CAT modeling

Question 1

CAT models are recent tool that combine various sciences to help better quantify

Answer 1

risk posed by natural disasters such as hurricanes and EQs

Question 2

CAT models used by

Answer 2

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 CAT bonds
4. regulators: to assess insurer work
5. emergency management agencies: to determine impact of actual event and coordinate emergency response to areas most likely in need

Question 3

for insurers and reinsurers that are exposed to CAT risk, the use of a CAT model helps facilitate 2 main risk management strategies:

Answer 3

1. risk reduction: primarily included non-renewing policies, limiting coverage offered, increasing deductibles, and increasing rats
2. risk transfer: primarily includes purchasing reinsurance or issuing CAT bonds

Question 4

regular statistical tools used are often inappropriate for applying to CAT losses because

Answer 4

1. there is insufficient historical claim data for CATs
2. limited data that is available is often inappropriate due to changing factors

Question 5

CAT models have 4 components

Answer 5

1. hazard module: simulates natural disasters based on probabilities of different event parameters
2. inventory module: contains properties at risk and their characteristics; exposure module
3. vulnerability module: estimates susceptibility to damage of each property given a specific simulated CAT and property info
4. loss module: quantifies the direct (physical damage) & indirect (business interruption or relocation costs) loss of event on each property

Question 6

Hazard Module has 3 main parameters

Answer 6

1. location: EQ locations depend on locations of fault or seismic zones, hurricanes are more likely to occur in certain areas
2. frequency: parameter has biggest uncertainty
3. severity: includes multiple characteristics

Question 7

hazard module process in general

Answer 7

• historical data can be used to generate initial probability distributions for this module but those distributions are generally refined with scientific knowledge
• when CAT model is run, module would simulate a large # of possible events based on probability distributions of event parameters
• for each simulated event, module would also estimate intensity of event at different specific locations

Question 8

• models can estimate losses for entire industry, single insurer’s portfolio, individual risks
• depends on _____ ____ into model

Answer 8

inventory input

Question 9

for aggregate analysis of modeled regions, modelers construct annually updatable databases from government and private sources that includes # of properties and their values broken down by

Answer 9

Zip

LOB

Coverage

Occupancy type (important for estimating contents damage

Construction type (most important variable for damageability

Question 10

more detailed the input

Answer 10

more reliable the output

Question 11

for modeling important individual buildings

Answer 11

insurer can conduct a site-specific analysis to obtain more detailed info for input into models

Question 12

Vulnerability Module

Answer 12

estimates damage to properties from simulated events

Question 13

there are several approaches to obtain relationship between hazard and resulting damage

Answer 13

1. engineering judgement: based on expert opinion
2. building response analysis: based on advanced engineering techniques
3. class-based building response analysis: modify building response analysis to make it more appropriate for portfolio risk assessment; divides risks into different classes of buildings based on building characteristics

Question 14

engineering judgement advantage and disadvantage

Answer 14

• advantage=simple
• disadvantage=arbitrary and not easy to update as new info becomes available

Question 15

building response analysis advantage and disadvantage

Answer 15

• advantage=more accurate
• disadvantage=being based on specific buildings and thus not appropriate to apply for entire portfolio of policies

Question 16

2 steps of class-based building response analysis

Answer 16

a. ID of typical buildings
- typical building from each class is analyzed in detail
b. evaluation of building performance
- for each class, relationship between intensity of force and level of expected damage of typical building is generated
- this is applied to all buildings in class
- enables generation of damage ratios which are ratios of repair cost to replacement cost; damage ratios and functions are created for each coverage
- when model is run for actual portfolio, model would look up damage ratios for each building for each simulated event in order to calculate expected damage

Question 17

Loss Module: 2 main approaches to determine monetary loss from a CAT event

Answer 17

1. link the event parameters directly to expected loss
   - primarily based on expert opinion
   - cannot be easily updated to reflect new construction techniques, building codes etc.
2. estimate physical damage from event and use cost analysis to translate this into monetary loss

Question 18

3 types of exceedance probability curves

Answer 18

1. Occurrence exceedance probability
   - probability that loss for at least 1 event exceeds specified loss amount during a given time period
   - useful to insurer interested in buying per occurrence XOL
2. aggregate exceedance probability
   - probability that sum of all losses exceeds specified loss amount during a given time period
   - useful to insurer interested in buying aggregate reinsurance
3. conditional exceedance probability
   - probability that amount on single event exceeds a specified loss amount given that the event occurs
   - useful to insurer in setting reserves after event occurs

Question 19

based on graph of exceedance probability

Answer 19

insurers can decide what level of risk is tolerable and make risk management decisions to deal with unacceptable levels of risk

Question 20

in general, there are 2 conditions for insurer to be willing to provide coverage to a risk:

Answer 20

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

Question 21

because risk is insurable, doesn’t mean

Answer 21

its profitable so insurer needs to charge rate that is both profitable and produces adequate demand (ie affordable)

Question 22

considerations in setting rates for CAT events

Answer 22

State regulations

Competition

Uncertainty of losses

Highly correlated losses (CAT losses are not independent; do not follow law of large #s, single event can produce significant losses)

Adverse selection

Moral hazard

Liquidity of assets (liquid assets produce lower returns so need to charge higher premium to reflect this opportunity cost)

Question 23

4 ratemaking principles

Answer 23

CAT models help devise rates that follow them:

