Section C - Catastrophe Pricing

Question 1

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Who uses Catastrophe Models? (5)

Answer 1

1. Insurers & reinsurers: To assess their exposure to risk.

2. Reinsurance brokers: To assess risk for their clients to send to reinsurers.

3. Capital markets: To price catastrophe bonds.

4. Regulators: To assess insurer work (i.e., to review rates based on models).

5. Emergency Management Agencies: To determine the impact of an actual event (post occurrence), and coordinate an emergency response to areas most likely in need.

Question 2

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Briefly Describe the Main Components

of a Catastrophe Model (4)

Answer 2

Hazard Module: Simulates natural disasters based on probabilities of different event parameters (i.e., for earthquakes, this would include epicenter and Richter scale magnitude).[Produces parameters of the catastrophe]

Exposure (Inventory) Module: Contains the properties at risk and their characteristics (i.e., insurer’s portfolio of insured homes, including construction type, insured amount, property location, etc.).

[Contains information (locations, construction type, age, etc) about the insurer’s portfolio of properties]

Vulnerability Module: Estimates the susceptibility to damage of each property given a specific simulated catastrophe and property information (i.e., brick construction is good against hurricanes, but poor against earthquakes).

Loss Module: Translates physical damage from the Vulnerability module, to ground-up losses, and then into Insured losses.

Quantifies the direct & indirect losses of the event on each property. Direct losses include physical damage, while indirect losses include things like business interruption or relocation costs.

Question 3

What are the 3 main parameters of Hazard Module?

Answer 3

1. Location: Earthquake locations depend on locations of faults or seismic zones, hurricanes are more likely to occur in certain areas.

2. Frequency: This parameter has the biggest uncertainty.

3. Severity: This includes multiple characteristics. For example, earthquakes would include depth and fault characteristics in addition to just Richter scale magnitude. This would also reflect an upper bound on what is physically possible.

Question 4

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Considerations in the Hazard Module when

Generating the LOCATION of a Catastrophe:

Earthquakes (4)

Hurricanes (4)

Answer 4

LOCATION CONSIDERATIONS:

Earthquakes:

1. Known, Mapped Fault Lines
2. Polygonal Source Zones: not all quakes happen on known faults
3. Paleoseismic Data: prehistoric EQ activity seen in offsets in geological features (e.g. exhumed fault zones)
4. Geodetic Survey Data: GPS data about earth’s crust movement

Hurricanes:

1. Storm formation requires large expanses of warm ocean water
2. Storm Track
3. Land Fall location
4. Track Angle at Land Fall (what ange do you hit the coast at)

Question 5

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Considerations in the Hazard Module when Generating the FREQUENCY of a Catastrophe:

Earthquakes (3)

Hurricanes (3)

Answer 5

FREQUENCY CONSIDERATIONS:

Earthquake:

1. Stress History of the Fault
2. Re-occurrence Rate for a Fault
3. Gutenburge-Richter relationship: relates magnitude to frequency

Hurricane:

1. Requires Warm water (+80˚F ) and absence of Vertical Shear
   * winds that change appreciably (заметно) in magnitude or direction with hight*　
2. The Lack of Coriolis Force near the Equator reduces Likelihood
   * required for spiraling circulation of winds*
3. Most Active Months: North: Aug, Sep

                                     South: Jan, Feb

Frequency is the most uncertain part of the Hazard Module

Question 6

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Describe the Severity Component of the

Hazard Module of a Catastrophe Model

Inputs used for Earthquakes (6)

Inputs used for Hurricanes (6)

Answer 6

SEVERITY COMPONENT:

Fits theoretical probability distributions to the event characteristics at (1) the source and (2) at affected buildings; based on historical data

Source Severity Determinants:

Earthquake:

1. Magnitude
2. Focal depth
3. Fault -rupture characteristics

Hurricane:

1. Barometric Pressure
2. Forward or translation speed
3. Radius of maximum winds
4. Track angle at landfall

Local Intensity Determinants

Earthquake:

1. Source mechanism - normal vs. thrust and reverse vs. strike and slip
2. Intervening geological material
3. Local soil materials

Hurricane:

1. Horizontal drag/surface f riction
2. Forward wind speed - determines how long a hurricane batters an area

Question 7

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Information the Exposure (Inventory) Database

should have about the Insured Risks (8)

(Exposure Module)

Answer 7

1. Number of Properties by zip code

2. Line of Business residential, commercial, industrial,…

3. Coverage building, contents, loss of use, …

4. Occupancy Class provides insight into kinds/value of

contents in building

5. Construction Type f rame, mason, engineered… - (this is the most important variable for damageability, i.e., brick is good against hurricanes but bad against earthquakes)

6. Risk Specific Characteristics roof pitch, f loor-wall connection,

age, height, retro fitting, etc…

7. Site Specific Analysis beam, column, joints, partitions

8. Regional Building Codes Construction practices

The more detailed the input into the models, the more reliable the output.

