Grossi Flashcards
Identify who uses Cat models and for what (5)
- Insurers & reinsurers
To assess their exposure risk
Main stakeholders - Reinsurance brokers
To assess risk risk for their clients to send to reinsurers - Capital markets
To price catastrophe bonds - Regulators
To assess insurer work (review rates) - Emergency Management Agencies
To determine the impact of an actual event (past occurrence) and coordinate an emergency response to areas most likely in need
Identify 2 risk management strategies facilitated by CAT models
- Risk reduction
Primarily includes non-renewing policies, limiting coverage offered, increasing deductibles and increasing rates. - Risk transfer
Primarily includes purchasing reinsurance or issuing cat bonds.
State 2 reasons why regular statistical tools used by actuaries are often inappropriate for cat losses
- There is insufficient historical claim data for cats
- The limited data available is often inappropriate due to changing factors (property values, cost of repair, building codes)
Briefly describe the 4 modules (components) in CAT model
- Hazard module
Simulates natural disasters based on probabilities of different event parameters. - Inventory module
Contains properties at risk and their characteristics.
Most important is location. - Vulnerability module
Estimates susceptibility to damage of each property given specific simulated cat and property informations. - Loss module
Quantifies direct and indirect losses of event on each property.
Translates physical damage into monetary loss.
Contrast direct and indirect losses
Direct losses include physical damage
Indirect losses include things like business interruption or relocation costs
Describe the 3 main parameters in Hazard module
- Location
Eqk locations depend on location of faults or seismic zones.
Hurricanes are more likely to occur in certain areas. - Frequency
This parameter has the biggest uncertainty, but is it critical because damage & loss probabilities are directly related to this value. - Severity
For eqks, would include depth and fault characteristics in addition to Richter magnitude.
For hurricanes, would include projected path and wind speed.
Describe 3 approaches to obtain relationship between hazard and resulting damage in vulnerability module
- Engineer judgment
Based on expert opinion
+: simple
-: arbitrary and not easy to update for new info - Building response analysis
Based on advanced engineering techniques
+: more accurate
-: Based on specific buildings, cannot be applied to entire portfolio - 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.
Identify the 2 main approaches to translate physical damage to monetary loss in Loss module
- 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. - First estimate physical damage from event and then use cost analysis to translate into monetary loss.
Explain Exceedence Probability Curves
Graphical representation of probability that certain level of loss will be surpassed in given time period.
Contrast Exceedence Probability curves and GIS maps
GIS map = loss in spatial manner
EP curve = loss in temporal manner
List the 3 types of EP Curves
- 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. - 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. - 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.
Identify 3 uses of EP curves
- Determine size and distribution of potential losses in portfolio
- Determine what coverage to offer
- Determine at what price to over coverage
- Determine % of risks that should be transferred to reinsurer and/or capital market
Calculate OEP and Average Annual Loss (AAL)
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
- Sort events in decreasing order by size (E1 is largest event)
- OEP(Li) = P(L>Li) = 1 - P(L<Li) = 1 - product of (1-pj) for j = 1,…, i-1
True or False?
Sum of all pi can be smaller than 1.
True, since it is possible that no event occurs.
Calculate CEP(Li)
CEP(Li) = OEP(Li) / (1 - P(no event))
State 2 conditions for a risk to be insurable
- Ability to identify and quantify probability of events and severity of loss
- Ability to set premiums for each customer
If both are satisfied, risk is considered insurable
Describe 4 considerations when setting rates covering cat events
- State regulations
- Competition
- Uncertainty of losses
- Highly correlated losses: not independent (spatially correlated) so do not follow law of large numbers. Single even can produce significant losses.
- Adverse selection: occurs when insurer cannot distinguish between E(Loss) for different risk categories while insured selects price/coverage more favourable to him.
- Moral hazard: increased E(Loss) caused by behaviour of PH.
- 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.
State the 4 ratemaking principles
- A rate is an estimate of expected value of future costs.
Should provide for all costs such that insurance system is financially sound. - A rate provides for all costs associated with transfer of risk
Ensures equity among insureds is maintained - A rate provides for costs associated with individual risk transfer
- 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)
Explain how to determine whether to provide coverage (survival constraint)
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
Calculate policy premium for cats using simple ratemaking model
P = AAL + Risk Load + Expense Load
Describe the Expense Load
Expense load reflects administrative costs involved in insurance contracts and is comprised of factors such as LAEs, process fees, taxes, commissions and profit
Describe the Risk Load
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
Describe the 2 attributes that help determining equitable AAL
- Structure attributes
Relate to physical performance of building during a cat (construction type, occupancy type, building codes, construction year, etc) - 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.
