Catastrophe Model Structure

CATASTROPHE MODEL STRUCTURE

A catastrophe model that can be used in modelling insurance losses includes
all the primary elements mentioned above. It starts with generating a natural catastrophe event such as a hurricane or an earthquake, then determines its physical characteristics at the locations where insured properties
are situated, and finally determines the degree of damage caused to the properties and the total financial loss to the insurance companies.

The model effectively simulates many (sometimes as high as a million or
even more) hypothetical years and accumulates the loss statistics over these
hypothetical years. The large number of simulations is essential when
dealing with very rare events.

The basic structure of the catastrophe models has been described in this
and the previous chapter. Figure 4.16 shows a structure of a catastrophe
model that is designed specifically for the hurricane hazard; it also shows
some of the parameters that are generated by the model in intermediate
steps in order to arrive at the final result, aggregate financial loss.

Most (but not all) modules of the model are relatively independent of each
other, with one feeding its output into the next one. Each module is critical
in that it affects the end result to a significant degree. This structure explains
the need for the wide-ranging multidisciplinary expertise required for
developing such a model.

The distribution of aggregate insurance losses is the primary piece of
information used in the analysis of indemnity catastrophe bonds. A model
like the one outlined in Figure 4.16 also allows us to produce the probability
distributions of total industry losses or of catastrophic events without referencing
insurance losses, which are needed in the analysis of catastrophe
bonds with industry loss and parametric triggers respectively. Not all
elements of the model might need to be utilised in these cases.

MODELLING TERRORISM RISK

Modelling the risk of terrorist attacks has unique challenges not present in
modelling natural catastrophes. Similar to natural catastrophes, acts of
terrorism are represented by a sample of historical observations. However,
the applicability of such data to the present can be limited in that the political,
societal and technological landscape has probably changed since the
historical observations were made.

Until September 11 of 2001, our assessment of potential terrorist attacks was certainly different. In addition to the changing sociopolitical and technological landscape, there is also the human
factor of terrorists dynamically trying to choose the targets, weapons and
operational means of implementing an attack.
The article on securitising extreme mortality risk provides an overview
of how the risk of terrorism was modelled in some of the extreme mortality

bonds. In summary, the model developed by Milliman for those transactions
was based in part on a multi-level logic tree approach. At each level of
the logic tree, three choices were possible: �success� of the terrorist attack,
resulting in a random number of deaths in the predetermined range;

  �failure� of the terrorist attack; and escalation to the next level of severity
(greater number of deaths). The third choice led to the next level of the decision
tree, where the same choices were presented. At every level,
probabilities of each outcome � �success�, �failure� and escalation � were
determined by fitting a distribution to the actual observations over the
previous six-year period (that included 2001).

The model was simple and based on a very limited number of observations; however, it is not clear that more mathematically sophisticated models add value unless they are based
on additional external information.
The terrorism model described in the chapter on extreme mortality securitisation
focuses entirely on the risk of mortality due to acts of terrorism.
Property and other damage resulting from terrorism was not directly modelled.

Risk Management Solutions (RMS) has developed its own proprietary
terrorism risk model for the US, as well as a global model. The model is
based in part on the game theory approach to reflect changes in the landscape.
The situation is constantly evolving: as antiterrorism measures and
higher security are implemented, terrorists change their tactics and potential
targets. The moving target creates modelling difficulties that cannot be
addressed in a mathematical model but require extensive expert input. In
fact, this might be one of the cases where scenario analysis is preferable to a
fully probabilistic framework.

Using expert input is required to first build a database of potential targets.
Prioritising the targets is the next step; it requires the analysis of both the
target�s attractiveness to a terrorist and the degree of the target protection.
As the latter factors change, the priorities are adjusted as well. The database
of potential targets also contains data on potential damage to life and on
economic loss from a terrorist attack.

A terrorism model should also incorporate the fact of the existence of
several attack modes based on various weapons that could be used. In addition
to conventional weapons, chemical, biological, radiological or nuclear
(CBRN) weapons can be utilised, each with its own probability of occurrence
and potential damage.

The choice of terrorism weapons can also be site-specific, as some weapons would be more natural choices for attacks on specific sites. Finally, the mode of attack might be unconventional but it might not fit in the CBRN category either. The attack on the World Trade
Center in 2001 provides an example of such a type of weapon.

The RMS probabilistic terrorism model is a bold attempt to combine
rather sophisticated approaches taken from game theory, with extensive input on potential targets, threat levels and terrorist behaviour modes, in
order to quantify the risk of losses from terrorism, with the focus on large
losses that can be called catastrophic.

