Grossi

Question 1

Identify who uses Cat models and for what (5)

Answer 1

1. Insurers & reinsurers
   To assess their exposure risk
   Main stakeholders
2. Reinsurance brokers
   To assess risk risk for their clients to send to reinsurers
3. Capital markets
   To price catastrophe bonds
4. Regulators
   To assess insurer work (review rates)
5. Emergency Management Agencies
   To determine the impact of an actual event (past occurrence) and coordinate an emergency response to areas most likely in need

Question 2

Identify 2 risk management strategies facilitated by CAT models

Answer 2

1. Risk reduction
   Primarily includes non-renewing policies, limiting coverage offered, increasing deductibles and increasing rates.
2. Risk transfer
   Primarily includes purchasing reinsurance or issuing cat bonds.

Question 3

State 2 reasons why regular statistical tools used by actuaries are often inappropriate for cat losses

Answer 3

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

Question 4

Briefly describe the 4 modules (components) in CAT model

Answer 4

1. Hazard module
   Simulates natural disasters based on probabilities of different event parameters.
2. Inventory module
   Contains properties at risk and their characteristics.
   Most important is location.
3. Vulnerability module
   Estimates susceptibility to damage of each property given specific simulated cat and property informations.
4. Loss module
   Quantifies direct and indirect losses of event on each property.
   Translates physical damage into monetary loss.

Question 5

Contrast direct and indirect losses

Answer 5

Direct losses include physical damage

Indirect losses include things like business interruption or relocation costs

Question 6

Describe the 3 main parameters in Hazard module

Answer 6

1. Location
   Eqk locations depend on location of faults or seismic zones.
   Hurricanes are more likely to occur in certain areas.
2. Frequency
   This parameter has the biggest uncertainty, but is it critical because damage & loss probabilities are directly related to this value.
3. Severity
   For eqks, would include depth and fault characteristics in addition to Richter magnitude.
   For hurricanes, would include projected path and wind speed.

Question 7

Describe 3 approaches to obtain relationship between hazard and resulting damage in vulnerability module

Answer 7

1. Engineer judgment
   Based on expert opinion
   +: simple
   -: arbitrary and not easy to update for new info
2. Building response analysis
   Based on advanced engineering techniques
   +: more accurate
   -: Based on specific buildings, cannot be applied to entire portfolio
3. Class-based building response analysis
   Modify building response analysis to make it more appropriate for portfolio risk assessment by dividing risks into different classes of buildings.

Question 8

Identify the 2 main approaches to translate physical damage to monetary loss in Loss module

Answer 8

1. Link event parameter directly to expected loss (damage curve)
   Primarily based on expert opinion.
   Cannot be easily updated to reflect new construction techniques, building codes, repair costs, etc.
2. First estimate physical damage from event and then use cost analysis to translate into monetary loss.

Question 9

Explain Exceedence Probability Curves

Answer 9

Graphical representation of probability that certain level of loss will be surpassed in given time period.

Question 10

Contrast Exceedence Probability curves and GIS maps

Answer 10

GIS map = loss in spatial manner

EP curve = loss in temporal manner

Question 11

List the 3 types of EP Curves

Answer 11

1. Occurrence Exceedence Probability (OEP)
   Prob that loss for at least one event exceeds specified loss amount during given time period.
   Could be useful to insurer interested in purchasing per-occ XOL reinsurance.
2. Aggregate Exceedence Probability (AEP)
   Prob that sum of all losses exceed specified loss amount during given time period.
   Could be useful to insurer interested in purchasing aggregate reinsurance treaty.
3. Conditional Exceedence Probability (CEP)
   Prob that amount of a single event exceeds specified loss amount given event occurs.
   Could be useful to insurer setting reserves after event occurs.

Question 12

Identify 3 uses of EP curves

Answer 12

1. Determine size and distribution of potential losses in portfolio
2. Determine what coverage to offer
3. Determine at what price to over coverage
4. Determine % of risks that should be transferred to reinsurer and/or capital market

Question 13

Calculate OEP and Average Annual Loss (AAL)

Answer 13

Each event Ei has prob pi of occurring with known loss Li

E(Loss for Ei) = E(Li) = pi*Li

E(Loss over all possible events) = AAL = sum of pi*Li over all i

1. Sort events in decreasing order by size (E1 is largest event)
2. OEP(Li) = P(L>Li) = 1 - P(L<Li) = 1 - product of (1-pj) for j = 1,…, i-1

Question 14

True or False?
Sum of all pi can be smaller than 1.

Answer 14

True, since it is possible that no event occurs.

