In this issue:-
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and windstorms are among the most serious climatological perils in New South
Wales, each of them accounting for roughly one third of all severe weather events.
Although these phenomena occur rather infrequently, the associated losses may
feature prominently in the loss records of insurance companies. The recent Sydney
hailstorm of April 1999 is a good example of the damage potential of severe
hailstorms in urban areas (NHQ, 2/1999). The estimated $1.6 billion insured
loss makes it, in insurance terms, Australia's most costly natural disaster.
The fact that the fourth and sixth most costly insured losses recorded by the
Insurance Council of Australia over the last 30 years are also attributed to
hailstorms (i.e. Sydney 1990, $348 million; Brisbane 1985, $299 million) reinforces
the damage potential of this peril.
From the perspective of insurance or reinsurance companies, the damage potential and losses associated with such hailstorms can be modelled in two different ways: using the traditional approach based on experience and extrapolation of past losses, or through stochastic modelling based on physical characteristics and impact patterns of actual hailstorms. While the former approach is still favoured by many insurers, the latter method is increasingly gaining in popularity. Both methods require comprehensive information about the exposure and vulnerability of the portfolios to be modelled, and both are commonly used to assist direct insurers and reinsurers in pricing catastrophe reinsurance programs.
Notwithstanding certain similarities in the treatment of the exposure and vulnerability data, the two methods display major differences in their handling of the climatological data. In the case of the extrapolation method, the emphasis is very much on loss return periods and the underlying climatological information tends to be of poor or very poor quality. Furthermore, this approach usually focuses on the estimation of a single value, the Probable Maximum Loss (PML). Currently, this method seems to be entrenched in the industry, despite the fact that it cannot produce physically meaningful and defendable results for long return periods that can easily exceed the life or experience span of individual underwriters and company loss histories.
Stochastic modelling of hailstorms, on the other hand, can provide a total loss profile over all return periods and has the potential to provide more reliable estimates of losses located in the tail of the loss distribution (longer return periods). The prerequisites for such an approach are however, good quality climatological data. Given the existence of such quality data sets, such as the Natural Hazards Research Centre (NHRC) hail database, stochastic modelling can produce comprehensive loss profiles for particular portfolios as well as generate a range of "what if" scenarios. Such information can assist managers in areas such as pricing strategy, corporate planning, portfolio management and analysis of reinsurance programs.
One such application of stochastic models, which cannot be easily achieved through extrapolation modelling, is demonstrated by the example of potential motor vehicle losses due to the April 1999 Sydney hailstorm. The results of this simulation, shown in Figure 1, were generated with the help of HailAUS, a hail loss model for Sydney and Brisbane developed by the NHRC. Despite the impact this storm made on all sectors of society, the major climatological parameters (i.e., storm area and maximum hailstone size) associated with the hailstorm were not unprecedented in the Sydney area. In fact, with a return period in the order of 25-30 years, these parameters display a relatively high frequency (NHQ, 2/1999). Thus, other factors such as location, timing and path of the storm played important roles in determining the size of the $1600 million total loss.
Figure1. Distribution of possible car (a) and house (b) losses due to hail associated with the April 1999 Sydney hailstorm. (Produced by the HailAUS model run with a constant hailstone size and hailstorm area, but otherwise stochastically simulated storm parameters and car movement patterns).
The damage to motor vehicles (houses) resulting from the April 1999 Sydney storm accounted for approximately $409 million ($422 million) out of the total $1600 million loss. In contrast to the extrapolation method, stochastic models can help to put this loss value into meaningful perspective. The (calibrated) HailAUS model, for example, allows us to assess whether the $409 million car loss, which corresponds to a return period substantially above 100 years ($422 million loss for houses corresponding to a return period below 100 years) is the maximum possible loss to cars in the Sydney area given the physical size of the April 1999 Sydney storm.
To achieve this, the respective hailstone size and storm area can be held constant in the model, while all other physical parameters (e.g. storm alignment, storm centre, month, day, time of day, car concentration pattern, etc.) are run through several thousands of stochastic iterations. The resulting loss distributions of a 50,000-storm simulation are shown in Figure 1. The results indicate that the recorded $409 million car loss ($422 million house loss) is indeed located in the tail section of the distribution, although several percent of hypothetical April 1999 storm scenarios (other time and location combinations) produced even higher losses. In fact, the model indicates that the experienced losses of $409 million and $422 million, respectively, were only about two-thirds the size of the maximum losses ($650 million and $690 million, respectively) possible for such a hailstorm. The distributions of losses shown in Figure 1 can be considered as very realistic, as the actual losses of $409 million (cars) and $422 million (houses) differ only marginally from the model estimates of $402 million for cars and $464 million for houses.
