The first step in any risk management process is quantifying the risk to be managed, usually through an analysis of historical loss information. However, the assessment of catastrophe risk differs significantly from traditional insurance risks such as automobile collision, fire, or life (mor- tality). These risks are characterized as high-frequency, low-severity (to the insurer, not to the insured) events, and usually affect only one or several risks per occurrence and historical data are usually sufficient to estimate the likelihood of future losses, in terms of both frequency and severity. However, the risk of natural disasters is low-frequency and high- severity. The severity is high because the causative events are large-scale earthquakes or meteorological phenomena affecting thousands of square kilometers, sometimes impacting hundreds of thousands of properties. And since the events are infrequent, historical data are usually insuffi- cient to estimate future monetary losses. Risk assessment needs to be prospective, anticipating scientifically credible events that could happen in the future, but have not yet taken place.
Using current computer technology and the latest earth- and meteor- ological-science information, specialist consulting companies have developed models of earthquakes and other perils, such as hurricanes,
Catastrophe Risk Modeling
cyclones, and floods. These models are now deemed essential by insurers, reinsurers, and government agencies around the world to assess the risk of loss from catastrophic events.
Since model estimates of event severity and frequency, and of conse- quent losses, involve some uncertainty, models are usually constructed using probabilistic formulations that can incorporate this uncertainty into the risk assessment.
Methodology
A typical probabilistic earthquake risk model used by insurers has the five following components, as shown in Figure A3.1.
Stochastic module: The stochastic module describes the physical
parameters, the location, and the frequency of stochastic events. It gen- erates thousands of stochastic events based on historical data and experts’ opinions. Event Loss Table (ELT) EngineEP EP Curves Stochastic module
Describes the physical parameters, location and frequency of stochastic events.
Hazard module
Determine the peak-gust wind speed/peak ground-shaking intensity, etc. for the site.
Vulnerability module
Calculates mean damage ratio (i.e., loss/value) and coefficient of variations to buildings and contents, and resulting loss of use.
Financial analysis module
Calculates different financial loss perspectives for each location considering the insurance/reinsurance policies. Building Information • Construction Class • Number of Stories • Age • Occupancy • Etc. Values at Risk • Building • Contents • Business Interruption / Loss of Use Exposure Location • Address • Postal Code, County or
CRESTA Zone Insurance Structure • Limits • Deductibles • Etc. Portfolio input data Analytical modules Peril-specific
Figure A3.1 Probabilistic Catastrophe Risk Model Modules
Catastrophe Risk Modeling 129
Hazard module: The hazard module defines the frequency and severity
of earthquakes at a specific location within the region of interest. This is done by analyzing historical frequencies and reviewing scientific studies performed on the severity and frequencies in the region of interest. Rele- vant parameters used to define the hazard include location of earthquake faults, their geometry (length, depth, and angle of dip), recurrence fre- quency, and attenuation of ground motion (the amount of ground shaking at a specific distance from the earthquake source). In addition, conditions of site soils need to be included, because variations in local soils can either amplify or reduce the impact of ground shaking. Once the hazard param- eters for each earthquake source are established, stochastic event sets are generated, which define the frequency and severity (hazard) of thousands of stochastic earthquake events. The hazard is defined via an instrumental ground-shaking measure such as peak ground acceleration, peak ground velocity, spectral acceleration, or a qualitative intensity scale, such as Mod- ified Mercalli Intensity (MMI).
The assets at risk—which for an insurance portfolio represents the exposure location and the building information (for example, replace- ment value, type of construction)—are used in combination with the haz- ard module. Property location is essential, since distance from the insured property to each earthquake source greatly influences the level of ground shaking that can be expected in a future earthquake. And with the loca- tion established, local soil information can be incorporated to better esti- mate likely ground shaking.
Vulnerability module: Vulnerability is measured by the damage factor
(D), which is the ratio of the repair cost and the total insured value (TIV). Depending on the type of structural system (for example, frame or walls), the method and time of construction, and the construction mate- rials, specific vulnerability functions are defined. Vulnerability functions typically have been developed based on analysis of claims data from dis- asters throughout the world, engineering-based analytical studies, expert opinions, testing, or a combination of all of these. Vulnerability func- tions have been developed for structural damage, as well as for business interruption losses and damage to contents.
Financial analysis module: This module calculates different financial
loss perspectives for each location considering the insurance/reinsurance policies. An important element of this calculation is the insurance
information, which is expressed through deductibles (d), limits (l), and total insured value (TIV). The quality of the insurance data can vary from crude to very detailed, which will affect the level of uncertainty in the estimation of losses. The gross loss at a property or group of properties is a function of damage and the insurance information, d, l, and TIV, relevant to the properties. This produces a probability distri- bution of loss. The mean, standard deviation, and the loss exceedance curve are estimated from the loss distribution. Net loss to a primary insurer and losses to reinsurers are further calculated based on the appropriate insurance information relevant to facultative reinsurance and treaties. In all cases, the relevant probabilistic information (for example, the expected loss of a treaty layer) is based on gross loss data and the relationship between the loss of interest (for example, treaty layer loss) and gross loss.