Ch7: Catastrophe Models

Catastrophe Models

• Catastrophe models are thoroughly examined in this chapter, originally introduced in Subject SP8.
• Section 1 covers the background and basic structure of these models, along with the concept of secondary uncertainty.
• Section 2 focuses on the primary perils assessed by these models, both natural and human-made.
• Section 3 explores how insurers can account for exposures lacking a specific catastrophe model.
• Section 4 outlines the major applications of catastrophe models.
• Section 5 presents challenges and factors to consider when utilizing these models.
• Section 6 lists some of the commercially available models.

Catastrophe Modelling vs. Traditional Rating

• Traditional rating methods are better suited for high-frequency, low-severity risks.
• Catastrophe models are better suited for low-frequency, high-severity risks
• Observed losses might not accurately represent underlying risks due to short observation periods relative to loss return periods.
• A key actuarial assumption for high-frequency, low-severity risks is that the past reasonably predicts the future.
• This assumption is less reliable for rare or uncertain events in terms of frequency or severity.
• Examples of low-frequency, high-severity risks include natural hazards like hurricanes and earthquakes, or human-made events, such as terror attacks.
• A ten-year burning cost model may not reliably price earthquake risk on a fault with a 250-year return period.
• Modern catastrophe models developed in response to catastrophes like Hurricane Andrew in the early 1990s.
• Catastrophe bonds were introduced in the early 1990s and accelerated model development.

Factors in Sophistication of Models

• Advances in computer hardware enable more complex calculations and simulations
• The development of GIS (Geographical Information Systems) provides better spatial analysis of risk.
• The occurrence of more catastrophe events with detailed exposure and loss data provides a larger data pool for modelling.
• An increased scientific understanding of the hazards helps calibrate and refine models.
• More accurate measurement of physical characteristics of events allows for finer granularity in models.
• GIS integrates hardware, software, and data for geographically-referenced information.
• Catastrophe models are developed by specialty commercial vendors like AIR, RMS, and CoreLogic (previously EQECAT).
• AIR and RMS were developed in the late 1980s, with CoreLogic entering the market in the 1990s.
• Models have expanded from natural perils to man-made perils like terrorism
• Model development focuses on areas where insurers have the greatest exposure and interest
• Higher investment in areas means a greater confidence in their results
• Accuracy and detail of available data significantly impact reliability.
• Vendors invest more in improving data for models that insurers are most interested.
• Immature data recording systems in developing countries can limit available data.
• Models initially examine historical events and research underlying causes.
• Models create possible future event sets, including events not historically observed.
• Earthquake models use paleoseismology and sediment core samples.
• Past and future events combine to create the stochastic event set.
• Paleoseismology studies geological sediments and rocks for signs of ancient earthquakes.
• The model calculates the effect of events on insured portfolio exposures.
• The model applies insurance contract terms like deductibles, limits, and peril-specific sub-limits.
• The model can also apply reinsurance programmes.

Allowances in Catastrophe Modelling

• Changes in demographics and building vulnerability
• Changing event frequencies over time
• Varying impact severity of events
• Changes in the portfolio in more detail than crude ‘as-if’ calculations.
• Allowances are based on the latest research in seismology, meteorology, hydrodynamics, and structural/geotechnical engineering.
• Allowances can be made for building codes, construction types, engineering surveys, and loss mitigation.
• Raw data in commercially available models is often 'hidden' to avoid plagiarism and scrutiny

