded when they were directly observed. This has led to a seeming increase in the occurrence of tornadoes in the historical record, when in fact the occurrence of tornadoes is fairly stable over time, but there has been an increase in the observation of tornadoes. There are a number of different approaches that the cat modeling companies use to reduce the effect of this artificial trend.

Climate variability - The earth's climate has a number of cycles that can affect the generation of catastrophic events. An example of this is the El Nino Southern Oscillation (ENSO) which can dramatically affect the occurrence of hurricanes in the Atlantic basin. During the negative phase of ENSO (La Nina) hurricanes are much more likely to occur than during the positive phase (El Nino).

The data generally used by the cat models is the "all years" dataset and the statistics are generated by the model on that basis, eg the occurrence of events and the losses incurred as the average over all the years simulated. However, insurers typically write contracts one year into the future. For example, if the climate is entering a La Nina state where the probability of hurricane occurrence is higher than the average over all years, the models are more likely to calculate an expected loss lower than it should be. The reverse is true in El Nino years were the models are more likely to generate an expected loss higher than it should be.

The problem of conditioning the model on climate state has been largely unaddressed by the cat modeling community.

Claims data - To develop damage functions, cat models use claims data from insurance companies. However, these data are subject to the following four problems:

- Data source - insurance companies typically do not share claims data;

- Veracity - have all a damaged buildings' properties been captured?

- Hazard - what windspeed caused the observed damage? and;

- Location - how accurate is the location of the building?


Each of these four issues can lead to errors in generating the damage functions.

Few would doubt the positive impact which the implementation of catastrophe models has had on the industry's ability to adequately quantify its risk exposures and price accordingly. However, no matter how complex and sophisticated these models become the unpredictability of nature will continue to challenge their effectiveness.

Dr Steve Smith is vice president of ReAdvisory, a service of Carvill, and spearheads ReAdvisory's catastrophe modelling efforts. Dr Smith has been researching weather phenomena for 11 years including the last five years in the insurance and reinsurance market.

LEARNING FROM KATRINA

Cat models have traditionally done well in calculating the expected loss from a storm which is "dry" (eg has little in the way of flooding). However "wet" storms present a significant challenge.

The flooding seen in New Orleans came from two sources, namely storm surge and river flooding. The storm surge created by Katrina's winds blowing south over Lake Pontchartrain weakened and eventually toppled the flood defenses (the levees) of New Orleans. Additionally, the city saw over eight inches of rain which the drainage system in New Orleans struggled to cope with.

Storm surge flooding is dealt with fairly well in the models while river flooding is more problematic. A river flood is created by a confluence of conditions, specifically:

- Meteorological conditions - floods cannot exist without rain. Hurricanes typically produce significant amounts of precipitation. However, actually modeling rainfall is one of the trickier problems in atmospheric science. As can been seen in figure 2, the rainfall from Hurricane Katrina has a very complex spatial pattern.

- Historical conditions - floods do not simply occur because there has been heavy rain. Understanding the physical conditions of the river (saturated soil and full rivers) is critical to understanding where and when a river will flood.

- Flood defenses - riverbanks can be raised, either permanently or temporarily in anticipation of a flood. Understanding exactly where these defenses are and to what level they provide protection is also of great importance.