Catastrophe Models for Property Casualty Insurers

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					          The Need for Casualty Catastrophe Models
          A Way to Prepare for the ‘Next Asbestos’
     By Matthew Ball, Yi Jing and Landon Sullivan

     Casualty catastrophes pose a risk too serious to ignore, yet until now
     models to estimate mass torts from these events were not readily available.
     modeling advances now make it possible to prepare for the “next asbestos.”

Overview                                                   business exposed, the claim-handling unit assigned
                                                           to the losses or a financial threshold. Often, an
Insurers bound by Solvency II will be required to          event will be considered a casualty catastrophe if
explicitly estimate the potential impact of mass           total losses and related expenses exceed some
torts, casualty catastrophes or “binary events”            dollar amount, frequently $50 million or $100 million.
as part of insurers’ technical provisions. Even            In the U.S., many of these events occur each year.
where it is not currently a regulatory requirement,
many casualty insurers are already aware that              Asbestos is by far the largest mass tort experienced
understanding their potential exposures to mass            by the casualty insurance industry, and it resulted
torts is critical for continued financial integrity and    in a new awareness of the risks facing the financial     “asbestos is by far
an important consideration within a sophisticated          integrity of insurers. Many insurers want to be           the largest mass tort
enterprise risk management framework.                      financially prepared for the next asbestos. Studying
                                                                                                                     experienced by the
                                                           asbestos, such as its:
While natural catastrophes are normally the primary                                                                  casualty insurance
threat to a non-life insurer’s short-term solvency,        • Widespread use
                                                                                                                     industry, and it resulted
casualty catastrophes can also pose a risk too             • Involvement in multiple industries
                                                           • Signature disease, mesothelioma, with long              in a new awareness of the
serious to ignore. The increased sophistication of
natural catastrophe modeling over the past 20 years          latency                                                 risks facing the financial
has allowed property insurers to better measure and        • Decades of exposure                                     integrity of insurers.”
manage their catastrophic exposure. Now, recently          may yield some clues about the characteristics of
developed models are available to help casualty            the next industry-changing mass tort.
business writers exposed to mass torts evaluate
and understand their risks. Approaches used to
model these risks and some interesting results from
case studies are described in this article.

Definition and Examples of Mass Torts
Since there are no typical mass torts, there is no
precise way to define them. A mass tort can be
caused by a specific type of event or product.
Typically, there are multiple plaintiffs and defendants,
possibly with a class-action status. Unlike natural
catastrophes, the specific cause of a mass tort will
almost never repeat itself. The entities liable for
a mass tort, once discovered, are under intense
pressure to avoid future losses. So mass torts are
often unique and unexpected. In addition, insurers
define mass torts differently, often by the line of