Basic Structure of Catastrophe Models

• Event Module: Consists of a database of stochastic events (an event set), each defined by physical parameters, location, annual probability, and frequency of occurrence. It contains many thousands of possible events, even though historical records may only comprise a few hundred. May also contain a historical event set, allowing users to model current portfolios for specific past events.
• Hazard Module: Determines the hazard of each event at each location, this is the consequence of the event that causes damage (wind speed is the primary cause of damage for a hurricane; ground shaking, for an earthquake). Will specify, for example, that if a storm happens, it is likely to result in wind damage, some floods, etc.
• Inventory (or Exposure) Module: A detailed exposure database of insured systems and structures. Details such as age, occupancy, construction and number of storeys are included, along with more specific data like roof anchors in hurricane models, or soft storeys in earthquake models. Contains the values of buildings and contents to be insured, allowing a distinction between values and insured limits.
• Vulnerability Module: Moduled loss based on value of exposures to be insured. Degree of loss to a system or structure from exposure to a hazard (often expressed as a percentage of sum insured). Models losses from loss of use or business interruption from physical damage at the insured location.
• Financial Analysis Module: Consists of a database of policy conditions (limits, excess, sub-limits, coverage terms) to translate the total ground-up loss into a gross insured loss. May also apply reinsurance purchased to protect the portfolio, then the catastrophe excess of loss is applied separately.
• Models use data input by the user (insurer or reinsurer) for the inventory and financial analysis modules.
• The event and hazard modules are based on the assessment of the causes of the events (seismological assessment for Earthquakes).
• The vulnerability module is based on the engineering assessment.

Perspectives of Modelled Losses

• Ground up
• Gross of all reinsurance
• Net of facultative, risk excess of loss, and proportional reinsurance before applying catastrophe excess of loss reinsurance is applied/often termed “net pre-cat”
• Net of all reinsurance
• Models will calculate losses after reinsurance, these perspectives include some additional approximations.
• Catastrophe excess of loss reinsurance typically covers losses arising from an event in 72 hours.
• Catastrophe models don't distinguish and apply entire modelled loss to the reinsurance.
• Models are typically not equipped to model subtle nuances of any atypical reinsurance.
• It's prudent to review all of the modelled loss perspectives to ensure that reinsurance is being modelled as it applies to the portfolio.

Aggregate vs. Detailed Models

• Aggregate Models: Use aggregate exposures (sums insured) in an area with industry average losses to estimate likely losses when detailed information on exposed risks is unknown. This works well when insured risks are representative of industry averages (size and construction).
• Detailed Models: Use individual insured risk information to calculate the likely loss for each insured risk, before summing to get aggregate losses.
• Cost and time are the main factors to consider.

Secondary Uncertainty

• Secondary uncertainty feature reflects uncertainty over a given event’s impact.
• A well-constructed house may have a roof damaged by flying debris, changing its ability to withstand a hurricane.
• This is uncertainty about the exact insured loss, rather than uncertainty about which events will happen.
• Models are typically run with secondary uncertainty switched on when available.
• It forms part of the vulnerability and financial analysis modules of the catastrophe model.
• Secondary uncertainty can complicate use of modelling results.
• Vendors may provide a statistical severity distribution for each modelled event, rather than a single point estimate.
• Investigation of likelihood of exceeding a certain value requires calculating this likelihood for every event based on its specific severity distribution.

Key Perils Modelled

• This section focuses on frequently covered perils; it has geographical and less actuarial components. The key perils include:
  • Tropical Cyclones: Windstorms.
  • Extra-Tropical Cyclones: Windstorms.
  • Tornadoes.
  • Earthquakes.
  • Hailstorms.
  • Winter Storms.
  • Floods.
  • Infections Disease.
  • Terrorism.

Windstorm Types

• Tropical Cyclones: Includes tropical storms, hurricanes, and typhoons.
• Extra-Tropical Cyclones: Like windstorms seen in Europe.
• Tornadoes.
• Tropical Cyclones: Include storm systems that are characterized by a low-pressure center and thunderstorms that produce strong winds and heavy rain. Depending on strength and location, they are referred to as hurricanes, typhoons, topical storms, or depressions.
• Saffir-Simpson hurricane scale: Rates intensity based on sustained surface wind speed and gust speed over the amount of time period.