Describe 2 challenges faced by regulators when reviewing models
Regulators have historically not been supportive of use of CAT models in ratemaking because:
- It is difficult for regulators to evaluate models since they require subject matter experts
- 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)
Briefly describe the California Earthquake Authority (CEA)
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
List 4 CEA’s ratemaking constraints
- Rates should be actuarially sound (not excessive, inadequate or unfairly discriminatory)
- Scientific information should be consistent with available geophysical data and current knowledge of scientific community
- Rates should not be adjusted to provide rates lower for higher risks or higher for low risks (adverse selection)
- PH who retrofitted homes to withstand eqk shake damage should receive a 5% discount if actuarially sound
Describe 4 challenges to initial CEA rates
- Eqk recurrence rates
Models produced frequency rates that were more than twice historical - 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. - Damage estimates
Damage curves based on only 1 event (Northbridge) - Underinsurance Factor
Modeled losses expressed as % of insured value. If buildings underinsured, estimated losses are underestimated. - 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. - 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. - 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 - Retrofit discount
Discount was based only on engineering experts and not on actual empirical loss data.
Commissions ruled appropriate. - 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.
Describe the 4 open issues for using cat models in ratemaking
- Regulatory acceptance
Regulators do not have technical expertise to assess reasonableness of model assumptions, inputs and outputs. - Public acceptance
Has been low as models have usually resulted in rate increases. - Actuarial acceptance
Important for actuaries to become familiar with components of models because models lie outside usual actuarial expertise. - Model to Model variance
Signifiant differences between output of different models due to varying scientific and engineering data and assumptions used
Identify the 5 ASB requirements for actuaries to use CAT model
- Determine appropriate reliance on experts
- Have basic understanding of model
- Evaluate whether model is appropriate for intended application
- Determine appropriate use of model
- Determine appropriate validation has occurred
Describe 2 types of uncertainty related to cat models
- 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 - Epistemic
Uncertainty due to lack of knowledge of hazard.
Cat version of parameter risk.
Can be reduced
identify 3 sources of epistemic uncertainty
- Limited scientific knowledge
- Limited historical data
- Cross-disciplinary nature of cat models
- Lack of data to create GIS databases
- Lack of accurate data on true market values
- Incomplete/inaccurate info on inventory’s description
Identify 3 sources of aleatory risk
- Frequency of hazard occurrence
- Fragility of building
- Capacity of individual structural events
- Cost of repair
Describe 2 ways to incorporate uncertainty in CAT models
- 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. - 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.
Identify advantages and disadvantages of Logic Trees
Advantages:
1. Tractability
2. Usefulness as tool to communicate risk
3. Computing power allows handling of large DBs
Disadvantages:
1. Weights are often based on expert opinion = biased
2. Requires set of simplifying assumptions
Describe how OEP values from different models can be weighted
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.
Describe 3 special issues insures need to account for in managing risk for CATs
Since cats can impact multiple properties simultaneously, important to assess cat risk at portfolio level in addition to individual risk level.
3 special issues:
- Data Quality
Need to make sure data in used in inventory model is adequate.
Increasing data quality can reduce epistemic uncertainty - Uncertainty Modeling
Losses should not be allocated to stakeholders based solely on expected value, but instead based on probability distributions. - Impact of correlation
Having more diversified portfolio reduces risk of single event resulting in damages to large portion of portfolio.
List 3 considerations to add new policy to portfolio
- Magnitude of risk
- Correlation with existing portfolio
- Highest price risk is willing to pay
Explain the Bottom-Up approach to quantify portfolio risk
- Model losses at location level
- Aggregate losses across all locations for each policy
- Aggregate losses across all policies for each portfolio
- Aggregate losses across all portfolios.
For any 2 of 4 basic modules of a cat model, provide an example of epistemic risk.
- Hazard module: incorrectly estimate frequency of cat events due to lack of historical data or limited scientific knowledge
- Inventory module: insufficient or inaccurate information about books of business, causing inaccurate estimates of loss
- 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
- Loss module: Mappings between building damage and cost of repair could be inaccurate, cause inaccurate total cost estimates
For any 2 of the 4 basic modules of CAT model, provide an example of aleatory risk.
- Hazard module: very large catastrophic event occurs on tail end of magnitude distribution and insurer had not held enough capital for this
- 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.
- Vulnerability module: medium size cat event could cause more damage than expected.
- Loss module: court could require an insurer to pay for claims that were not covered, creating significant additional loss.
Briefly explain how catastrophe models support the 4 ratemaking principles.
- By providing increased accuracy in projecting expected future cost of a risk transfer compared to the prior methods used.
- Provide better estimates of the effect on losses of location, structural attributes, occupancy, mitigation measures and line of business.
- Enables better classification of risks and thus increased equity in rates between insureds.
- Provide more accurate estimates of the expected value of all future costs associated with an individual risk transfer.