Question 8

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Approaches for Sizing Damage Amount during Modeling Property Damage in the _Vulnerability Module _(2)

Which Approach is Superior?

Answer 8

Two approaches to Engineering Analysis:

1. Engineering Judgment – based on expert opinion.

Adv: Simple Disadv: Arbitrary , hard to update for new info

2. Building Response Analysis – based on advanced engineering techniques. Superior approach; but tailored for only application to specific buildings and locations

Adv: More accurate

Disadv: Not appropriate for assesment of entire portfolio of policies

Question 9

Describe Class-Based building response analysis

(one of the Approaches to obtain the relationship b/w the hazard and the resulting damage)

Answer 9

Due to the disadvantages of the prior 2 methods (Engineering judgment and Building response analysis), a commonly used alternative is to modify the building response analysis to make it more appropriate for portfolio risk assessment. This is done by dividing the risks into different classes of buildings based on building characteristics. Two steps are then performed for each class:

(a) Identification of Typical Buildings: A typical building from each class is analyzed in detail.

(b) Evaluation of Building Performance: For each class, the relationship between the intensity of the force and the level of expected damage of the typical building is generated (a damage function). This is then applied to all buildings of the class. This enables the generation of damage ratios, which are ratios of the repair cost to the replacement cost. Damage ratios and functions are created for each coverage.

Severity expressed as

Damage Ratio = Repair Cost / Replace Cost

When a model is run for an actual portfolio, the model would look up the damage ratios for each building (based on its building class and local intensity) for each simulated event in order to calculate expected damages.

Question 10

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Define Damage function

Answer 10

Relates the damage of a building to the intencity of the event

Question 11

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Steps in Determining the Insured Losses in the Loss Module (2)

Specific Insurance Considerations (5)

Answer 11

• Determine the Restoration Strategy based on the Degree of Damage: Replace or Repair
• Determine Insured Loss given the Restoration Strategy

based on:

1. Deductibles (coverage, site specific, or blanket) -or-Attachment points
2. Coverage Limits (single or multiple locations)
3. Loss Triggers
4. Coinsurance
5. Risk Specific Reinsurance terms

Question 12

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Loss Module:

2 main approaches to determine the monetary loss:

Answer 12

1. Link the parameters of the event DIRECTLY to the monetary loss. Impact mainly determined by experts opinion (as opposed to engineering analysis). Disadvantage: Can’t be easily updated to reflect new information (construction technology/ build codes/ repair costs…)

2. Determine PHYSICAL DAMAGE from the event, and use engineering analysis to convert into monetary loss. Adv: Accurate, objective, easy to update. Disadv: More difficult to implement.

The insured loss can then be computed from the total loss by applying policy conditions, such as coverage limits and sublimits, deductibles by coverage, coinsurance, and risk specific reinsurance.

Question 13

*** c.2.a

Conditions for Insurability of a Risk (3)

Answer 13

Conditions for Insurability:

1. Able to Estimate the Probability of an Event Occurring
2. Able to Quantify Size of Losses likely to be Incurred
3. Able to Set Premiums for each Customer Class
   * Higher premiums needed when there is more uncertainly around estimates*

Question 14

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Insurability Challenges Catastrophe Events pose (2)

Answer 14

Challenges to Insuring Catastrophe Events:

1. Involve potentially High Losses from Extremely Uncertain Events
2. Losses are Spatially Correlated: simultaneous losses to many risks from a single event

Question 15

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Insurability of Cat Risks (C.2.a)

Answer 15

1. Hard to estimate probability of an event
2. Hard to Quantify the size of losses
3. Hard to charge adequate premiums

* Losses are Spatially Correlated - simultaneous losses to many risks from a single event

Question 16

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How do Firms Determine Whether to

Provide Coverage or not (3)

Answer 16

1. Firms are interested in Maximizing expected Profits subject to satisfying a Constraint related to the Survival of the Firm
2. The Survival Constraint is addressed by choosing a portfolio with an overall expected probability of insolvency less than some threshold - p
3. For Cat coverage, the Exceedance Probability (EP) curve is a useful tool for evaluating this criteria

Question 17

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Classifications of Uncertainty (2) related to cat models:

Considerations in Catastrophe Models

for the Different Classes of Uncertainty (2)

Answer 17

Aleatory: inherent randomness associated with natural hazard events; cannot be reduced by collecting additional data. This is usually reflected in the probability distributions. This is the cat version of process risk.