                                                                                                                            Emphasis 2011/4 | 11
“Casualty catastrophe modeling does not answer the question of
 what the next asbestos will be, but it does answer the question
 of how the next asbestos might affect us.”
                             Other examples of mass torts include the financial       First, there are significant differences in opinion
                             crisis that started in 2007, Chinese drywall, the        over what the next game-changing mass tort will
                             BP oil spill, product recalls, fen-phen and the          look like: the cause and size, the number of entities
                             severe side effects of some other pharmaceutical         involved and insurance available to respond. For
                             products. Some natural catastrophes, such as the         instance, cancer from cell phone use would probably
                             Northridge earthquake, can cause mass torts. The         affect only a handful of large companies — telecoms
                             1994 earthquake shook the San Fernando Valley            and their manufacturers. In contrast, lawsuits
                             20 miles outside Los Angeles, causing considerable       alleging damages due to climate change could
                             loss of life and damage. Steel-framed buildings,         impact virtually any company that has contributed
                             once thought to be largely earthquake-proof, were        to the emission of greenhouse gases. In 2008,
   Matthew Ball              among those worst hit. Subsequently, the method          lawyers involved in the suits against the tobacco
   Specializes in property
   & casualty risk           of welding was blamed, and it is estimated that the      industry 10 years earlier applied similar tactics in
   consulting and            steel industry spent over a billion dollars repairing    Kivalina v. ExxonMobil Corp., et al.* The suit seeks
   software.                 the damage. Potential causes of future mass torts        compensation from 23 large energy companies
   Towers Watson,
   Bermuda                   could be related to cell phones or climate change.       and emitters of greenhouse gases that allegedly
                                                                                      misled the public about their contributions to global
                             Enterprise Risk Management                               warming. Although the case was dismissed, it has
                                                                                      been appealed to the Ninth Circuit Court of Appeals.
                             Gathering together claim, underwriting and risk
                                                                                      In a related case, AES v. Steadfast determined
                             personnel can advance enterprise risk management
                                                                                      that insurers are not obligated to defend insureds
                             by identifying reasonably foreseeable future mass
                                                                                      against acts relating to climate change, at least in
                             torts and the policies that may be exposed. However,
                                                                                      Virginia. It remains to be seen whether other states
                             even with a very experienced team, it can be difficult
                                                                                      will follow suit. Legal action will almost certainly
                             to quantify potential exposure to a future mass tort.
                                                                                      continue to unfold for some time.
                             These experts face questions such as: What is the
   Yi Jing                   likelihood of such an event? How much would the          These examples differ from natural catastrophes,
   Specializes in property   event cost if it occurred? Which policies would be       where it is generally understood that the next big
   & casualty risk           exposed? What is the likely financial impact on our      insurance event will involve a tornado, earthquake,
   consulting and
   software.                 policies if the event occurred?                          flood or hurricane striking a densely populated city
   Towers Watson,                                                                     in a developed nation. For natural catastrophes,
   Hartford                  One productive approach is to compare empirical
                                                                                      there are a limited number of perils and locations
                             scenarios generated with previous mass tort claim
                                                                                      to consider, and historical cases can be rigorously
                             emergence. By investigating the size of losses, the
                                                                                      studied with the aid of meteorologists and
                             number of claims and the coverage triggered by
                                                                                      engineers. However, it is likely that the next mass
                             historical mass torts, insurers can begin to piece
                                                                                      tort will be due to a peril that is not well understood
                             together a more robust picture of their potential
                                                                                      right now.
                             exposure to these types of events.
                                                                                      Another key difference is that natural catastrophe
                             Challenges of Modeling Casualty                          events are often known and widely reported
                             Catastrophes                                             immediately. Although the claims sometimes take
                                                                                      years to completely settle, estimates of losses from
   Landon Sullivan           Sophisticated models have been employed to
                                                                                      these events made only a few months after the
   Specializes in property   quantify the impact of natural catastrophes. While
   & casualty risk
                                                                                      natural catastrophe usually prove to be reasonably
                             the results of these models spark controversy
   consulting and                                                                     close to the actual losses. Not so with mass torts.
   software.                 from time to time, the general acceptance of these
                                                                                      The ultimate financial effects of an unknown mass
   Towers Watson,            models by the insurance, reinsurance, rating and
                                                                                      tort can remain hidden to an insurer for many years,
                             regulatory communities has been a great success.
                                                                                      unreported on financial statements.
                             Why do mass tort models remain behind?

                                                             Figure 1. Casualty catastrophe events by a sample of allegations/causes
                                                             Number of Events: 291
                                                             Estimated Costs: $542 billion
                                                                 Types of Allegations/Causes                    Lines of Business
Modeling Approaches                                          •   Antitrust                            •   Aviation
These obstacles can be overcome. Instead of                  •   Asbestos                             •   Directors and Officers
modeling the physical characteristics of an event,           •   Automobile accident                  •   Employment Practices Liability
such as location, wind speed, diameter or seismic            •   Breach of contract                   •   Errors and Omissions
intensity for a natural catastrophe, the insurance-          •   Collapsed structure                  •   General Liability — Excluding
related characteristics of a mass tort event can be          •   Director negligence                      Products
modeled: total losses, number of affected entities,          •   Discrimination                       •   Marine
reporting lag, triggered policy years and the potential      •   Drugs for mothers, infants           •   Medical Malpractice
correlations between these characteristics. This                 or children                          •   Pollution
casualty catastrophe modeling does not answer the            •   Explosion                            •   Products — Excluding
question of what the next asbestos will be, but it           •   Fire                                     Pharmaceuticals
does answer the question of how the next asbestos            •   Firm causes financial damages        •   Products — Pharmaceuticals
might affect us. It does this by allowing an insurance       •   Negligent care
company to better understand the magnitude and               •   Oil spill
properties of latent claims that may affect their            •   Plane crash
liabilities, which can lead to better pricing for future     •   Poisoning/contamination
events that may not be reflected in historical data          •   Pollution/chemical exposure
and mitigation of exposure to these events through           •   Product causes medical damage
policy terms.                                                •   Product causes property damage
                                                             •   Product unsafe
Key steps in our modeling approach include:                  •   Securities fraud
1. Gathering historical information on casualty              •   Securities negligence
   catastrophe events                                        •   Train collision
2. Adjusting the ultimate cost of historical casualty        •   Vehicle unsafe
   catastrophes to a common future point in time
3. Parameterizing the frequency and severity of
   historical casualty catastrophes by line of
                                                           Casualty Catastrophe Database                            “instead of modeling the