The input is dynamic in that the new developments such as antiterrorism measures, information on potential types of weapons that might be in the hands of terrorists, and even the level
of �chatter� detected by the intelligence community can in theory be
reflected in the inputs into the model or in adjusting some of its parameters.
The overall framework appears to allow a growing degree of sophistication
and the incorporation of additional information on a dynamic basis.

The practical implementation, however, presents numerous challenges.
In assessing a difficult-to-quantify risk such as terrorism, it is particularly
important to augment the probabilistic approach with scenario analysis.
Along with allowing for reasonability testing, scenario analysis introduces
one more way to use expert judgement in analysing exposure to the risk of
terrorist attacks.

MODELLING PANDEMIC FLU RISK

The risk of a global pandemic of an infectious disease is not insignificant.
The chances of a pandemic of a serious disease with a high level of mortality
might be small, but the consequences of such an event would be catastrophic.
Focusing on insurance losses, there would be a spike in mortality rates resulting in life insurance losses of possibly a catastrophic nature, as well as an avalanche of medical claims resulting in huge health insurance losses.

The latter might be the case even if the mortality rate is not high but
the severity of the disease is. Finally, there would be property-casualty
insurance losses. These would obviously include business-interruption
insurance losses. However, it is possible that other lines of property-casualty
insurance business might suffer even greater losses, even though such losses
are usually not fully contemplated in catastrophe risk analysis.

The chapter on extreme mortality bonds describes how pandemics have
been modelled in the context of evaluating their potential impact on
mortality rates resulting in a mortality spike. In analysing the risk of
pandemics, the main focus is flu pandemics, since these are considered to
represent the great majority of this type of risk in modern times.

Milliman created a model for analysing the risk of mortality spikes due to flu pandemics in catastrophe mortality bonds. The model separated the frequency and severity components, parameters of which were estimated based on the available historical data. The data for
frequency was considered over a long (multi-century) period of time, at least in some cases. Binomial distribution was used for annual frequency, which is a natural choice in modelling the frequency of such events.

Severity data was based on five or six data points in the more recent history. In at least one
of the securitisations, Milliman modelled severity as a percentage of excess
mortality fitted to these historical data points, one of which was adjusted by
placing a cap on broad mortality improvements in the general population.
(See the fitted severity curve for excess mortality resulting from pandemics
for the Tartan Capital securitisation, in the chapter on the securitisation of
extreme mortality risk.)

The Milliman model then simulates the pandemic
results by sampling from the frequency and severity distributions. The
current Milliman model�s results are sensitive to the distribution of age and
gender. The binomial frequency distribution assumes that the probability of a
pandemic is the same in any year. It is likely that the current risk of a flu
pandemic is elevated above the average historical levels.

This can be reflected by adjusting the mean of the binomial distribution; significant
judgement and expert input are required to properly make this adjustment.
The Milliman model is of the type that is sometimes called actuarial, in
that frequency and severity are modelled separately based on available
historical data. Another approach � the epidemiological one � is used in the
model developed by RMS.

It is based on a standard epidemiological approach known as SIR modelling (susceptible, infectious, recovered), which allows us to take into account additional variables such as vaccination, immunity, viral characteristics and lethality in a more direct way. The
RMS model presents a more sophisticated approach from the mathematical
point of view; but whether it is better than the simpler Milliman model is not
fully clear, since it requires a number of inputs that introduce uncertainty
and have the potential to skew the results. In the longer term, however, the
RMS model is likely a better one to use for modelling pandemic risk.

The Swiss Re internal model is reported to be a combination of the actuarial
and epidemiological types. The excess mortality rates are estimated
based on historical data as in the Milliman model, but are then adjusted to
take into account the changes that have happened since those observed
events. These changes include new virus threats, vaccinations, better standards
of medical care, etc. A significant degree of judgement is used in
making these adjustments.

The article on securitisation of extreme mortality risk shows a fully
stochastic model of the spread of a pandemic, implemented on the Los
Alamos National Lab supercomputer. This approach is probably the one that will eventually become the standard. Right now it is not realistic. Of the
models described above, the RMS model is the closest to this approach.

PRACTICAL MODELLING OF CATASTROPHE RISK

It is not certain that everything is uncertain.
Blaise Pascal

The time of occurrence of a natural catastrophe is unpredictable. Its magnitude
is unpredictable too. So is the damage it causes in its wake. This is the
inherent uncertainty associated with such events as hurricanes or earthquakes.
When it comes to natural catastrophes, we are in the country where
predictions do not work.

Manmade catastrophes are in the same territory. The goal of modelling catastrophic events in the context of insurance securitisation as well as in general is to minimise the uncertainty
surrounding the probability distribution of possible outcomes. The closest to
certainty is the one who most precisely identifies and quantifies the uncertainty
of these random variables.

