03_Grossi Flashcards
Describe the four basic components of a cat model.
- Hazard
* Describes the natural catastrophe
* Description might include items such as earthquake epicenter location, projected hurricane path, hurricane wind speed, etc. - Inventory
* Describes the portfolio of properties at risk
* Description might include items such as the location of each exposed property, the construction type of a building, the number of stories of a building, etc. - Vulnerability
* Combines the hazard with the exposed properties to calculate the physical impact of the hazard on the properties. In other words, this module determines the severity of the impact on the property - Loss
* Determines the direct and indirect losses of the hazard on the exposed properties.
Direct losses include physical damage, while indirect losses include things like business interruption or relocation cost
Identify four stakeholders of cat models. Briefly describe how each stakeholder uses cat model output.
- Insurers use model output to understand what level of reinsurance protection is needed to ensure solvency in the event of a catastrophe
- Reinsurers use model output to price cat covers
- Capital markets use model output to price cat bonds
- Emergency management agencies use model output to understand where the largest concentration of loss will occur in the event of a specific catastrophe (ex. large earthquake)
Occurrence Exceedance Probability (OEP) vs. Aggregate Exceedance Probability (AEP) vs. Conditional Exceedance Probability (CEP)
- OEP – the probability that at least one loss exceeds the specific loss amount
- AEP – the probability that the sum of all losses during a given period exceeds some point
- CEP – the probability that the amount of a single event exceeds a specific loss amount
The Grossi textbook focuses on the OEP.
Briefly describe an OEP curve.
An OEP curve plots losses on the 𝑥-axis and occurrence exceedance probabilities on the 𝑦-axis.
An insurer sets $10M as an acceptable level of loss at a 1% probability of exceedance. Suppose the loss amount at a 1% OEP is greater than $10M.
Identify three ways in which the insurer can reduce its 1% loss to an acceptable level.
- Reduce its portfolio
- Transfer the excess amount above $10M to a reinsurer
- Purchase a cat bond to cover the excess amount above $10M
Briefly describe the probable maximum loss (PML).
The PML is the loss amount that corresponds to an acceptable OEP. PMLs are often framed in terms of the return period, which is simply the reciprocal of the OEP.
It is the largest loss an insurer can reasonably be expected to experience
Two Conditions for a Risk to be Considered Insurable
- The ability to identify and quantify the chances of the event occurring (i.e., frequency) and the extent of the losses likely to be incurred (i.e., severity)
- The ability to set premiums for each potential customer or class of customers
Briefly describe three factors that influence the rate charged by the insurer for a risk.
- Uncertainty of Losses – If insurers are unable to produce precise estimates of the risk, they might set higher premiums to account for the additional uncertainty
- Supply Shortages – If the capacity of the insurance industry is reduced due to recent large losses (ex. large hurricane), then insurers might charge higher premiums
- Highly Correlated Losses – If losses are highly correlated (ex. property losses from cats), then insurers might charge higher premiums
Formula for the Survival Constraint
Pr(𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠 > (𝑛𝑧 + 𝐴)) < 𝑝1
Where 𝑛 = maximum number of policies satisfying constraint, 𝑧 = insurance premium for each policy, 𝐴 = surplus, and 𝑝1 is some probability threshold.
An insurer satisfies the survival constraint by choosing a portfolio of risks with an overall expected probability of insolvency less than some threshold 𝑝1.
Note that customer demand comes into play here. Larger values of 𝑧 can reduce demand, which may result in the insurer leaving the market if it cannot generate a positive expected profit.
Provide an example of how an insurer might integrate cat risk assessment with risk management.
Assume that the stakeholder is an insurer. The insurer uses catastrophe model output to assess catastrophe risk. The insurer’s decision rule for developing risk management strategies is to maximize expected profits subject to meeting the survival constraint.
The insurer determines that risk transfer through reinsurance is an appropriate risk management strategy to maximize expected profits while keeping the probability of insolvency at an acceptable level. Note that the book mentions that another broad risk management strategy is risk reduction (ex. mitigation).
Describe a “probabilistic risk analysis” in the context of a cat model.
The hazard and vulnerability modules comprise the “probabilistic risk analysis” in a cat model. The hazard module estimates the probability that the physical parameters of the hazard will exceed various levels. The vulnerability module estimates the probability that structure damage will exceed various levels as a result of the hazard.
Identify three general elements addressed in the hazard module.
- The most likely locations of future events
- The frequency of future events
- The severity of future events
For the earthquake and hurricane hazards, provide two features of the hazard that might help identify the locations of future events.
Earthquakes
1. Faults
2. Seismic Zones
Hurricanes
1. Storms tracks
2. Historical landfall locations
It’s also important to understand that smoothing techniques are implemented in cat models to allow simulated earthquakes and hurricanes to occur in areas that have not been historically impacted.
To estimate the damage potential of natural hazards, a cat model must estimate their physical parameters at two spots. Identify those two spots.
