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Many approaches exist for use in assessing catastrophe risks. Under Quantitative Impact Study 4 (QIS4), the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS) provided a list of those that can be used for Solvency II compliance and, in the interim, managing risk and capital effectively. The full stochastic modeling of catastrophe risk using an internal model, such as Guy Carpenter’s G-Cat® tools and MetaRisk®, provides the most information.

What Are Cat Risks?

Non-life catastrophe (cat) risks are low-frequency, high-severity events that are often not captured adequately by the premium and reserve risk charge. Solvency II regulation tries to mitigate this effect through the introduction of a cat risk sub-module, which is combined with the premium and reserve risks sub-module to comprise the non-life underwriting risk module.

For non-life companies, cat risk contributes substantially to the overall Solvency Capital Requirement (SCR), as currently discussed under Solvency II. The following graph displays the relative weights of the premium, reserve and cat risk components as well as the diversification effects at the non-life underwriting risk module level, as collected as a result of the QIS4 exercise.

Premium and reserve risk was generally dominant in the composition of the non-life underwriting risk for most companies, though the cat risk was, on average, the main component for captives. This relationship may reflect the more frequent use of personalized scenarios by captives instead of the factor-based method to evaluate the cat risk component.

How is the Capital Charge for Cat Risk Assessed?

Under QIS 4, the cat risk charge could be derived using one of three approaches:

• The factor-based approach (known as Method 1), under which a standard formula based on premium income by line of business is used, was selected by 31 percent of the non-life participants. This approach must be used when scenarios are not available. 
• The first scenario-based approach (known as Method 2) uses regional scenarios provided by regulators that vary significantly by country. 39 percent of the non-life participants based their calculations on Method 2.
• Newly introduced in QIS4 was Method 3 under which companies have the choice to use personalized scenarios according to the classes of business written and geographical concentration based on their own assessments of non-life Cat risk that is relevant to their risk exposure. 24 percent of the non-life participants opted for this personalized approach.

Method 1: Standard Approach

If no regional scenarios are provided, a simple factor-based approach is applied. Factors are provided for all non-life lines of business.¹

Method 2: Scenarios

If regional scenarios are provided by the local supervisor (the supervisor of the relevant territory - not necessarily the insurer’s own supervisor), they replace the standard formula of Method 1. Regional scenarios include natural catastrophes and man-made catastrophes. If participants have material exposure in more than one region, they are requested to consider the scenarios for each such region (i.e., they are requested to run more independent regional scenarios). For QIS4, no trans-regional scenarios have been developed. A trans-regional scenario is one in which a single catastrophic event simultaneously impacts more than one region.

The capital charge for non-life cat risk is determined as follows:

 where the summation is over those specified catastrophes that exceed the materiality threshold.²

CATi = Cost for scenario i, net of reinsurance, allowing for the cost of reinstatement premiums, loss of profit commissions and any exceptional costs incurred by the firm in post event management.

In the QIS4 exercise, more companies (39 percent) opted for Method 2 than for either Method 1 or Method 3. In cases in which the local supervisor provided specific scenarios, it is assumed that these scenarios represent the “two-centennial” (1-in-200) events. In most cases however, the return period is different from 1-in-200. For example, the Windstorm Cat scenario Lothar+Martin for France has been assessed by the supervisor to correspond to a return period of 1-in-500 Aggregate Exceedance Probability (AEP) by EQECAT and 1-in-692 AEP by RMS.

The natural cat scenarios have not been provided for each country. Those available can be grouped into the main four perils by country:

For man-made catastrophes, regional scenarios are provided for several countries as listed in Exhibit 5.

Method 3: Personalized Scenarios

Under Method 3, companies may use personalized catastrophe scenarios according to the classes of business written and geographic concentration.
In Method 3 only, companies have the option to calibrate their cat risk on an occurrence basis or an annual basis.

Occurence Basis

Cat scenarios are defined on the basis of the occurrence of a single event, e.g., single windstorm, flood, earthquake, fire, or explosion. The scenarios to be selected are those that the firm anticipates will exceed the materiality threshold, which is 25 percent of the most severe scenario.

CATi = Cost for scenario i, net of reinsurance, allowing for the cost of reinstatement premiums, loss of profit commission and any exceptional costs incurred by the firm in post event management.

Annual Basis

For most firms, the SCR calibration in line with a 99.5 percent confidence level over a one-year time horizon is likely to involve the occurrence of not one catastrophic event, but a series of catastrophic events over the forthcoming 12 months. In many reinsurance treaties, distinct catastrophic events are subject to separate retentions, as well as different reinstatements and associated costs. Therefore when participants have to simulate a series of events to derive NL_CAT, they should take into account the impact of those separate retentions, reinstatements and associated costs on their non-life cat risk exposure.