Available models

The previous chapter identified the three main providers of commercial
catastrophe-modelling software used in the analysis of potential insurance
losses. In addition to AIR Worldwide, EQECAT and Risk Management
Solutions, there are additional providers of either software or consulting
services based on proprietary software for modelling of catastrophic insurance
losses.

These tend to focus on one type of hazard in a specific
geographic area. For example, Applied Research Associates� hurricane
model and URS�s earthquake models (combined and modified under the
Baseline Management umbrella) are now covering all of the US. There are
also some noncommercial models such as the Florida Public Hurricane Loss
model (for Florida hurricane risk only) and FEMA�s HAZUS tool, which in
its modified form can be used for modelling insurance losses.

While a number of external models exist, in practice only the main three,
AIR Worldwide, EQECAT and Risk Management Solutions, have been
utilised in securitisation of insurance risk. This is reflective of the complete
domination of these three companies in the insurance and reinsurance
industry and the credibility they have earned over the years.

Problems � realor perceived � with modelling software developed by these companies have
been pointed out on a number of occasions. However, they do have the track
record and credibility that no competitor possesses.
Some companies in the industry, in particular reinsurance companies, have developed their own proprietary models of insurance catastrophe risk.

However, these are generally not full catastrophe models but rather the software
that sits on top of the three established models and uses their output
to obtain its own estimate, which might be different from the results of each
of the underlying models.

While not every peril in every geographical area can be modelled, there
now exist catastrophe models covering all the key areas of insurance exposure.
Table 4.5 shows an incomplete list of the existing peril models and the
countries for which they have been created. In almost all circumstances, all
three major modelling companies would have these models.

While many individual models � for specific perils and countries � are
available, not all of them have the same degree of credibility. Models for
some regions and perils are based on more extensive research and have
existed for a longer period of time. The longer period of time has created
more opportunities for model validation and refinement. Not surprisingly,
the three most refined models cover:

1. North Atlantic hurricanes (in particular Florida and the other Gulf
states in the US);
2. California earthquakes; and
3. Japanese earthquakes.

These three represent the biggest catastrophe risks for the insurance
industry. They combine high concentration of insured exposure and high
probability of catastrophic events. Even though the models produced by the
three modelling firms have existed for a long time, their results differ, sometimes
significantly, from one firm to another, and significant adjustments to
each of them have been made even very recently.

The net result is the uncertainty that still exists in quantifying catastrophe insurance exposure
even in the areas where the research has been extensive and the investment
in model development quite sizable.

It is important to carefully analyse whether indirect effects of natural
catastrophes have been modelled, and, if so, how. These indirect effects
include, for example, flood following a hurricane and fire following an
earthquake. These secondary effects might result in more damage than the
primary ones, and their proper modelling is critical.

Unmodelled losses

One of the most common examples of unmodelled losses are those that
reflect improper data coding, resulting in wrong or incomplete entry of

Period	Peril	Country+
Hurricanes, cyclones and storms	North America, Mexico and Caribbean	US (including Alaska), Mexico, Bahamas, Barbados, Bermuda, Cayman Islands, Dominican Republic, Jamaica, Puerto Rico, Trinidad and Tobago
	Europe	Austria, Belgium, Denmark, France, Germany, Ireland, Netherlands, Norway, Sweden, Switzerland, UK (including flood)
	Asia-Pacific	Australia, China (including Hong Kong), Hawaii (US), Japan, Philippines, Taiwan
Earthquakes	North America, Mexico and Caribbean	US (including Alaska), Canada, Mexico, Bahamas, Barbados, Cayman Islands, Dominican Republic, Jamaica, Puerto Rico, Trinidad and Tobago
	Central and South America	Belize, Chile, Costa Rica, Colombia, El Salvador, Guatemala, Honduras, Nicaragua, Panama, Peru, Venezuela
	Europe and Middle East	Greece, Israel, Italy, Portugal, Switzerland, Turkey
	Asia-Pacific	Australia, China, Hawaii (US), Indonesia, Japan, New Zealand, Philippines, Taiwan
Tornado and related	North America	Canada, US
Terrorism	North America	US (worldwide terrorism models also exist but their credibility level is unclear)
Flu pandemic	Worldwide	Worldwide

exposure into the model. This is part of the pervasive issue of data quality
described below.
It is not unusual for some of the insured exposure not to be reflected in the
models because they are not designed to handle specific types of coverage.
Additional perils, related to the main one but in an indirect fashion, would
probably not be taken into account by the model.