Epistemic: uncertainty due to lack of information or knowledge of the hazard (our fault as modelers). This is the cat version of parameter risk.

Model developers:
• try Not to ignore or double count the uncertainties

• they do Not necessarily distinguish between the two types

What is Aleatory today, or in one model, may be Epistemic tomorrow, or in another model

245

Question 18

*** c.2.b

Describe the Sources of Uncertainty in Catastrophe Modeling (3)

Answer 18

1. Natural Hazards are Not Completely Understood
2. Cross Disciplinary Nature of Models - each discipline’s added assumptions increase uncertainty. Usually involce interaction of experts in seismology or meteorology, structural engineers and actuaries
3. Lack of Data - effects the hazard, exposure, vulnerability, and Loss modules:
   i. Incomplete Information on Hazard Source
   ii. Partial Information on a Structure’s Characteristics
   iii. Use of Laboratory Testing and Expert Opinion to Establish Vulnerability
   iv. Deficient Information on Repair Costs
   v. Lack of Accurate Data on True Market Values

Question 19

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Epistemic uncertainty comes about for the following reasons: (6)

Answer 19

1. Limited scientific knowledge.
2. Limited historical data.
3. Cross-disciplinary nature of the catastrophe models: they involve interaction of experts in seismology or meteorology, structural engineers, and actuaries. Each adds their own assumptions.
4. Lack of data to create the Geographic Information System (GIS) databases. (i.e., soil types by area)
5. Lack of accurate data on true market values (i.e., modelers might use outdated property tax assessment data)
6. Laboratory testing of structural material has been limited to certain types of materials. Therefore there is a limited understanding of how other materials perform.

Question 20

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Methods for Quantifying Uncertainty in Catastrophe Models (3) (2 main ways to incorporate uncertainty into cat models)

i.e. mothods for working throught uncertainty in parameter selection and quantifying the effects of different assumptions

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Answer 20

Logic Trees :
Adv: Tractable; useful for communication risk to stakeholders
Disadv: weights are often based on expert opinion, and thus may be biased

Displays the alternative parameter values or mathematical relationships, along with associated weights for each alternative. Alternatives are then weighted together to produce estimates for each parameter or relationship.

1. Alternative Assumptions are identified for uncertain parameters
2. Relative Weightings are assigned to each Alternative
3. Estimates of Expected Outcomes are calculated using a weighted linear combination of all possible outcomes

Simulation :
Adv: Can model compex processes

Simulation can be used to model a real system by building a model that attempts to replicate the system’s behavior. Simulation can be used to handle more complicated scenarios than logic trees can handle, and it can be used to derive probability distributions. Unlike logic trees, simulation can be used for both discrete and continuous distributions.

OR

1. Uncertain parameters are represented by a probability distribution
2. Multiple Simulations are run which sample from the distributions

• Monte Carlo - computationally intensive; requires many samples
• Latin Hypercube – more efficient; significantly reduces # samples needed
3. Statistical Analysis is conducted on the *Sampled Values *to estimate performance measures (i.e. exceedance probability curves)

Simulation can be used to derive prob distribution

Combination:* Often used to estimate EP curves*

You can also generate Exceedance Probability curves using a combination of logic trees and simulation. Under this method, each branch of the logic tree represents an alternative that samples from a probability distribution using a simulation. Then each branch can generate its own EP curve. You can then calculate a mean, a median, and confidence intervals for a combined EP curve using the curves for the different branches.

Similar to the concept of combining EP curves from different branches of a logic tree within the same model is the concept of combining EP curves from different models. The graph below shows EP curves from 3 different models for the hurricane exposure in Florida. The fact that each model has different outputs is an impact of the uncertainty in modeling. One way model users deal with this is by weighting together the outputs of multiple models.

Question 21

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What two types of risk management strategies do Cat models help to facilitate?

Answer 21

1. Risk Reduction: This primarily includes non-renewing policies, limiting coverage offered, increasing deductibles, and increasing rates.

2. Risk Transfer: This primarily includes purchasing reinsurance or issuing catastrophe bonds.

Question 22

Why regular statistical tools used by actuaries are often inappropriate for applying to cat losses?

Answer 22

1. There is insufficient historical claim data for catastrophes.
2. The limited data that is available is often inappropriate due to changing factors (i.e., property values, costs of repair, building codes, etc.)

As a result of the large uncertainty surrounding catastrophes, it is appropriate to use a probabilistic approach when analyzing them.