Personalized cat scenarios should always reflect the full 12-month exposure. For example, a single flood risk scenario might include the financial impact of multiple events during a single 12-month period.

Twenty-four percent of QIS 4 participants used a personalized scenario method to evaluate the cat risk sub-module.

Although this approach best reflects the specific risk exposures of each undertaking — and is certainly the most appropriate method to assess the cat risk charge — insurers may not select consistent scenarios. Also modeling tools from different vendors produce significantly different results. Consequently, this approach raises a possible risk of an uneven playing field among companies.

Through the personalized scenarios approach, CEIOPS provides the option to use partial internal models in the standard formula. Guy Carpenter’s internally developed models, such as G-CAT Thames flood, G-CAT France subsidence, G-CAT Pan-CEE flood, and G-CAT South Africa Earthquake, provide risk exposure assessment and gross loss estimates by occurrence. G-CAT results can be analysed further by Guy Carpenter’s MetaRisk simulation platform to derive the loss exceedance curve for the portfolio. Alternatively, loss exceedance curves can also be taken from available vendor models provided by AIR, EQECAT and RMS and aggregated in MetaRisk.

MetaRisk provides results either on an occurrence basis or on an annual basis by combining several portfolios and several perils to derive exceedance curves both gross and net of reinsurance as shown below.

Further Considerations

In both Methods 2 and 3, all scenarios are modeled as uncorrelated: they are treated independently both in space and time. In practice, though, a cross-border insurer should also consider the effect of an event in one country on insureds in another — e.g., the impact of an earthquake in southeastern France on cities and towns in northwestern Italy.³ CEIOPS is aware of this problem and agrees that “scientific [e.g., geological, meteorological, hydrological, seismologic] models are necessary to understand the geographical scope of a specific event as well as to reflect the tendency of events to happen in clusters (both in space and time).”⁴ But for the moment, CEIOPS has not decided how to improve the assessment of cat risk in the standard formula.

Exhibits:

1. Map with Flood Scenarios
2. Map with Storm Scenarios
3. Map with Earthquake Scenarios
4. Map with Hailstorm Scenarios
5. Man-Made Scenarios
6. Specific German Proposal for Cat Scenarios

Exhibit 1: Map with Flood Scenarios

Click map for full-sized view

 Exhibit 2: Map with Storm Scenarios

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Exhibit 3: Map with Earthquake Scenarios

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 Exhibit 4: Map with Hailstorm Scenarios

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Exhibit 5: Man-Made Scenarios

France

• Two insured aircraft colliding over a major city with the highest exposure for the firm
• Extreme motor accident (level-crossing accident causing a train crash with severe loss of life or a chemical spill resulting in contamination and poisoning)
• Total loss to the largest single property risk and resulting losses to other contracts
• Terrorist attack or aircraft crash in a sporting or musical event
• Third-party liability: major consumer product (including pharmaceutical) withdrawal with extensive health damage claims
• Third-party liability: major drinking water pollution disaster

Malta

• Insolvency of a major bank
• Crash of a plane in a densely populated area

Norway

• Explosive fire in the Oslofjord tunnel (or another in the Oslo area) with claim cost = 100 ME
• Event hitting a firm with many employees (defined as 400 employees) leading to 125 ME of claims costs (or a more appropriate definition provided by the company)
• Fire scenario causing property damage with the maximum claims costs

Slovenia

• Financial crisis with default of 5 percent of all credit insurance

Spain

Accident

• The scenario is the collision in air of two Airbus A380 full of passengers of Spanish nationality over a highly populated industrial area.
• The market loss derived from the impact of this accident is EUR293,000,000.
• Participants should apply to this figure their market share of gross premiums earned in this line of business for the year 2007 (taking into account that the gross premiums earned in this line of business for the total market in the year 2007 were EUR945,081,278) to derive the gross charge of accident catastrophe risk.

Motor Third-Party Liability

• The scenario is a collision of two vehicles in a tunnel of two directions, essential for the traffic of goods and people with death victims and injured people of different intensity, material damage to the tunnels and indirect damages.
• The impact of this catastrophe in Spain is quantified in EUR211 million.
• Participants should apply to this figure their market share of gross premiums earned in this line of business for the year 2007 (taking into account that the gross premiums earned in this line of business for the total market in the year 2007 were EUR6,905,012,355) to derive the gross charge of motor third-party liability catastrophe risk.