Finally, there might be insurance losses due to catastrophic events that have never been contemplated in the original coverage but still have to be paid by insurance
companies. Care should be taken to make sure that all losses that can be
modelled by catastrophe software are input, and any other losses evaluated
separately.

The issue of data quality is usually raised not in the context of the data
used to formulate and parameterise the models, but in assessing the reliability
and completeness of the data on the details of the exposure in applying
a catastrophe model to a portfolio of insurance policies. 

Quality of the insurance data serving as input into catastrophe models is an industry-wide issue
introducing a significant degree of uncertainty to results of the modelling
process. Best practices are still in the process of being developed, and the
quality of data can vary widely from one insurance company to another.
Improper data coding or not capturing all the relevant exposure data in
sufficient detail is also an indication of deficiencies in the underwriting
process.

Implications for investors can be significant. Two insurance-linked securities,
such as catastrophe bonds with indemnity trigger, might appear very
similar but in reality have different risk profiles because of the different

Modelling results presented to investors

As a reminder of the primary goal of the analysis, Panel 4.4 shows the
summary output of the risk analysis performed for an indemnity catastrophe
bond (see the chapter on property catastrophe bonds for additional
information). It is no more than a summary, but it is often the main part of
the information included in the offering circulars, no matter how long the
risk analysis section appears to be.

DATA QUALITY

The quality of data used in catastrophe models is as important as the quality
of the models themselves. Data used to create and parameterise the models
affects the precision and correctness of modelling results. Many elements of
the existing models have been built so that they can take advantage of the
most reliable data available. For example, certain hurricane data available
from the National Oceanic and Atmospheric Administration databases
include measurements at six-hour intervals. Models have been constructed
specifically to take the six-hour intervals into account, as other data is either
unavailable or not fully reliable. This is also the data used to validate the
models.

ILLUSTRATIVE SUMMARY OUTPUT OF RISK ANALYSIS OF A CATASTROPHE BOND

A simplified catastrophe bond description is presented below. The
coverage attaches at US$5 billion of ultimate net loss resulting from a single
occurrence of a hurricane.

Transaction parameters

Covered risk :                               Hurricane affecting specific insurance portfolio
Trigger:                                         Indemnity per occurrence (UNL)
Attachment:                                  level US$5.0 billion
Exhaustion:                                   level US$5.5 billion
Insurance percentage:                 50%
Principal amount:                        US$250 million

Based on the per-occurrence exceedance probabilities resulting from catastrophe
modelling of the subject insurance portfolio, key risk measures are
calculated. The expected loss in this example is 1.48% per annum. The
attachment probability is 1.70%.

Risk measures	Base case  (standard catalogue) (%)	Warm Sea Surface Temperature catalogue (%)
Attachment probability	1.70	2.54
Exhaustion probability	1.30	1.83
Expected loss	1.48	2.15

In this example, modelling was done twice: first with parameterisation
based on the long-term historical averages of hurricane activity in the
covered territory, and then based on the so-called Warm Sea Surface
Temperature catalogue to take into account the greater chance of hurricane
activity in the current period. The latter is of most interest since it is believed
to present results that are more realistic.

This summary does not include many of the other important elements of
risk analysis. However, it does show the two figures of most interest to
investors: expected loss and attachment probability. Expected loss provided
in the offering circular serves as the starting point for analysis performed by
investors.

degrees of uncertainty related to data quality and underwriting standards in
general. In evaluating such insurance-linked securities, the few investors
familiar with underwriting processes of individual insurance companies can
have an advantage over those not possessing this level of expertise.
The seemingly inconsequential issue of data quality can play a much
greater role in modelling catastrophe risk than we would expect. It presents
a good illustration of the �garbage in, garbage out� principle, and could be
an important element of the analysis performed by investors.

INVESTOR AND CATASTROPHE MODELLING

Investors in catastrophe insurance-linked securities are presented with
numerous choices and decisions in their analysis. Most of them have been
mentioned or alluded to above.

The questions to be answered are numerous. Which catastrophe model is
most appropriate for a specific type of risk exposure? How different are the
results of different models? Are there known biases in some models related
to specific perils or geographical regions? Are models for one region more
credible than for another?

How can we quantify the additional uncertainty
related to the lower credibility of some models? Are there ways to validate
some modelling results? What are the primary sources of uncertainty in the
modelling? How do we quantify the additional uncertainty of securities
with indemnity as opposed to parametric trigger?

The list of questions never ends, which once again underscores the advantages
of having modelling expertise in the analysis of insurance-linked
securities. It almost makes us wonder whether the informational disadvantage
of the investor is too great to play the ILS game. The disadvantage is
relative to both the sponsors of catastrophe bonds and to reinsurance
companies that often invest in these securities. Both seem to have the level of expertise that an investor is usually unable to achieve.