Figure 2. Variability of the modelled mean annual aggregate loss values for cars in the Sydney region as a function of the number of model iterations. (Loss values are calculated and plotted after each additional 1000 years of simulation).
This example was run on the ensemble of vehicle exposure data for ICA Zones 41-43, but such a simulation can be easily tailored for portfolios of individual companies or selected postcodes. The NHRC offers various types of consultancies based on the hail model.
While the results of most extrapolation methods are inherently noisy (displaying fluctuating results after every major event due to the short loss data period used) an often-asked question by the insurance sector relates to the uncertainties associated with the synthetic loss estimates and the stability of the model results (convergence of the model). These two parameters are partly a function of the completeness of the climatological data and of the number of iterations applied to the model. While any model result will contain some uncertainties, the distributions used in the HailAUS hazard occurrence module are based on the best hail data set available in this country (over 800 hailstorms, which represent only the more recent part of the original NHRC hail data set for Sydney). The same module uses a full Monte Carlo method, and therefore needs to be run for several thousand iterations in order to achieve convergence and to represent the tail sections of the respective distributions realistically. In the case of the HailAUS model, the number of iterations typically has to be in the order of 10,000 years to achieve a convergence of the mean loss value below 1 percent (in the order of 3000 years to achieve a convergence of the mean loss below 3 percent). A graphical example of the convergence characteristics of the HailAUS model, which shows the variability of the mean annual loss aggregate values for cars for the range of 3000-25000 simulation years, is presented in Figure 2.
Recently, the four partners decided to support a second stage of the project that will focus on extending the scope and spatial coverage of the current model. Additional features will include:
* increasing the spatial coverage to areas located to the north and south of Sydney, i.e. ICA zones 40 and 44 (Figure 3)
* incorporating an optional, experimental El Niño-Southern Oscillation (ENSO) cycle into the hazard occurrence module
* and improving the quality of model results through addition of the April 1999 Sydney hailstorm data (NHQ, 2/1999).
The spatially extended HailAUS will includeWollongong and Gosford regions (Figure 3), which are of interest to many direct insurers. Similar to the first model version, which concentrated on ICA zones 41-43, version 2 of the model will be able to produce two types of loss estimates (annual aggregates or individual storm basis) applicable to the entire region, individual ICA zones or individual postcodes. Loss profiles will be derived either from in-built model data, representing all units at risk, or from individual company portfolios.
Figure 4. Theoretical Southern Oscillation Index (SOI) cycle favouring a more frequent hailstorm development in the Sydney region i.e. rising SOI between July and November, falling SOI thereafter. (La Niña (El Niño) conditions are marked by positive (negative) SOI values. Autumn months (shaded) are not considered in the analysis due to strong fluctuations of the SOI during this period.)
The second major feature of the HailAUS model version 2 will be the incorporation of an experimental El Niño-Southern Oscillation (ENSO) cycle into the hazard occurrence module. As mentioned in NHQ 4/1997, the ENSO, which is an ocean-atmosphere coupled phenomenon, has a strong influence on the east Australian climate; (partly) as its consequence, the probability of reaching the mean annual hailstorm number in the Sydney region tends to vary considerably from year to year. In fact the probability values tend to depend on the type of the annual Southern Oscillation Index (SOI) cycle. The Southern Oscillation Index measures the strength of the El Niño-Southern Oscillation signal; negative (positive) Southern Oscillation Index values, corresponding to El Niño (La Niña) periods, tend to be associated with drier-than-normal (wetter than normal) conditions in eastern Australia. Certain Southern Oscillation Index cycles, such as the one shown in Figure 4, appear to favour more frequent hailstorm development, and thus a substantially higher annual number of hailstorms in the Sydney region.
This experimental feature will enable a type of sensitivity analysis to be performed on the annual number of hailstorms. It will provide composite scenarios for extreme El Niño-Southern Oscillation cycles and allow a more critical and informed approach to hail loss pricing.
These stochastic results provide useful additional information, which can be used in conjunction with existing approaches. Moreover, they broaden the spectrum of model risk scenarios, which are already readily available for other perils, such as tropical cyclones or earthquakes.
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Natural Hazards Research
Natural Hazards Research