Question 15

Calculate CEP(Li)

Answer 15

CEP(Li) = OEP(Li) / (1 - P(no event))

Question 16

State 2 conditions for a risk to be insurable

Answer 16

1. Ability to identify and quantify probability of events and severity of loss
2. Ability to set premiums for each customer

If both are satisfied, risk is considered insurable

Question 17

Describe 4 considerations when setting rates covering cat events

Answer 17

1. State regulations
2. Competition
3. Uncertainty of losses
4. Highly correlated losses: not independent (spatially correlated) so do not follow law of large numbers. Single even can produce significant losses.
5. Adverse selection: occurs when insurer cannot distinguish between E(Loss) for different risk categories while insured selects price/coverage more favourable to him.
6. Moral hazard: increased E(Loss) caused by behaviour of PH.
7. Liquidity of assets: insurers need cash to pay for cat losses, which means they need to hold sufficient liquid assets. Since liquid assets produce lower returns, insurers need to charge higher premium to reflect opportunity cost.

Question 18

State the 4 ratemaking principles

Answer 18

1. A rate is an estimate of expected value of future costs.
   Should provide for all costs such that insurance system is financially sound.
2. A rate provides for all costs associated with transfer of risk
   Ensures equity among insureds is maintained
3. A rate provides for costs associated with individual risk transfer
4. A rate is reasonable and not excessive or unfairly discriminatory if it is an actuarially sound estimate of expected value of all future costs associated with individual risk transfer

Actuarially sound = (1) + (2) + (3)

Question 19

Explain how to determine whether to provide coverage (survival constraint)

Answer 19

Assume insurer wants prob of insolvency < p1

There are n policies with identical premium Z

Current surplus is A

Insurer can write business as long as P(Loss > nZ + A) < p1

Question 20

Calculate policy premium for cats using sample ratemaking model

Answer 20

P = AAL + Risk Load + Expense Load

Question 21

Describe the Expense Load

Answer 21

Expense load reflects administrative costs involved in insurance contracts and is comprised of factors such as LAEs, process fees, taxes, commissions and profit

Question 22

Describe the Risk Load

Answer 22

Depends on uncertainty of AAL

One possible approach is based on standard deviation of OEP curve:
sigma = (sum of (Li^2 * pi) - AAL^2)^0.5

Question 23

Describe the 2 attributes that help determining equitable AAL

Answer 23

1. Structure attributes
   Relate to physical performance of building during a cat (construction type, occupancy type, building codes, construction year, etc)
2. Location attributes
   Relate to proximity and susceptibility to hazard of building
   Reflects degree to which structures are subject to damage from hazards as function of location.

Question 24

Describe 2 challenges faced by regulators when reviewing models

Answer 24

Regulators have historically not been supportive of use of CAT models in ratemaking because:

1. It is difficult for regulators to evaluate models since they require subject matter experts
2. Modelling firms are unwilling to share key proprietary elements of their models, especially in states that require gov documents to be publicly available (sunshine laws)

Question 25

Briefly describe the California Earthquake Authority (CEA)

Answer 25

Formed in 1996 after Northbridge eqk caused billions of dollars.

Insurers were threatened to leave cali market due to loss potential

Cali legislature created CEA as a publicly managed insurer for eqk risk in cali

Question 26

List 4 CEA’s ratemaking constraints

Answer 26

1. Rates should be actuarially sound (not excessive, inadequate or unfairly discriminatory)
2. Scientific information should be consistent with available geophysical data and current knowledge of scientific community
3. Rates should not be adjusted to provide rates lower for higher risks or higher for low risks (adverse selection)
4. PH who retrofitted homes to withstand eqk shake damage should receive a 5% discount if actuarially sound

Question 27

Describe 4 challenges to initial CEA rates

Answer 27

1. Eqk recurrence rates
   Models produced frequency rates that were more than twice historical
2. Uncertainty values in estimating time dependent probabilities
   Models assumed eqk follows random poisson distr., however it’s possible that prob of eqk is dependent on time since prior eqk.
3. Damage estimates
   Damage curves based on only 1 event (Northbridge)
4. Underinsurance Factor
   Modeled losses expressed as % of insured value. If buildings underinsured, estimated losses are underestimated.
5. Demand surge
   Difficult to quantify increased costs of parts and labor caused by increased demand/limited supply following a CAT due to limited historical data.
6. Policy sublimates
   Data not detailed enough to identify losses subject to policy sublimates, so actuaries had to reduce model estimated losses to account for specific CEA policy sublimits.
7. Rating plan deviation
   CEA rates were by territory so individual territories grouped high and lower risks together at same rate for affordability reasons
   Commissioner ruled actuarially sound
8. Retrofit discount
   Discount was based only on engineering experts and not on actual empirical loss data.
   Commissions ruled appropriate.
9. Changing deductibles and coverage limits
   CEA proposed a 15% d and $500/$1500 limit on contents/additional living expenses which represents a reduction in benefits from previous standard eqk form.

