Grossi Flashcards
(21 cards)
Catastrophe Models
What is it? Who uses it?
Cat models combined various sciences (physics, geology, actuarial science) to quantify the risk posed by natural disasters (catastrophies) such as hurricanes and earthquakes
- Insurers/Reinsurers: to assess their exposure to risk
- Reinsurance brokers: to assess risk to their clients
- Capital markets: to price cat bonds
- Regulators: to review rates based on models
- Emergency Management Agencies (EMA): to determine impact of a catastrophe and coordinate an emergency response
Risk Management Strategy from Catastrophe Models
For insurers and re-insurers
Risk Reduction - non-renew policies, limiting coverage, increasing deductible, increasing rates
Risk Transfer - purchasing reinsurance, issue cat bonds
Why are Cat Models better than historical data?
- Insufficient historical claim data (also varying definition of a catastrophe)
- Cats are inherently infrequent
- Outdated data - property values, cost of repair, building codes changing
Components of Catastrophe Model
Hazard Module
What is it? What are the parameters?
Simulates natural disasters based on probabilities of different event parameters
- Location - EQ and hurricanes are more common in certain areas
- Frequency - this parameter has biggest uncertainty
- Severity - using multiple characteristics. e.g. EQ uses depth and scale magnitute
Components of Catastrophe Model
Inventory/Exposure Module
What is it? What are the parameters?
Contains property data and their characteristics
For insured homes, e.g. construction type, insured amount, property location
- Zip code
- LOB (residential, commential, industrial, etc)
- Type of coverage
- Occupancy type
- Construction type
Components of Catastrophe Model
Vulnerability Module
What is it? What are the approaches?
Estimates the vulnerability (suseptibility) to damage for each property given a specific simulated cat and property info
- Engineering judgement (expert opinion). Advantage - simple | Disadvantage - arbitrary and not easy to update with new data
- Building response analysis (advanced engineering techniques). Advantages - more accurate | Disadvantage - based on specific building and not appropriate to apply to entire portfolio of buildings
- Class-based building response analysis - modify the building response analysis to make it more appropriate for an entire portfolio
Components of Catastrophe Models
Loss Module
What is it? What are the approaches?
Quantifies direct (e.g. physical damage) and indirect (e.g. business interruption) losses of the cat on each property
- Link event parameters directly to expected loss. Based on expert opinion - simple. Cannot be easily updated to reflect new data (construction types, building codes, repair costs)
- Estimate physical damage from an event, use cost analysis to translate this into monetary loss. Calcuate insured loss by applying policy conditions (limits, deductible, reinsurance, etc)
Insurability Conditions
- Able to identify and quantify the frequency and severity of a loss
- Able to set premiums for each insured
Considerations in Setting Rates for Cats
- Regulation
- Competition
- Uncertainty of losses - higher risk load is needed
- Highly correlated losses - cat losses are not independent
- Adverse selection
- Moral hazard
- Liquidity of assets - insurers will need to have cash during potential cat losses. Liquid asset lower investment returns
Determine Whether to Provide Coverage
n policies, z premium, A surplus
Assume insurer wants probability of insolvency to be < p1
- Provide coverage if P(Loss > n * Prem + surplus) < p1
- p1 = exceedance probability = S(x) = 1- F(x)
n policies, z premium, A surplus
Simple Ratemaking Model
Premium Formula
Premium = Average Annual Loss (AAL) + Risk Load + Expense Load
AAL = sum(pi * Li)
One possible risk load = SD of OEP curve = sqrt(sum(Li^2 * pi) - AAL^2)
Why Regulators Not Supportive of Cat Models
- Difficult to evaluate the models since they require subject matter experts
- Insureds are unwilling to share key elements of their model, espeicially in states that require documents to be publicly available
Regulators understand cat models are a scientifically rational approach to quantifying potential risk, but are afraid insurers are using it as “justification” for charging higher rates
California Earthquake Authority (CEA)
Why was it formed? Constraints in ratemaking
Insurers threatening to leave CA due to EQ risk back in the 90s. CA created CEA as a publically manager insurer for EQ risk, so that insurers can continue to provide other coverages
The CEA was given some constraints in ratemaking:
* Rates needed to be actuarially sound (not excessive inadequate or unfairly discriminatory)
* If scientific information was used in ratemaking:
* it should be consistent with available geophysical data
* the current knowledge of the scientific community
California Earthquake Authority (CEA) Challenges
- the models produced earthquake frequency rates that were twice the historical frequency
- models usually assumed earthquake followed a random poisson distribution but it is possible the EQ is dependent on the time since the prior EQ
- damage curves used by most models were based on only 1 event
- modeled losses expressed as a % of insured value, but if buildings are underinsured then estimated losses will be understated
- it is difficult to quantify the increased costs of parts and labor caused by the increased demand following a catstrophe due to limited historical data
- CEA 5% discount that retrofitted their home to better withstand EQs, based on engineering experts, not loss data
Open Issues in Using Cat Models
Regulatory Acceptance - regulars do not have technical expertise to access reasonableness of model assumptions, inputs and outputs.
* Some states have created independent technical experts to certify the models are reasonable
Low public acceptance because models have usually resulted in rate increases
Actuarial acceptance - it is important for actuaries to become familiar with models, but they lie outside of usual actuarial expertise. ASB requires actuaries:
* Determine appropriate reliance on experts
* Have basic understanding of the model
* Evaluate whether the model is appropriate for intended application
* Determine that appropriate validation has occurred
Model to Model Variance - different models give different outputs based on different assumptions and data used
Insurance Portfolio Management (Cat Risk)
Special issues to account for in managing portfolio risk
- Data quality - insurers need to make sure their data that is used in inventory module is accurate. Increasing data quality can reduce epistemic uncertainty
- Uncertainty Modeling - losses should not be allocated to stakeholders solely based on expected value, but instead 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
Insurance Portfolio Management
Residential vs Commercial Policies
Residential
* single location with limits by coverage (building, contents, etc) with single deductible
* insurer should have moderately detailed data about the property
Commercial
* Multiple locations, limits/sublimits, and deductibles
* Higher replacement costs
* Insurer should have highly detailed data about these properties
Insurance Portfolio Management
Whether to add a new policy to the portfolio, UW should consider:
- The magnitude of the risk
- Correlation with the existing portfolio
- The highest price that the risk/insured is willing to pay
Aleatory vs Epistemic Uncertainty
Aleatory - the inherent randomness associated with natural hazard events (process risk for cats)
Epistemic - uncertainty due to our lack of knowledge of the hazard (parameter risk for cats)
Insurance Portfolio Management
Bottom Up Approach to Portfolio Modeling
- Model losses at location level
- Aggregate loss across all locations for each policies
- Aggregate losses across all policies in each portfolio
- Aggregate losses across portfolios
Can also aggregate losses by zip code or other rating variables - use this info to tailor their business
Exceedance Probability Curves (OEP)
What is it? Purpose?
OEP = P(X>x) = S(x)
* To calculate the PML for a given return period
* To evaluate if the protfolio meets a solvency goal (e.g. $10M as acceptable for a 1% exceedance probability)
* To calculate the Average Annual Loss (AAL)
* For insurers to determine size and distribution of a portfolio’s potential loss
* To determine the proportion of risk that needs to be transferred to a reinsurer
* To determine the types and locations of risks they’d like to insure