The answer to this question is more optimistic than it appears to be, however. Investors can and
do participate in this market and generate attractive risk-adjusted returns.
While reinsurance companies in their role as investors seem to have some
expertise that few investors possess, it is not necessarily the type of expertise
that is most important in ILS investing.

Investors have the capital markets outlook that is usually lacking in insurance and reinsurance companies investing in insurance-linked securities. This capital markets view gives
investors an advantage in some areas even when they are disadvantaged at
others. Ultimately, the conclusion is simple: modelling is critical, and without modelling expertise it is impossible to generate high-risk adjusted returns
on a consistent basis. The industry is slowly coming to this realisation.
Managing catastrophe risk on a portfolio basis is one of the most critical
elements of ILS investing. The choice of modelling tools is now available for
this purpose; it is also discussed in the chapter on modelling portfolios of
catastrophe insurance-linked securities.

CATASTROPHE BOND REMODELLING

Almost every cat bond transaction has involved the analysis performed by
one of the three main modelling agencies, AIR Worldwide, EQECAT and
RMS. The summary of the analysis is included in the offering documents; a
data file such as an Excel spreadsheet might also be provided as part of the
offering circulars.

This raises the question of the differences between
models. The annual expected loss or probability of attachment calculated by
AIR Worldwide might differ, perhaps significantly, from the annual
expected loss or probability of attachment if they were calculated by one of
the other models based on the same data.

Leaving aside for a moment the question of which model is �better�, in
the ideal world an investor would like to see the analysis performed by all
three modelling firms and then make their own conclusions. �Remodelling�
refers to analysing a catastrophe bond by a modelling firm that did not
perform the initial analysis that was included in the offering documents and
used in pricing of the bond.

If the security has a parametric trigger, all the
data is available and another modelling firm can easily perform its own
analysis so that the results can be compared. Comparison is much more
difficult for indemnity catastrophe bonds. For these bonds, it is necessary to
have full exposure information in order to perform the analysis. Such information
is never provided to investors; only summaries are included in the
offering circulars.

In order to perform the analysis, in this situation another modelling firm
has to make a choice between two simplifying assumptions. One of them is
to assume the correctness of the analysis, such as the values of expected loss,
attachment probability and the exhaustion probability. Based on these
figures and the exposure summary in the offering circular, the modeller then
tries to work back to the inputs to arrive at exposure expressed at a greater
level of detail than is provided in the documentation.

The exposure information is important in portfolio management, where it allows us to monitor
exposure accumulation over many securities and properly establish the
risk�return tradeoffs on a portfolio basis.

Another choice would be to start with the exposure summary in the
investor documents, and try to estimate what the exposure is at a more
detailed level. This could be done by supplementing the exposure data
provided with publicly available data on the geographic and line-of-business
distribution of exposure for the sponsor, as well as the possible
knowledge by the modeller of the underwriting processes of the sponsor.

The resultant expected loss and the exceedance probability would then
differ from those in the offering circular. This type of analysis can now be performed very fast, even during the initial marketing stage before the bond pricing has been finalised. This topic
is revisited later in greater detail.

HURRICANE FORECASTING

�Hurricane forecasting� refers to probabilistic predictions of hurricane
activity in the short term. These are not actual forecasts but probability
distributions of potential outcomes based on the most current data. These
forecasts refer to the upcoming hurricane season or a season already in
progress.

William Gray, for all intents and purposes, pioneered the field of hurricane
forecasting. He developed a number of forecasting methodologies with
a special focus on North Atlantic hurricanes. Phil Klotzbach, who has taken
from him the leadership of the hurricane forecasting project, in 2009 started
issuing 15-day forecasts in addition to the seasonal ones.

This is a big change from issuing forecasts from the one to five times a year common for hurricane forecasters. The Klotzbach/Gray group has proven its skill over the
years of issuing hurricane forecasts for the North Atlantic. Its methodology
is continuing to evolve, but in most general terms it is based on identifying and monitoring several atmospheric and/or oceanic physical variables,
either global or relatively localised, that are relatively independent of each
other and have been shown, by utilising statistical analysis tools, to serve as
good predictors of the following North Atlantic hurricane season.

NOAA issues hurricane forecasts too, as do several research groups
around the world. It appears that as of 2009 only the Klotzbach/Gray group
has been able to clearly demonstrate its skill in forecasting probability of
major hurricane landfalls in the US.

Other groups either do not issue forecasts associated with landfalls or have not been recognised for their skill in successfully forecasting landfalls. In insurance catastrophe modelling, landfalls
are of major importance, while hurricanes that bypass land are of
interest only if they have the potential to damage oil platforms.