   business                                                                                                           physical characteristics of
                                                           A key step in the modeling process is gathering the
4. Simulating future casualty catastrophes by line         historical information in casualty catastrophe events      an event, such as location,
   of business using a frequency-severity approach         to assist in the parameterization of the model, as         wind speed, diameter
5. For each simulated casualty catastrophe,                shown in step 1 of our modeling approach.                  or seismic intensity for
   allocating the industry-level ultimate losses to
                                                           Over the past few decades, we have built a database        a natural catastrophe,
   policy year and insurer
                                                           of historical mass torts containing both quantitative      the insurance-related
6. Reviewing the resulting distribution of casualty
                                                           and qualitative information. The database is
   catastrophe claims at the industry or insurer                                                                      characteristics of a
                                                           intended to include any event over a threshold
   level by line of business, by policy year and in
                                                           of $100 million and currently includes estimated           mass tort event can be
                                                           ultimate losses of over $500 billion in total from         modeled.”
7. Conducting sensitivity testing of the model’s
                                                           almost 300 events from the 1950s to the present.
   assumptions and parameters, and comparing
                                                           The events are grouped by a number of allegations
   with other empirical estimates from expert
                                                           or causes, such as asbestos, fraud and negligence,
   judgment and making adjustments if necessary
                                                           and lines of business, such as general liability and
                                                           product liability, which are listed in Figure 1. The
                                                           database has been successfully used to calibrate
                                                           various parameters of mass tort models, for
                                                           example, frequency and severity parameters by line
                                                           of business, allegation or cause, year of first and
                                                           last exposure, and the number of claimants and
                                                           insureds affected.

                                                                                                                             Emphasis 2011/4 | 13
     Casualty Catastrophe Modeling in Practice
     A Case Study                                                              the average losses; however, the relative volatility of the loss
     The case study detailed here illustrates how casualty                     distribution at higher percentiles is increased. The shape of
     catastrophe modeling can work in practice and some of the                 the distribution of insured losses and its average value are
     insights companies can gain from the analysis.                            sensitive to the types of casualty catastrophe events, the
                                                                               allocation of the loss by policy year and insured, and the
     To illustrate our modeling approach and the importance of
                                                                               specific policy terms.
     tailoring the model to an insurer’s book of business, we
     have created a simple fictitious company and run the model                In Scenario 4, we assume the insurer is exposed only to
     reflecting differing assumption sets:                                     general liability policies and has no product exposure. Since
                                                                               product policies have experienced some of the largest
     •   Policy terms
     •   Policy years exposed                                                  casualty catastrophe losses historically, the shape of the
     •   Lines of business exposed                                             distribution of insured losses excluding product exposure is
     •   Concentration of book of business by line, years and layers           less skewed than the base case.

     The assumptions for the base case and alternative scenarios,              In Scenario 5, we assume the insurer is exposed only to
     together with the model results, are summarized in Figure 2.              pharmaceutical product exposures. While there are fewer such
     For example, the base case (Scenario 1) assumes the insurer               catastrophes each year, they are often more severe than typical
     wrote general liability and product liability policies over the           general liability losses, thereby resulting in a more skewed
     last 10 years (2001 – 2010). The base case assumes the                    distribution of insured losses relative to the base case.
     insurer wrote a 20% share of primary first-dollar coverage and            In Scenario 6, we assume the insurer has been writing
     that the insurer consistently insured 25% of the entities in the          business for 30 years rather than 10 years. As expected, the
     industry. The alternate scenarios vary individual assumptions             average insured losses increase as more years are exposed
     to illustrate the sensitivity of model results as described below         to latent claims that trigger long coverage periods, such as
     in more detail.                                                           asbestos. However, although three times as many years are
     As expected, the distribution of ultimate losses for each                 exposed, the insured losses are not three times larger since
     scenario is highly skewed with very low losses most of                    the older years are triggered less often. Interestingly, although
     the time and is therefore considered binary in nature. This               the relative size of the average losses has increased, the
     skewness is illustrated more clearly in Figure 3, which shows             relative risk in the extreme percentiles of the insured loss
     the full distribution of claims for the base case.                        distribution relative to the mean is not lessened.