Health (Short-Term)

• The scenario considered is one corresponding to a flu pandemic.
• The charge of this scenario is the result of multiplying the units of exposure by the cost corresponding to the groups of ages according to the following table:

Sweden

• Financial crisis resulting in a market loss of 200 ME affecting credit and suretyship
• Epidemic resulting in a market loss of 100 ME affecting Accident and Health - Others/Default

Exhibit 6: German Proposals for Cat Scenarios

Natural Catastrophes

• Assessment of German natural catastrophe risk does not refer to actual events. It is a factor-based approach.
• For each type of risk, formulae are given which incorporate
  • Sum insured
  • Proportional Reinsurance 
  • Non-Proportional Reinsurance
  •  Regional Exposure Factors (not for flood)
• Type of risk

Flood

The capital required for the flood risk in property insurance is derived as follows:

Click formula for full-sized version

Where

r_Flood = the relative risk retention of quota share reinsurance in property insurance

V_Flood = the sum of insured for property insurance in the insurer’s portfolio at the balance sheet date; policies which exclude flood risk shall not be taken into account

X_1,Flood = the retention of cat XL or SL for flood risk

X_2,Flood = the ceiling of the cat XL or SL for flood risk

Windstorm

Click formula for full-sized version

r_Storm = the relative risk retention of quota share reinsurance in storm insurance, home owners comprehensive insurance, and extended coverage (EC)

R_Storm = the regional exposure factor for storm risk

V_Storm = the sum insured for storm insurance, home owners comprehensive insurance, and extended coverage comprised in the insurer’s portfolio at the balance sheet date

X_1,Storm = the retention of cat XL or SL for storm insurance, home owners comprehensive insurance, and EC

X_2,Storm = the ceiling of the storm cat XL or SL for storm insurance, home owners comprehensive insurance, and EC

The regional exposure factor R_Storm is derived as follows:

RI_Storm,K = the regional storm index of postcode area K

V_Storm,K = the sum insured for storm insurance, home owners comprehensive insurance, and EC comprised of the insurer’s portfolio at the balance sheet date in postcode area K

Earthquake

The capital required for the earthquake risk in property insurance is derived as follows:

Click formula for full-sized version

r_EQ = the relative risk retention of quota share reinsurance in property insurance

V_EQ = the sum insured for property insurance in the insurer’s portfolio at the balance sheet date; policies which exclude earthquake risk shall not be taken into account

R_EQ = the regional exposure factor for earthquake risk

X_1,EQ = the retention of the cat XL or SL for earthquake risk

X_2,EQ = the ceiling of the cat XL or SL for earthquake risk

The regional exposure factor R_EQ is derived as follows:

Motor Comprehensive Insurance (Hail, Storm, Lightning, and Flood Risk)

Click formula for full-sized version

r_Motor = the relative risk retention of quota share reinsurance in motor comprehensive insurance

MSB = EUR65

R_Motor = the regional exposure factor for natural hazard in motor insurance

N = the number of contracts in motor comprehensive insurance within the last business year prior to the balance sheet date

X_1,Motor = the retention of cat XL or SL for motor comprehensive insurance

X_2,Motor = the ceiling of the cat XL or SL for motor comprehensive insurance

The regional exposure for R_Motor is derived as follows:

Aggregation fo Natural Catastrophe Sub-Risks

The capital charge NL_NatCAT for natural catastrophe risk is determined by aggregating the capital requirements for storm risk, flood risk, earthquake risk in property insurance and natural hazard risk in motor insurance by means of the linear correlation technique and a correlation matrix as follows:

Contributors:

• Susan Witcraft, Managing Director, Minneapolis, +1.952.2143
• Frank Achtert, Managing Director, Munich, +49.89.28.66.03.361
• Arturo Lozano-Munoz, Managing Director, Madrid, +34.91.344.79.82
• Don Mango, Managing Director, Morristown, +1.973.285.7941
• Eddy Vanbeneden, Managing Director, Brussels, +32.2.674.98.11
• Sebastien Portman, Vice President, Zurich, +41.44.285.9322
• Benoît Butel, Vice President, Paris, +33.1.56.76.48.26
• Carl Haughton, Vice President, Madrid, +34.91.210.06.07

Footnotes:

1. For the description of this approach see http://www.ceiops.eu/media/docman/Technical%20Specifications%20QIS4.doc#_Toc194748327, page 205.
2. The materiality threshold is set as 25 percent of the cost of the most severe scenario. Therefore, participants will take into account a) the most severe scenario and b) additionally any other scenario whose cost exceeds 25 percent of the cost of the most severe scenario.
3. The German regulator has provided a correlation matrix which can give an idea of correlation among natural catastrophe scenarios.
4. https://www.ceiops.eu/media/files/publications/reports/Stock-taking-report-on-the-use-of-Internal-Models-in-Insurance.pdf, page 30