The forecasts create additional opportunities for optimising risk-adjusted
return on a portfolio basis. They also provide input into pricing of all
affected insurance-linked securities, and in particular ILWs, securitised reinsurance
and catastrophe bonds close to expiration.

Live cats

The term �hurricane forecasting� is also used in reference to probabilistic
assessment of development of the storms and hurricanes that have already
formed and might make a landfall. The ability to trade the risk of natural
catastrophic events that can occur in the very near future � from several days
to several hours � creates opportunities for those who can obtain better
information on the projected path and potential damage from the hurricane
and to better take advantage of the situation. It also creates opportunities to
offload excess risk if necessary.

This �live cat� trading can be done on a more
intelligent basis when short-term hurricane forecasts have a relative degree
of credibility.

The topic of hurricane forecasting is revisited in the chapters on ILWs and
catastrophe derivatives and on managing investment portfolios of insurance
catastrophe risk.

CLIMATE CHANGE
The trouble with our times is that the future is not what it used to be.
Paul Val�ry

Climate change has been mentioned more than once in the context of modelling
catastrophe risk. The expectations of the future climate state are
different from its current one. The effects of climate change relevant to hurricane
activity, in particular the increase in sea-surface temperature, can
already be observed. These changes make it harder to rely on the old
approach of forming conclusions about future natural catastrophe activity
based entirely on prior historical observations.

The future frequency and severity of hurricane events might be a function of atmospheric and oceanic processes that are different from the ones in the period of historical observations.
The focus of an investor in the analysis of insurance-linked securities tied
to the risk of natural catastrophes is on the relatively short time horizon.
Changes expected to take place over a long period of time are of less significance
due to their minimal impact on catastrophe-linked securities that
tend to have short tenor.

Unless there is a clearly observable trend, this view
suggests disregarding recent changes and relying primarily on the longterm averages of hurricane frequency and severity. If the speed of the
climate change is rapid, though, this view might be incorrect; there is a need
also to reflect the developing new environment in evaluating the risk of
future hurricanes. In addition, it is possible that the climate changes have
already altered the atmospheric and oceanic processes, probably starting a
number of years ago.

This view would necessitate immediately taking
climate change into account. In simple terms, we can then see the observed
historical sample of hurricane activity as consisting of two parts: the first,
longer, period when the conditions were relatively constant and the variability
was due to natural statistical fluctuations; and the second period
encompassing more recent years when a trend might be present in the
changing atmospheric and oceanic conditions that influence hurricane
activity. The trend might be accelerating, as suggested by all of the global
warming theories.

The decision regarding whether we are in the period of heightened hurricane
activity and whether this activity is likely to accelerate in the very near
future is an important one both for insurance companies with significant
hurricane risk accumulation and for investors in catastrophe insurancelinked
securities. The majority have decided that we are now in a period of
climate change that has higher probability of hurricane activity than
suggested by long-term historical averages.

The modelling firms have incorporated this approach by creating an option in their software models to allow users to make their own choice about whether to base the analysis on
long-term averages or assume higher levels of hurricane activity than
suggested by the history. The latter option is referred to as using the Warm
Sea Temperature Conditioned Catalogue of events when no additional
trends are taken into account.

The decision to use higher levels of potential hurricane activity as the
primary modelling approach is not tied directly to the acceptance of the
global warming theory; as mentioned earlier, the shorter-term climate
processes of an oscillating nature can provide a sufficient reason for
believing we are in an environment more conducive to hurricane development
than in the past.

SPONSOR PERSPECTIVE ON MODELLING

The importance of catastrophe modelling for insurance and reinsurance
companies is apparent. Modelling catastrophe insurance risk is part of the
enterprise risk management (ERM) process. Its results are used in making
decisions on the best ways to employ company capital. They are an important input in decisions on whether to retain the risk, reinsure some of it or
transfer it to the capital markets.

The transfer to the capital markets can be
in the form of sponsoring insurance-linked securities such as catastrophe
bonds or in the form of hedging catastrophe exposure by purchasing ILWs
or catastrophe derivatives. Another option available to insurance and reinsurance
companies is to rebalance or reduce their underwriting to lower the
overall exposure to catastrophe risk.

For companies writing insurance that creates catastrophe exposure,
modelling the risk of catastrophes is part of the standard business processes
of underwriting and risk management; it is used also in capital allocation.
Facilitating risk securitisation is not the primary goal of catastrophe modelling,
even though the decision to transfer some of the risk to capital markets
might be based on the modelling results. Instead, the emphasis is on total
risk exposure.