Tropical Cyclone Aspects

• Track - Path of hurricane
• Storm Radius
• Forward Speed - Speed at which the tropical cyclone moves
• Rate of decay of the wind field - Wind speed reduction as a function of distance from storm center
• Central pressure - The lower the central pressure, the faster the winds will spiral around the eye of the storm.
• The annual frequency of tropical cyclones is not constant but varies over decades.
• Each year different agencies provide different forecasts for seasonal tropical cyclones.
• The actual number of tropical cyclones in a season can vary significantly from pre-season forecasts.
• Differences in storm and wind activity can occur if apparent climate effects take hold
• Hurricane season forecasting is still in relative infancy, particularly when dissected down to the number of major landfalling hurricanes.
• Catastrophe model vendors usually give two sets of event rates known as “near-term” (medium-term) and “long-term.”
• Near-term rates are conditioned on current observations (sea-surface temperatures) and give the activity estimate for the next few years.
• Long- term rates give an unconditional estimate using the full historical record, not depending on the current climate.
• There is some debate as to if climate change has increased the intensity and/or number of hurricanes and typhoons
• Increased sea surface temperatures may cause more frequent storms.
• Increase in vertical wind shear (difference in wind speed over short distance) may inhibit formation.

Accuracy Factors for Tropical Cyclone Models

• Frequency of tropical cyclones in magnitudes.
• Quality of Peril Data.
• Availability of exposure and claim data.
• Length of time over which data is collected.
• Level of adherence to building standards.
• Changes in demographics.
• The level of investment by the model vendor depends on the potential insurance loss.
• Model iteration increases reliability as it’s tested against experience.
• From a potential insured loss perspective, the US is considered to be the most significant territory.
• Insurance coverage that can be modelled:
  • Damage to Buildings.
  • Damage to Conten
  • Loss of use costs that arise directly from damage to buildings

More Aspects of Tropical Cyclone Modelling

• Static inland marine risks such as cargo.
• Watercraft such as Yachts.
• Physical motor Damage.
• Inland marine is difficult to model as assessing location at certain times is hard
• It is important to be aware of limitation with models/some models don’t assess potential liability losses.
• Due to a limited amount of historic events, the models must depend on assumptions that are based on observations in other regions.
• There may also be paleotempestology studies for the region which help build a picture of past activities.
• The models must estimate a given hypothetical windstorm on building as claims data won’t cover many factors.
• Models must rely on the engineering studies to estimate the damage to contents.
• Thought should be given to all factors when looking at confidence that should be placed on a modelling result for a particular terrority.
• Tropical models have features that can be switched on/off- such as storm surge.
• Storm surges can give rise to flooding.
• Insurers may cover “wind” but not “flood”, however when a hurricane accompanies with flooding there may be disagreement about what damage was caused by.

Examples of Coverage Diputes

• Hurricane Katrina (2005)
• Hurricane Ike (2008)
• Insurers claimed victory and made payouts on so-called “slab disputes”.

Loss Amplification

• Demand surge is the increase in amount of costs following a catastrophe.
• Model vendors refer to loss amplification as coverage slippage where courts decide the insured brokerage is broader.

Extra-Tropical Cyclones (ETCs)

• ETCs include cyclonic storms that occur outside of the topical regions.
• There is little temperature difference at a given height in cyclone, but ETCs have significant ones.
• ETCs are frontal storms that form on warm and air masses. The most extreme storms will form where there is the strongest temperature contrast.
• Type of windstorm commonly seen in Europe and UK.

List of Europe Ect Weather Events

• Klaus (2009)
• Kyrill (2007)
• Martin (1999)
• Lothar (1999)
• Daria/90A (1990)
• Great Storm of 1987 (87J)
• Severe cluster will contain a number of storms and will not be well modelled by a static Poisson Process. Poisson process breaks the number of claim in the interval starts.
• Models similar to those of tropical cyclones. However major ETC events occur less frequent.
• The way clustering is addressed also has a large effect.

Tornadoes

• A violent rotating column of area that can be underneath a cumuliform and is visible funnel column
• It is typically 100 yards but can be much smaller.
• Cumuliform consists of a cloud that shows vertical development.
• Funnel shaped cloud of condensed water.
• They are not well defined and have arguments to separate the same funnel.
• Come from any direction and can have erratic paths.
• They come from seconds to an hour.
• In the US short term forecasts are available over the year.
• Damage is very localized damage and the properties can be damaged but not touch the untouched.
• In the US, models are less reliable with difficulties in modelling.

Factors that Affect Tornado Models

• The change of scale to measure damage. The F scale measures scale 30 years prior to 2007.
• Subjective element of scale.
• Introducing Doppler that is able to identify the tornadoes
• Multipole Tornadoes
• Small affected area
• Standard building
• Changes in demographics
• Level of investment
• The model iteration
• Occurs of a sudden slip, build ups of stress.