1. rate is estimate of expected value of future costs
2. rate provides for all costs associated with transfer of risk
3. rate provides for costs associated with individual risk transfer
4. rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is actuarially sound estimate of expected value of all future costs associated with individual risk transfer

Question 24

cat model can help determine both

Answer 24

the AAL and risk load

Question 25

model can help determine equitable AAL for different risks based on

Answer 25

1. structure attributes: these relate to physical performance of building during a cat 2. location attributes: these relate to proximity and susceptibility to hazard of building

Question 26

regulators have historically not been supportive of use of cat models in ratemaking because

Answer 26

1. it is difficult for regulators to evaluate modes since they require subject matter experts 2. modeling firms are unwilling to share key proprietary elements of their models especially in states that require government documents to be publicly available - models present a conflict for regulators since they present a scientifically rational approach to quantifying potential risk but models could also be used by insurers as justification for charging higher rates - note there are some publicly available cat models that can be used by regulators to compare with models created by private companies

Question 27

2 main ways to incorporate uncertainty into cat models

Answer 27

1. logic trees 2. simulation techniques

Question 28

logic trees

Answer 28

- displays alternative parameter values or mathematical relationships along with associated weights for each alternative - alternatives are weighted together to produce estimates for each parameter or relationship - advantages: tractability, usefulness as tool to communicate risk - disadvantages: weights are often based on expert opinion and may be biased

Question 29

simulation techniques

Answer 29

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

Question 30

can also use exceedance probability curves using a combo of logic trees and simulation

Answer 30

- under this method, each brand of logic tree represents alternative that samples from a probability distribution using a simulation - each branch can generate its own EP curve - can calculate a mean, median, and Cis for a combined EP curve using curves for different branches - similar to concept of combining EP curves from different branches of logic tree within same model is concept of combining EP curves from different models - model users deal with uncertainty of modeling by weighting together outputs of multiple models

Question 31

3 special issues insurers need to account for in managing their portfolio risk

Answer 31

1. data quality - insurers need to make sure their data is sued in inventory module is accurate - increasing data quality can reduce epistemic uncertainty - particularly true for important variables like construction type or age of building 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 a more diversified portfolio reduces risk of single event resulting in damages to large portion of portfolio

Question 32

residential v commerical policies

Answer 32

- residential policies have single location with limits by coverage and usually a single deductible; insurer should have moderately detailed data about properties - commercial policies may have buildings in multiple locations covered by the same policy; each building would usually have high replacement cost and there may be limits and deductibles that vary by location in addition to policy level limits and deductibles; given larger amount of risk, insurer should have highly detailed data about these properties

Question 33

when deciding whether or not to add a new policy to portfolio, underwriters should consider

Answer 33

Magnitude of risk Correlation with existing portfolio Highest price that risk is willing to pay -cat models help make decision more objective by quantifying risk posed

Question 34

Bottom up approach to portfolio modeling

Answer 34

- following steps: 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. if insurer has multiple portfolios, aggregate losses across portfolios - instead of aggregating losses for entire portfolio, insurers can also aggregate losses by zip code - can use this work to identify high risk zip codes for which they might want to limit their exposure, possibly by curtailing new business - losses by stakeholder can be visualized with loss diagrams

Question 35

in case with multiple portfolios

Answer 35

diversification across portfolios reduces impact of individual events to insurer

Question 36

company has decided to minimize risk. Explain which portfolio the insurer should eliminate.

Answer 36

Looking at the portfolios, you can visually see that portfolios 1 and 3 are positively correlated and both are negatively correlated with portfolio 2. To increase diversification, we should eliminate either portfolio 1 or 3. Since the standard deviation is higher for portfolio 3 than for portfolio 1, we should eliminate portfolio 3.

Question 37

potential problems with using catastrophe models for ratemaking.

Answer 37

* Model to model variance - the same input could produce very different results if another model is used. * Public acceptance - the public has been slow to accept the models since they generally result in higher rates. * Regulators have not widely accepted the use of models. It requires expertise to evaluate,modeling firms don’t release all proprietary aspects of models, and they often result in rate increases. * They lie outside most actuaries’ expertise. Therefore, actuaries must rely on outside experts. However, actuaries should still have a basic understanding of the model, validate results and inputs, and determine if it is appropriate for its intended purpose.

Question 38

exceedance probability curve represents.

Answer 38

An exceedance probability curve shows all possible levels of loss and the probability that the loss level will be exceeded in a given period of time. An occurrence EP curve shows the probability that at least 1 loss will exceed the loss level, while an aggregate EP curve shows the probability that the sum of all losses will exceed the loss level.

Question 39

common uses for exceedance probability curves.

Answer 39

• Calculate the PML for a given payout period. • Calculate if the portfolio meets a solvency goal. • Decide what proportion of risks should be ceded to reinsurers. • Used to calculate average annual loss. • Set level of conservativeness, such as PML in 1/X chance. • Used to find a strategy to change the portfolio if it is currently above the level of conservativeness. • Used by emergency response units to determine where damage might be and build strategies in times of catastrophes. • Used when running logic trees. Instead of using point estimates, each branch of the tree can have its own exceedance probability curve for the different outcomes, which can then be combined. • Emergency management services can use them to evaluate the potential risk of some regions and plan evacuations. • Reinsurance brokers can use them to evaluate the level of risk in their portfolios and estimate the impact of accepting new risks.