Modelling catastrophe risk is growing in importance at insurance
and reinsurance companies, as management see the benefits it delivers.
Quantification of catastrophe risk exposure is also driven by shareholders
and rating agencies. Regulators are also paying more attention to catastrophe
risk than ever in the past.

It would appear that the insurance industry has greater expertise in
modelling catastrophe risk than the investor community. While this is
generally true, there are investors who are very sophisticated in catastrophe
modelling, while the insurance industry expertise is generic and not focused
on the specific issues relevant to securitising insurance risk.

MODELLING AS A SOURCE OF COMPETITIVE ADVANTAGE TO INVESTORS

The primary risk of insurance-linked securities in almost all cases is, of
course, the insurance risk. The risk of catastrophic events is the one most
commonly transferred to investors; on the property insurance side the risk
of catastrophic events fully dominates insurance securitisation. To make an
informed decision, an ILS investor has to understand the risk profile of these
securities.

Without this understanding, it is impossible to make any intelligent
decisions on individual insurance-linked securities or their portfolios.
Catastrophe modelling and the risk analysis based on it are key to understanding
the risk profile of these securities.

(As pointed out earlier, there might be situations when an investor makes an informed decision to allocate a small portion of their assets to insurance-linked securities without developing
expertise in this asset class. These situations are rare.)

Since the ability to quantify risk and determine its proper price is based on catastrophe modelling and risk analysis, those investors better able to
understand the risk analysis section of the offering circulars for catastrophe
bonds have an immediate advantage over the rest of the investor community.
Properly interpreting the risk analysis section requires knowledge of
modelling techniques used, modelling software packages utilised, model
credibility, the way exposure data is captured, and other modelling-related
issues.

Those who have better understanding of these issues have an advantage
over those who do not. They are in a better position to quantify the
uncertainty, make adjustments if necessary, and extract more useful information
from the same risk analysis section of the offering circulars. This
advantage is not limited to catastrophe bonds and is applicable to all types
of catastrophe insurance-linked securities.

Finally, those investors who use catastrophe modelling tools themselves
have an extra advantage over those who do not. They tend to have a greater
degree of understanding of the assumptions underlying the models and the
types of uncertainty involved. The most sophisticated of them are able to
perform additional sensitivity analysis and scenario testing, to come up with
a better understanding of the risk profile of the security and the price to
charge for assuming this risk.

An example of the competitive advantage held by those with superior
understanding of catastrophe modelling tools can be found in the analysis
of California earthquake exposure. The difference in scientific views on
which part of the San Andreas fault is most ripe for a major earthquake
(referred to earlier in this chapter) is one of the reasons for the divergence in
results among commercial catastrophe models in estimating expected losses
at various exceedance levels from one part of California to another.

(The divergence is true at the time of writing; models evolve, and updates and
new releases are issued periodically.) Understanding the difference between
models is by itself a source of competitive advantage; having an informed opinion on which model is likely to produce more precise results for a
specific peril and geographical territory adds significantly to this competitive
advantage.

Even an informed view on the likely variability of results
around the expected mean for a specific peril and geographical territory,
and how it varies from model to model, is an informational advantage.
The use of models by investors is of particular importance in portfolio
management.

Without using real catastrophe models, all an investor can do
is to make very rough estimates of the risk accumulation by peril/geography
bucket and try to put limits on individual risk buckets. There is no
way to properly estimate risk-adjusted return for the portfolio, or how the
addition of a position will affect the overall risk�return profile. The investors
who are able to use modelling tools, both in the analysis of individual securities
and in portfolio management, have an important competitive
advantage, the value of which is magnified by the overall inefficiency of the
insurance-linked securities market.

MODELLING AS A SOURCE OF COMPETITIVE DISADVANTAGE TO INVESTORS

The appearance of models designed specifically for investors in insurancelinked
securities such as catastrophe bonds is changing the way some
investors are approaching ILS investing. Some of those who never utilised
catastrophe modelling tools before have now tried to use the new software
to model their ILS portfolios.

The models designed specifically for investors
are described elsewhere, including in the chapter on portfolio management.
They are much simpler to use and understand than the full-blown catastrophe
models used by insurance companies and, in most cases, by
modellers providing the risk analysis in structuring catastrophe bonds. They
do provide ways to analyse and visualise portfolio exposure, perform �what
if� analysis, and more. They appear to be simple to use.

The seeming simplicity of the tools is deceptive, however. By themselves
they do not provide more than a software platform to combine individual
cat bonds into one portfolio, with a semiautomatic way of calculating
several risk measures.

This platform is very useful to those who already
understand the modelling approaches, the assumptions used in modelling,
the differences between the models used for initial analysis, the degree of
possible unmodelled risk, and many other factors required for using modelling
tools and properly interpreting modelling results.

