Grossi Flashcards
Users of CAT models
Insurers/reinsurers: exposure
Reinsurance brokers: risk
Capital markets: CAT bonds
Regulators
Emergency Management Agencies
Why regular statistical tools are inappropriate for CAT losses
Insufficient historical claim data
Limited data available due to changing factors
Modules of CAT model
Hazard
Inventory
Vulnerability
Loss
Hazard module
Simulates natural disasters using probabilities of different parameters
Inventory module
Contains properties at risk and their characteristics
Also called the exposure module
Vulnerability module
Estimates susceptibility to damage of each property given simulated CAT
Loss module
Quantifies direct and indirect losses of the event on each property
Three main parameters of a hazard module
Frequency
Severity
Location
These have to do with simulated events, not exposures
Vulnerability module appraoches to estimating damage
Engineering judgment (simple, but arbitrary/not easy to update)
Building response analysis (more accurate, but based on specific buildings)
Class-based BRA
Class-based BRA steps
Divide risks into different classes of buildings
Identify a typical building and analyze in detail
Evaluate building performance to get a damage ratio
Damage ratio
Ratio of repair cost to replacement cost
Two main approaches to determine $ loss from CAT event
Link event parameters directly to expected loss (cannot easily be updated to reflect new information)
First estimate physical damage from an event and use a cost analysis to translate into $
Occurrence Exceedance Probability
Probability that the loss for at least one event exceeds specified loss amount
Useful in per-occurrence excess of loss reinsurance
Aggregate Exceedance Probability
Probability that sum of all losses exceeds specified loss amount
Useful in purchansing aggregate reinsurance
Conditional Exceedance Probability
Probability that the amount on a single event exceeds a specified loss amount, given that the event occurs
Useful for setting reserves after an event occurs
Probable Maximum Loss
Largest loss likely to occur in a given period of time
Occurrence Exceedance Probability, formula
OEP(Li) = 1 - Π(1 - pj)
Sort events in decreasing order by size
Conditional Exceedance Probability formula
CEP(Li) = OEP(Li) / [1 - P(no events)]
Conditions for an insurer to be willing to provide coverage to a risk
(Conditions for a risk to be insurable)
Ability to identify and quantify probability of event and severity of loss
Ability to set premiums for each customer
Considerations in setting rates for CATs
Regulators
Competition
Uncertainty of losses
Correlation of losses
Adverse selection
Moral hazard
Liquidity of assets
Determining whether to provide coverage
As long as P(Loss > nz + A) < p1
p1 is probability of insolvency
n is the # of policies
A is the current surplus
Risk load using standard deviation of OEP curve
How CAT models help determine equitable average annual losses
Structure Attributes
Location Attributes
Regulator concerns with CAT models
Not subject matter experts; makes it tough to evaluate
Modeling firms unwilling to share key proprietary elements
Conflict: present scientifically rational approach to quantifying risk, but may be used to justify increasing rates
CEA formation
After billions of dollars of loss due to 1994 Northridge earthquake
Created in 1996 as publicly managed insurer for EQ risk in CA
CEA constraints
Rates needed to be actuarially sound
If scientific information was used, it should be consistent with available data and current knowledge of scientific community
Issues raised during CEA rate hearings
Earthquake recurrence rates
Assumed time independence of earthquakes
Damage estimates (based only on Northridge EQ)
Underinsurance factor (understating estimated losses)
Demand surge
Policy sublimits
Rating plan deviation (by territory)
Retrofit discount
Open issues in using CAT models in ratemaking
Regulatory acceptance
Public acceptance
Actuarial acceptance
Model to model variance
ASB requirements when using a CAT model
Determine appropriate reliance on experts
Have a basic understanding of the model
Evaluate appropriateness for intended application
Determine if appropriately validated
Determine appropriate use of the model
Two types of uncertainty in CAT models
Aleatory
Epistemic
Aleatory uncertainty
Inherent randomness associated with natural hazard events (process risk)
Epistemic uncertainty
Uncertainty due to lack of knowledge of the hazard (parameter risk)
Reasons for epistemic uncertainty
Limited scientific knowledge
Limited historical data
Cross-disciplinary nature of CAT models
Lack of accurate data on true market values
Limited structural testing
Ways to quantify uncertainty
Logic Trees
Simulation Techniques
Logic trees
Displays alternative parameter values along with associated weights
Advantages: tractability, useful tool to communicate risk
Disadvantages: weights are subjective
Simulation techniques
Used to model a real system by building a model that attempts to replicate system’s behavior
Weighting CAT models, Grossi Text
50% weight on middle value, 25% weight on each outside value
Three special issues insurers need to account for in managing portfolio risk
Data quality
Uncertainty modeling (base loss allocation on probability distributions)
Impact of correlation
Considerations when adding a new policy to a portfolio
Magnitude of risk
Correlation with existing portfolio
Highest price that risk is willing to pay
Bottom-up approach to portfolio modeling
Model losses at location level
Aggregate for each policy
Aggregate for each portfolio
Aggregate across portfolio
Can also aggregate by zip or other rating variables to identify high risks
Loss diagram
$500K deductible
20% $3M xs $2M treaty based on ground up losses
30% pro-rata treaty
Critical questions concerning CAT risks
What is the AAL?
What is the likelihood of insolvency?