     Scenario 2 doubles the size of the insurer’s book of business.            In Scenario 7, the insurer writes 100% of 50 policies instead
     As expected, the average simulated losses also double.                    of only a 20% share of 250 policies. As expected, the mean
     However, due to the benefit of diversification, the risk is reduced       loss is the same. However, the distribution has become even
     in the extreme percentiles of the resulting loss distribution,            more skewed, and the relative risk in the tail has increased as
     where the insurer does not have double the losses.                        the book of business has become more concentrated.

     In Scenario 3, we assume the insurer wrote policies of $10                Additionally, the relationship or correlation between key
     million in excess of $10 million instead of primary coverage.             variables is an important assumption to test further
     As expected, the excess attachment of the coverage reduces                (see Correlation Options on page 16 for more details).

     Figure 2. Case study
                                                                   Number of   Number of                 Ratio to mean
                 Policy            Coverage                        insureds    entities     Mean in
      Scenario   terms     Share   period        Classes           per year    in market    $millions    50th    90th     95th    99th     99.5th
          1      Primary    20%    2001 – 2010   GL + Products         250        1,000        1,021      0.41     2.57    3.88    8.02    10.15
          2      Primary    20%    2001 – 2010   GL + Products         500        1,000        2,042      0.55     2.39    3.45    6.37     8.46
          3      10 x 10    20%    2001 – 2010   GL + Products         250        1,000           45      0.31     2.41    4.20   10.56    18.51
          4      Primary    20%    2001 – 2010   GL                    250        1,000          113      0.42     2.62    3.85    7.75     9.92
          5      Primary    20%    2001 – 2010   Products Pharma       250        1,000          300       —       2.84    5.58   14.82    21.16
          6      Primary    20%    1981 – 2010   GL + Products         250        1,000        1,203      0.40     2.53    3.84    8.32    10.67
           7     Primary   100%    2001 – 2010   GL + Products          50        1,000        1,021      0.08     2.45    4.76   13.37    21.63

    Figure 3. Distribution of ultimate modeled losses for the base scenario

                      Base case — Insurer’s losses                       Worst 5%
    Insured losses

                     0%   10% 20% 30% 40% 50% 60% 70% 80% 90% 100%     95% 95.5% 96% 96.5% 97% 97.5% 98% 98.5% 99% 99.5% 100%

                                           Percentile                                                Percentile

Allocation of Losses                                                 to be more appropriate for mass torts with very
                                                                     long latency (e.g., asbestos), where the claims can
Another key step in casualty catastrophe modeling                    be allocated across multiple policy years.* If, for
is the allocation of losses, as shown in step 5 of                   example, insurance policies are triggered over 30
our modeling approach. The allocation to policy year                 years, an insurer’s policy limits are likely to have
can reflect alternative assumptions (e.g., continuous                grown — a primary policy written in the 1950s may
or all sums). Once losses are allocated by year, they                be $50,000, while a primary policy written in the
can be allocated to a specific insurer’s coverage                    1990s may be $10 million — although its market
using a simple market-share or more precise policy-                  share may have remained relatively stable. Using
level approach.                                                      the policy-level approach, the sensitivity of insured
The market-share approach compares historical                        losses to changes in policy terms can be explicitly
company statistics, such as premium and ultimate                     tested, which can be valuable from an underwriting,
claims, with the corresponding industry statistics                   claim and management perspective.
to estimate an average market share of the                           *Cross and Doucette, “Measurement of Asbestos Bodily Injury Liabilities,”
                                                                      Proceedings of the Casualty Actuarial Society, Arlington, Virginia, LXXXIV, 1997
industry loss by line of business and policy year.
The insurer’s market share can be assumed
to vary around the estimated mean using an
appropriate statistical distribution. The market-
share simplification is most appropriate when the
characteristics of the insurer’s book of business
resemble a share of the overall industry, versus                 “Natural catastrophe events are often known
being concentrated in specific years or layers.
                                                                  and widely reported immediately. Not so with
The policy-level approach uses specific coverage
terms where available. It is more robust than                     mass torts. The ultimate financial effects of an
the market-share approach because it explicitly
reflects concentrations of risk or niches within the
                                                                  unknown mass tort can remain hidden to an
historical business. For example, it may include                  insurer for many years, unreported on financial
writing large shares of high-excess layers for Fortune
500 companies, versus writing small shares of                     statements.”
lower-excess layers across a large number of small
regional entities. The policy-level approach tends