For others, not possessing this expertise, the picture might be different. The availability of a
tool that is a black box to a user can have mixed consequences. The tools
themselves are not true black boxes: they are black boxes only to those who
do not have the requisite expertise to use them effectively.

While most ILS investors do not use these portfolio management tools,
some of those who do may be worse off than if they did not. The ability to
see all securities in one portfolio and have the software spit out risk
measures and other statistics can create the illusion of understanding and
properly managing portfolio risk when none is present.

Modelling can be very dangerous to investorswho lack the understanding
of howit is performed andwhat the resultsmean.Of course, the danger is not
in modelling, but in not having the level of expertise needed to understand
the modelling methods, output and implications. This problem has existed
for a very long time and is unrelated to the appearance of software tools
targeted specifically at the ILS investor.

Improper interpretation of the risk analysis section of offering circulars by some investors has been going on for so long because of the seeming simplicity of the data presented. It creates the
illusion of understanding, and that can be very dangerous. Some investors
have become proficient in the lingo of catastrophe bonds and relatedmodelling
but,without realising it, have not gained the level of expertise needed to
turnmodelling into a useful tool. To think they understand the risk of securitieswhen
they really do not creates a dangerous situation.

The false sense of security when it comes to risk management, and the
illusion of actively managing a portfolio to maximise its risk-adjusted
return, can lead to catastrophic results for some investors in catastrophe risk.
One more danger to point out is that the investors focused on modelling
catastrophe risk are sometimes focused on it too much, to the degree that
they do not pay the necessary attention to other types of risk associated with
insurance-linked securities.

These other risks are important in the analysis of
individual securities; it is also important to take them into account when
these securities become part of an investment portfolio.

The problems mentioned above would become obvious and self-correct
in investing in almost any other asset class. The level of historical returns
and their volatility by itself would be a clear indicator of investor expertise,
in most cases. Catastrophe ILS are tied to the risk of very rare events, and a
track record of several years says little about the level of risk-adjusted
returns generated.

TRENDS AND EXPECTATIONS

The importance of modelling in the analysis of insurance-linked securities is
impossible to overestimate. The specific type of modelling involved in the
probabilistic analysis of catastrophe events and the resulting insurance
losses is unusual in the investment world and requires specialised expertise.
The times when most investors made their decisions based on the rudimentary
analysis of the information in the offering documents have passed. A
greater level of sophistication is now required.

Insurance and reinsurance companies seeking to transfer some of their
risk to the capital markets in the form of insurance-linked securities
have dramatically improved and continue to improve their risk modelling
and management. They are more and more finding themselves in the position of being able to make fully informed decisions on the ways
to manage their catastrophe exposure and properly choose among such
options as reinsurance, securitisation and retaining catastrophe risk.

• Superior modelling skills and the ability to better interpret results of modelling catastrophic events are a major source of competitive advantage to the investors who have this level of expertise. As the importance of modelling is becoming more widely recognised, those who lack the expertise will find it increasingly difficult to compete effectively.
• The ability to model risk is particularly valuable in assembling and managing portfolios of insurance-linked securities. This skill is even more important at the portfolio management level than in determining the right price for a particular catastrophe bond or another security whose risk is linked to catastrophic events.
• Without models, it is impossible to assess the risk-adjusted return in investing in catastrophe-linked securities. Without understanding the risk profile of a security, investors are in no position to evaluate whether they are being properly compensated for assuming the risk.
• Track record of a fund investing in insurance-linked securities can often be meaningless and even misleading. Some of the investors who have been most successful on paper have achieved higher returns by taking on disproportionate amounts of risk, often unknowingly. Without properly utilised models, we cannot analyse this type of risk. When investing in the more traditional asset classes such as equities, track record of returns is usually very informative and revealing; but it is of less importance in investing in insurance-linked securities and can be considered only in the context of the risk that has been taken. Catastrophic events are, by their very definition, very rare, and it is possible for an investor to �be lucky� for quite a long period of time even when the investment portfolio is completely mismanaged.  advantage for an investor in insurance-linked securities. It also enables better decision making for sponsors in dealing with the issues of basis risk.
• Issues of data quality, understanding model limitations, credibility of models, and biases among existing models are key components of the type of expertise that can provide a competitive advantage.
• Important as the use of modelling tools is, better understanding of the assumptions and superior interpretation of the results are of even greater significance. These two can be the most important sources of competitive advantage.

This article provided but an introduction to selected concepts in modelling
catastrophic events in the context of analysing insurance risk securitisation.
Some additional information on the topic can be found in other post in this blog.
The issues touched on here should provide an understanding of why modelling
catastrophe risk is important and why it is so difficult.