Question 28

Describe the 4 open issues for using cat models in ratemaking

Answer 28

1. Regulatory acceptance
   Regulators do not have technical expertise to assess reasonableness of model assumptions, inputs and outputs.
2. Public acceptance
   Has been low as models have usually resulted in rate increases.
3. Actuarial acceptance
   Important for actuaries to become familiar with components of models because models lie outside usual actuarial expertise.
4. Model to Model variance
   Signifiant differences between output of different models due to varying scientific and engineering data and assumptions used

Question 29

Identify the 5 ASB requirements for actuaries to use CAT model

Answer 29

1. Determine appropriate reliance on experts
2. Have basic understanding of model
3. Evaluate whether model is appropriate for intended application
4. Determine appropriate use of model
5. Determine appropriate validation has occurred

Question 30

Describe 2 types of uncertainty related to cat models

Answer 30

1. Aleatory
   Inherent randomness associated with natural hazard events.
   usually reflected in prob distributions
   Cat version of process risk
   Cannot be reduced by collection of additional data
2. Epistemic
   Uncertainty due to lack of knowledge of hazard.
   Cat version of parameter risk.
   Can be reduced

Question 31

identify 3 sources of epistemic uncertainty

Answer 31

1. Limited scientific knowledge
2. Limited historical data
3. Cross-disciplinary nature of cat models
4. Lack of data to create GIS databases
5. Lack of accurate data on true market values
6. Incomplete/inaccurate info on inventory’s description

Question 32

Identify 3 sources of aleatory risk

Answer 32

1. Frequency of hazard occurrence
2. Fragility of building
3. Capacity of individual structural events
4. Cost of repair

Question 33

Describe 2 ways to incorporate uncertainty in CAT models

Answer 33

1. Logic Trees
   Displays alternative parameter values or math relationships, along with weights for each alternative.
   Alternatives then weighted together to produce estimates for each parameter/relationship.
2. Simulation Techniques
   Can be used to model real system by building model that attempts to replicate system’s behavior.
   Can be used to handle more complex scenarios.
   Can be used to derive prob distributions.
   Can be used for both discrete and continuous distributions.

Question 34

Identify advantages and disadvantages of Logic Trees

Answer 34

Advantages:
1. Tractability
2. Usefulness as tool to communicate risk
3. Computing power allows handling of large DBs

Disadvantage:
Weights are often based on expert opinion = biased

Question 35

Describe how OEP values from different models can be weighted

Answer 35

You can generate EP curves using combination of logic trees and simulation.

Each branch of logic tree represents an alternative that samples from prob distribution using simulation.

Each branch can generate its own EP curve.

Then, we can calculate mean, median, CI for combined EP curve using curves from different branches.

Question 36

Describe 3 special issues insures need to account for in managing risk for CATs

Answer 36

Since cats can impact multiple properties simultaneously, important to assess cat risk at portfolio level in addition to individual risk level.

3 special issues:

1. Data Quality
   Need to make sure data in used in inventory model is adequate.
   Increasing data quality can reduce epistemic uncertainty
2. Uncertainty Modeling
   Losses should not be allocated to stakeholders based solely on expected value, but instead based on probability distributions.
3. Impact of correlation
   Having more diversified portfolio reduces risk of single event resulting in damages to large portion of portfolio.

Question 37

List 3 considerations to add new policy to portfolio

Answer 37

1. Magnitude of risk
2. Correlation with existing portfolio
3. Highest price risk is willing to pay

Question 38

Explain the Bottom-Up approach to quantify portfolio risk

Answer 38

1. Model losses at location level
2. Aggregate losses across all locations for each policy
3. Aggregate losses across all policies for each portfolio
4. Aggregate losses across all portfolios.

Question 39

For any 2 of 4 basic modules of a cat model, provide an example of epistemic risk.

Answer 39

1. Hazard module: incorrectly estimate frequency of cat events due to lack of historical data or limited scientific knowledge
2. Inventory module: insufficient or inaccurate information about books of business, causing inaccurate estimates of loss
3. Vulnerability: limited understanding of how cat damage different types of properties with different building materials, so lack of knowledge can cause inaccurate possible damages estimates
4. Loss module: Mappings between building damage and cost of repair could be inaccurate, cause inaccurate total cost estimates

Question 40

For any 2 of the 4 basic modules of CAT model, provide an example of aleatory risk.

Answer 40

1. Hazard module: very large catastrophic event occurs on tail end of magnitude distribution and insurer had not held enough capital for this
2. Inventory module: insurer’s book of business has significantly shifted between time cat model was run and when event occurs, thus cat exposure was underpriced.
3. Vulnerability module: medium size cat event could cause more damage than expected.
4. Loss module: court could require an insurer to pay for claims that were not covered, creating significant additional loss.