- The source
- The sites of the affected building inventory (i.e., local intensity)
For earthquakes, source parameters includes things like earthquake magnitude and fault-rupture characteristics and local intensity parameters includes things like seismic wave amplitude which is impacted by the local terrain.
For hurricanes, source parameters include things like forward speed and barometric pressure and
local intensity parameters include things like local windfields which is also impacted by the local terrain.
Provide an example of a “source parameter” and a “local intensity parameter” for both earthquakes and hurricanes.
Earthquakes
1. Source parameter – earthquake magnitude
2. Local intensity parameter – seismic wave amplitude
Hurricanes
1. Source parameter – forward speed
2. Local intensity parameter – barometric pressure
Describe how the vulnerability module of a cat model assesses building damage for a large insurance portfolio.
To deal with large portfolios, we divide the building inventory into broad classes. Then, we choose a typical building from each class and analyze it using structure specific engineering methods. We assume that each building in that class will have the same response to the hazard.
Clearly, we should not expect every building within a class to perform in the same exact way. However, this method generally produces accurate estimates of mean damage on a portfolio basis.
Describe the two steps involved in vulnerability analysis.
- Identify and define typical buildings in the modeled region – in this step, we identify building classes by the most important factors that affect the structural response to the hazard being analyzed (ex. building material).
Then, we sub-divide each building class based on secondary modifiers such as roof or foundation type - Calculate the building performance to ground motion or winds of different intensities – in this step, we use a damage function to relate the structural damage to the event intensity
In general, the Loss Module is used to translate damage estimates from the vulnerability module into estimates of monetary loss.
In some cases, cat modelers have tried to link ground motion or wind intensity directly to the level of monetary loss. Briefly describe the main issue with this approach.
The main issue with this approach is that the damage functions based on expert opinion cannot be easily updated to reflect new construction techniques, building codes, repair costs, or information gained in the aftermath of actual events.
Describe two sources of uncertainty in cat models.
- Aleatory Uncertainty
* The uncertainty due to the inherent randomness associated with natural hazard events
* This uncertainty cannot be reduced by the collection of additional data
* This uncertainty is reflected via probability distributions - Epistemic Uncertainty
* The uncertainty due to lack of information or knowledge of the hazard
* This uncertainty can be reduced by the collection of additional data
Provide two examples of aleatory and epistemic uncertainty.
Aleatory Uncertainty
1. Frequency of a hazard occurrence (ex. cannot know exact time of occurrence)
2. Fragility of a building (ex. cannot know precise level of structural damage)
Epistemic Uncertainty
1. Limited scientific knowledge
2. Lack of historical data describing earthquake or hurricane occurrence make it more difficult to predict where they might occur
3. Lack of accurate data on true market values of the inventory properties can lead to inaccurate estimates of the insured loss
4. Lack of data to create the Geographic Information System (GIS) database (eg. soil condition)
Identify two common methods for incorporating uncertainty into cat modeling.
- Logic Trees
- Simulation Techniques
In the logic tree approach, alternative parameter values or mathematical relationships are identified and assigned various weights. The tree splits at each parameter or mathematical relationship creating more possible paths that the final cat model calculation can take.
At the end of the tree, we are left with a number of possible combinations of parameters or mathematical relationships, each with a different weight.
In the simulation approach, we assume a distribution for each uncertain parameter. Then, we sample from each parameter distribution and simulate an event based on those sampled parameters. If we do this thousands of times, we build a range of possible outcomes which can be used to understand the uncertainty for the hazards. This is Monte Carlo simulation.
Logic trees requires a set of simplifying assumptions in contrast to simulation techniques which can model extremely complex processes
Explain how one might create an OEP curve by combining a logic tree with Monte Carlo simulation.
- Suppose that the cat model requires five different parameters and/or mathematical calculations
- We let each branch of a logic tree represent a different set of assumptions for the five different parameters. These assumption sets are based on samples from the various probability distributions (this is the simulation component)
- We assume that we can produce an exhaustive list of all possible assumptions. Since we have an exhaustive list, we assign each assumption set a weight and those weights sum to 1
- For each assumption set, we create an OEP curve
- We can calculate the mean, median, standard deviation, etc. of the OEP curves using the assumption set weights
Formula for the Policyholder Premium Using Grossi & Kunreuther’s Ratemaking Model
𝑃𝑟𝑒𝑚𝑖𝑢𝑚 = 𝐴𝐴𝐿 + 𝑅𝑖𝑠𝑘 𝐿𝑜𝑎𝑑 + 𝐸𝑥𝑝𝑒𝑛𝑠𝑒 𝐿𝑜𝑎𝑑
Where AAL = average annual loss.
The risk load reflects the insurer’s concern with the survival constraint and the need for additional surplus capital.
[the insurer needs to hold additional surplus capital in order to take on riskier exposures]
The expense load reflects the administrative costs involved in insurance contracts (ex. LAE, premium taxes, commissions).
Identify the two critical factors for differentiating risks for ratemaking in a catastrophe setting.
- The structure attributes of the portfolio (i.e., the building inventory)
- The location attributes of the portfolio (i.e., the proximity to a hazard)
