C.1. Catastrophe modeling

Question 1

Who uses catastrophe models and how?

Answer 1

1. Insurers and 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 (e.g., toreview rates based on models).
5. Emergency management agencies. To determine the impact of an actual event, and coordinate an emergency response to areas most likely in need.

Question 2

Why regular statistical tools are inappropriate for catastrophe losses

Answer 2

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

Question 3

4 components of cat models

Answer 3

1. Hazard module: Simulates natural disasters based on probabilities of different event parameters (epicenter and Richter scale magnitude of an earthquake)
2. Inventory module: Contains the properties at risk and their characteristics (an insurer’s portfolio of insured homes, including details like construction type, insured amount, and property location).
3. Vulnerability module: Estimates the susceptibility to damage of each property given a specific simulated catastrophe and property information (brick construction is good against hurricanes but poor against earthquakes).
4. Loss module: Quantifies the direct (physical damage) and indirect losses (business interruption, relocation costs) of the event on each property.

Question 4

3 mains parameters of hazard module

Answer 4

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 the upper bound on what is physically possible.

Question 5

Ways to model relationship between hazards and resulting damage

Answer 5

1. Engineering judgement: base on expert opinion. It is simple, but also arbitrary and hard to update as new information becomes available.
2. Building response analysis: based on advanced engineering techniques. More accurate but based on specific buildings and not applicable to an entire portfolio of policies.
3. Class-base building reponse analysis: Diving the risks in different classes of buildings based on certain characteristics.

Question 6

Steps for class-bases building response analysis

Answer 6

1. Identification of typical buildings: A typical building from each class is analysed in detail.
2. Evaluation of building performance: For each class, a damage function is generated, linking the instensity of the force to the level of expected damage done to the typical building of the class. This enables the generation of damage ratios, which are ratios of repair costs to the replacement cost. Damage ratios and functions are created for each coverage.

Question 7

Approaches to determining monetary loss from an event

Answer 7

1. Link the event parameters directly to the expected loss. This is primarily based on expert opinion. While this seems straightforward, this cannot be updated to reflect new construction techniques, building codes, repair costs, etc.
2. The more recent approcha is to first estimate the physical damage from an event, and then use a cost analysis to translate this into monetary loss.

Question 8

Occurence exceedence probability definition and formula

Answer 8

Question 9

2 conditions on insurability on a risk

Answer 9

1. The ability and quantify the probability of an event and the severity of a loss
2. The ability to set a premium for each customer

Question 10

Considerations in setting rates for cat events

Answer 10

1. State regulations
2. Competition
3. Uncertainty of losses
4. Highly correlated losses
5. Adverse selection
6. Moral hazards
7. Liquidity assests

Question 11

Simple formula for deciding whether to write new business

Answer 11

Question 12

Simple ratemaking model premium formula

Answer 12

Question 13

Types of attributes for which a model can calculate AALs

Answer 13

• Structure attributes: These relate to the physical performance of a building during a catastrophe. Examplpes include construction type, occupancy type, building code, construction year.
• Location attributes: These relate to proximity and susceptibility to hazard of the building. Examples include distance for fault lines, distance from the coast, soil type, etc.

Question 14

Reasons regulators have not been supportive of cat models

Answer 14

• It is difficult for regulators to evaluate models since they require subject matter experts.
• Modling firms are unwilling to share key proprietary elements of their models, especially in states that require governments documents to be publicly available (“Sunshine laws”).

Question 15

How models present a conflict for regulators

Answer 15

Models present a conflict for regulators, since they present a scientifically rational approach to quantifying the potential risk, however, the models could also be used by insurers as justification for charging higher rates.

Question 16

CEA ratemaking constraints

Answer 16

• Rates needed to be actuarially sound (adequate, not excessive or unfairly discriminatory).
• If scientific information was used in ratemaking, it should be consistent with available geophysical data and the current knowledge of the scientific community.

Question 17

Examples of issues raised with initial CEA rates

Answer 17

• Earthquake recurrence rate
• Uncertainty values in estimating time dependent probabilities
• Damage estimates
• Underinsurance factor
• Demand surge
• Policy sublimits
• Rating plan deviation
• Retrofit discount

Question 18

Open issues in cat models in ratemaking

Answer 18

• Regulatory acceptance
• Public acceptance
• Actuarial acceptance
• Model to model variance

Question 19

ASB requirements for actuaries using cat models

Answer 19

• Determine appropriate reliance on experts
• Have a basic understanding of the model
• Evaluate whether the model is appropriate for the intended application
• Determine that appropriate validation has occurred
• Determine the appropriate use of the model

Question 20

Types of uncertainty in cat models

Answer 20

• Aleatory: The inherent randomness associated with natural hazard events. This is usually reflected in the probability distributions. This is the cat version of process risk.
• Epistemic: The uncertainty due to our lack of knowledge of the hazard. This is the cat version of parameter risk.

Question 21

Reasons for epistemic uncertainty

Answer 21

1. Limited scientific knowledge
2. Limited historical data
3. Cross disciplinary nature of cat models
4. Lack of data to create the Geographic Information System databases
5. Lack of accurate data on true market values
6. Limited understanding of material performance. (Laboratory testing of structural material is limited to certain types of materials only)

Question 22

Ways to incorporate uncertainty into models

Answer 22

1. Logic trees: Displays the alternative parameter values or mathematical relationships, along with associated weights for each alternative. Alternatives are then weighted together to produce weighted estimates for each parameter or relationship.
2. Simulation techniques: Simulation can be used to model a real system by building a model that attempts to replicate the system’s behavior.

Question 24

Special issues insurers need to account for in managing their portfolio risk

Answer 24

• Data quality: Insurers need to make sure the data used for the inventory module is accurate.
• Uncertainty modeling: Losses should be allocated to stakeholders based on probability distributions.
• Impact of correlation: Having a more diversified portfolio reduces the risk of a single event resulting in damages to a large portion of the portfolio.

Question 25

Underwriters considerations when adding a policy to the portfolio

Answer 25

* The magnitude of the risk * Correlation with the eisting portfolio * Highest premium the risk is willing to pay