                                                                                                                                                         Emphasis 2011/4 | 15
                 Correlation Options
                 Extremely large mass tort events tend to affect many                                                          Option A assumes there is independence or no relationship
                 entities. Therefore, the dependence or correlation between                                                    between event severity and the number of entities affected.
                 key event characteristics, such as event severity and the                                                     Options B and C incorporate dependence or correlation into
                 number of affected entities, is important. There are many                                                     the relationship by using two different statistical structures.
                 options available to incorporate correlation assumptions                                                      Both options result in positive correlation between the event
                 into mass tort models. The correlation can be introduced                                                      severity and number of entities affected. However, as the
                 using statistical techniques. Modeling software can help                                                      heat maps show, Option C also allows for a greater likelihood
                 make this job more efficient and more accurate, and improve                                                   of large events spread among fewer entities or small events
                 the communication of assumptions and results. Below we                                                        spread among many entities, compared with Option B, which
                 have displayed three illustrative dependency/correlation                                                      can be a feature for certain lines of business.
                 structures* graphically as heat maps. The warmer colors
                                                                                                                               Other key characteristics of a mass tort may also be related,
                 indicate more likelihood of mass tort events; the cooler
                                                                                                                               including reporting lag and number of years triggered.
                 colors, less likelihood.

         Figure 4. Correlation heat maps
                                  Correlation option A                                                  Correlation option B                                                 Correlation option C
         More entities affected

                                                                               More entities affected

                                                                                                                                                    More entities affected

                                        Greater event severity                                               Greater event severity                                                   Greater event severity

         *Option A: no correlation; Option B: rank normal copula with 50% correlation; Option C: multivariate student’s t copula with 50% correlation and one degree of freedom

                                                         Figure 5 illustrates the policy-level approach at a                                 individual policy terms are applied to determine the
                                                         high level. Future casualty catastrophe events are                                  insured losses. (If the market-share approach were
                                                         simulated by line of business using a frequency-                                    used, then a share of the industry loss would be
                                                         severity approach. For each event, the number                                       assumed to be insured, rather than considering the
                                                         of entities affected by the event is simulated.                                     insurer’s specific policy terms.) Using the policy-
                                                         Some of these entities will be within the insurers’                                 level approach, the model can be used to produce
                                                         book of business, while others will be insured                                      distributions of casualty catastrophe claims at the
                                                         by other insurers, self-insured or uninsured. For                                   insurer level by line of business, by policy year and
                                                         the insurer’s policyholders affected by the event,                                  in total.

Figure 5. Casualty catastrophe model flowchart

         Event Level                          Insured Level                          Insurer Level

        • Number of events,                • Event’s total losses
          N, is simulated
          using an appropriate             • Number of affected entities                No losses for insurer

          distribution                     • Line of business                                       NO
                                           • Report of lag
        • Event 1                          • Policy years triggered
                                                                                        Is this
        • Event 2          ...                                                     entity insured?
                                           • Event 1
        • Event 3          ...
                                           • Event 2             ...

                                                                                        • Overlay policy
        • Event N          ...

                                           • Event M             ...

Conclusions                                                  While casualty catastrophe models, by their nature,
                                                             may never be as sophisticated as some of the
The illustrative case study on page 14 is intended           natural catastrophe models available today, there
to demonstrate the types of information and                  is much that can be done to facilitate greater
insights that the casualty catastrophe model can             understanding of casualty catastrophe risks and
provide, in addition to satisfying certain regulatory        their potential impact on insurers’ balance sheets.
requirements. For example, casualty catastrophe
models can be used to:                                       For comments or questions, call or e-mail
                                                             Matthew Ball at +1 441 279 6706,
• Simulate latent claims for greater understanding ;
  of reserve risk and use in economic capital                Yi Jing at +1 860 843 7159,
  modeling                                         ; or
• Estimate and evidence the binary event                     Landon Sullivan at +1 860 843 7157,
  adjustment to be included in an insurer’s technical
  provision, as required by Solvency II
• Validate the reasonableness of the empirical
  scenarios developed based on underwriting, claim
  and risk experts’ judgment, and test the volatility
  inherent in these scenarios
• Tailor results to individual company profiles, such
  as older companies versus newer companies, or
  differences in the mix of business by line or layer
• Test the sensitivity of the resulting loss
  distributions to explicit changes in the various
  parameters such as trend factors, trigger
  protocols (e.g., continuous, all sums), frequency
  and severity parameters, unknown policy terms,
  concentration of book of business, correlation
  among key variables and other guidelines
• Prospectively measure the impact of different
  underwriting or risk management strategies for
  casualty business, such as entry into a different
  industry or writing different coverage layers

                                                                                                                   Emphasis 2011/4 | 17

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