Earthquake Details and Effects

• Accumulated energy is released from process to seismic levels. Known other effects.
• Losses could occur on:
  • Shake and injure
  • Rupture
  • Landslide
  • Liquefaction: substance acts as liquid.
  • Fire
  • Tsunamis
  • Sprinkler Leakage
• Extent of damage to shaking amplitude duration and frequency of groups
• A strength can be described based on intensity and magnitude.

Scales Used

• Magnitude scales assess the energy, the most common being the Moment of Magnitude.
• Was introduced as success to Richter Scale.
• Macroseismic intensity scales assess the effects that have taken place.

Details about Earthquake Models

• Used by the US, Southern Area and Indonesia
• Accuracy, Availability of record keeping/ claim data/studies
• Standard building.
• Model will include parameters:
  • Release and Magnitude.
  • Focal depth.
  • Area Fault.
• Increases with higher shaking and duration.
• The attenuations are higher there will be smaller areas of high material.

Event Frequency

• Using a distribution (ie, Poisson)
• Using time or Slip rates
• Using stress

Additional Features

• Leak of sprinklers
• At peak times or at any time
• A time is consider when people are at work.
• A user should also be aware of limitations.
• There is a number of other natural perils: hail, storm, flood and is weather related. Low frequency Genuine epidemics.

Aspects of Terror Modelling

• Terrorism Models are way constructed and outputs are used: probabilistic
• Assess expectation of losses from attacks (stochastic Module).
• Volitale Natures of the models is volatile and rely on deterministic.
• Modelling the attacks with large and extreme sizes.

Aspects of Small Medium Attacks

• Explosives
• Vehicle bombs or car bombs
• Hijack aircraft/ crashing
• Human included ones is referred to as man-made.

Non-Modelled Catastrophes

• Catastrophes for which an insurer has no model, but has exposures to the region-peril. The lack of model could be due to:
  • No model exists.
  • Company has chosen not to license or build its own.
  • Cost of models are viewed as high relative to the perceived benefits, where companies don't view the regions-peril are material.
• Such reasons are not an excuse for ignoring catastrophe risk.
• Solvency II requires insurers to consider all risks.

Association of British Insurers

• In 2014, they brought out a paper to help aid insurers and reinsurers assess catastrophe risk in its entirety.
• Paper focuses on property vs casualty damage classes.
• Quantify non-modelled risks.
• Considers 4 types which include perils:
  • Regional/no coverage models
  • No 3rd peril/effects coverage.
  • No lines coverage
  • Complex/no coverage
• Embed processes to find risks.
• Identify quantified areas of high risks.
• Review Models and Gaps.
• Policy/industries claims wordings/experience.

Quantification of Non-Modelled Risk

• By: -Catastrophe model Modification.
  • Actuarial and statistical using data internally and externally.
  • Geographical Mapping -Expert judgements
• Use of different models depends on time and cost
• An actuary communicates.

Uses of Catastrophe Models

• Understanding possible future catastrophe claims assists the general insurance actuary.
• One of the most common uses is too monitor aggregate insured loss.

Aspects and Benefits to Model Usage

• Use assessed portfolio and estimated different time period.
• Companies can then set limits for risk.
• The underwriters will be required to manage book in adherence
• Risk monitoring often forms part of enterprise
• Can report to management
• Helps assess aggregate exposure across Lloyds by understanding syndicates.
• Disaster scenarios helps know the extreme cases.
• Event scenarios are define every year and use evaluate each syndicate.
• Syndicates prepare specifically.

Details to Occurrence & Probabilities in Modelling

• Output in forms that give the probability a loss from single or annual loss from
• Event exceeding a given loss. This can be a useful method, it is crucial to use strong clustering due the fact it will be misleading

Details About Pricing Aspects

• Actuaries are use models can structuring pricing.
• Used in reinsurance loss or in property
• Assessment of catastrophe is used more often than a traditional cost/exposure risk
• Loading the contract can be manipulated
• The range with the load of the justification is a possible easy method.
• Pricing thus has many factors these different ways can affect it