Risk Management 365: 1st Exam

What is a Catastrophe Risk?

• A cause of severe loss or losses

• Affects many people at once

What makes Catastrophe Risks challenging?

• Hard to estimate/price: rare severe events

• Hard to fund loss events: losses are correlated

Law of Large Numbers

Repeat an experiment many times and the outcome will converge to expected value

Independent Risks

Chance of loss is uncorrelated across policy holders (e.g., auto insurance)

Difference between Independent and Catastrophe Risks

With Catastrophe risks, the chance of loss is correlated across policyholders (e.g., hurricane, terrorism)

If Losses > reserves

Loss leads to reduce in equity

Premiums Equation

Premiums = Expected Loss + Cost of Capital + Administrative Costs

Cost of Capital

The cost of protecting funds to pay claims

Protection Gap

the difference between the amount of insurance coverage that is economically beneficial and the coverage actually purchased

Barriers to CAT insurance markets

Demand

• Risk Misconception

• Affordability

• Charity Hazard - belief that disaster relief will address uninsured issues

• Biases in decision-making

Supply

• Financing Constraints

• Uncertanity

• Asymmetric Information (Adverse Selection/Moral Hazard)

Primary Perils

Really catastrophic risks (e.g., tropical storm, hurricane, cyclone, earthquake)

• Low frequency, high severity

• longstanding CAT models

• require lots of insurance industry capital

• Reinsurers are often “at capacity” for these risks

Secondary Perils

Examples (Wildfires, hail, (non-hurricane) floods, winter storms

• These can be catastrophic events

  • higher frequency, lower severity

  • Less developed CAT models, some perils are harder to model

  • growing issue: frequency increasing for many

    • climate change

    • urban development: increasing loss severity

CAT model uses

• Ratemaking

• Estimating Capital Needs

• Buying reinsurance

• Complying with Capital Regulation

• Meeting rating agency standard

CAT Model Inputs

• Insurer’s Portfolio of Properties

• Insurer’s Contract Features

CAT Model Outputs

• Average Annual Loss

• Exceedance Probability Curves

Hazard Module

Condition/Factor causing a loss (e.g., hurricane winds)

• similar to “perils” in insurance

Event Catalogue

• thousands of simulated events

• each event: realization of the hazard (e.g., hurricane path)

  • magnitude/intensity

  • probability - trends and historic records

  • trajectory

  • footprint

Exposure Module

Property (or people or business income) that could be lost in a severe event

• insurer typically provides exposure to model vendor including property location and value (e.g., replacement cost value)

Vulnerability Module

Estimates the hazard’s damages based on the built environment

• damage functions: equations mapping hazard intensity to property impacts

• Depends on:

  • building characteristics, occupancy, construction materials, age

  • Local/regional: building code adaptation, enforcement

• Includes

  • Direct Damages (e.g., buildings, contents)

  • Indirect Damages (e.g., additional living expenses, loss of use)

  • Demand Surge (e.g., increased cost of materials after big events)

What are damages reported on when it comes to the Vulnerability Module?

Damages are reported on the Mean Damage Ratio, the expected value of the ratio of the asset's repair cost to its replacement value.

Financial Loss Module

Translating damages into insured losses

• Models trained on insured loss data

Vulnerability Module Characteristic Types

• Primary Risk Characteristic

• Secondary Risk Characteristic

Primary Risk Characteristics

The most important features of a property in determining its vulnerability curve

• 4 characteristics used:

  • Location: exact GPA/address

  • Occupancy: building use, primary residence, warehouse, etc.

  • Construction Type: structure materials, wood, masonry, etc.

  • Number of Stories: matters for wind speeds, earthquakes, floods, etc.

Secondary Risk Characteristic

“Modifiers” that are typically less important but still meaningfully affect vulnerability.

• Varies by Peril:

  • Hurricane: roof shape, roof straps, window type, storm shutters

  • Earthquakes: structure bolted to foundation, “soft story”

  • Wildfires: defensible space, roof/siding material

  • Flood: basement, first floor evacuation

CAT Model Process

1. Draw random event from the stochastic catalogue

2. For every insured property, examine windspeeds at location

3. Determine mean damage ratio given the home’s construction

4. Apply damage ratio to home’s replacement cost

5. Apply insurance contract terms

6. Add up insured losses to get portfolio losses

7. Repeat steps 1-6 thousands of times

Average Annual Loss

Estimate of expected yearly loss

• Could be for a property, portfolio, business line, etc.

Exceedance Probability Curve

Likelihood that losses will exceed a certain amount in a given time

• Cat model output for a portfolio

Types on the Exceedance Probability Curve

• Occurrence

• Aggregate

Occurrence Exceedance Probability

Loss curve per event. Some reinsurance is on an occurrence basis

Aggregate Exceedance Probability

Accounts for the possibility of several events in the same year

Probable Maximum Loss

Size of loss at specific exceedance probability

• represents a specific point on the exceedance curve

• used by insurers, regulators, and credit rating agencies

Return Period

Probability of a certain severity disaster

• P(disaster) = 1/return period

Wildfire Hazard Module

Fuel Model

• Vegetation (e.g., grass or trees)

• Age (e.g., more dead trees in older forest)

• Moisture encounter (based on rain, temp)

Ignition Likelihood

• Natural (e.g., lightning)

• Humans (e.g., camp fire, power lines)

Fire Spread Simulation

• Topography (fire spreads faster uphill)

• Weather

• Branding/Spotting: modeling how embers build and then spread to new locations

Hurricane vs Wildfire Hazard

Hurricane

• Path based on atmospheric steering

• decay: smooth, windspeeds smoothly decrease from eye of storm

Wildfire

• path depends on fuel

• decay: extreme, uneven

Wildfire Vulnerability Module

Structure Hardening

• Roof material

• vents

• siding

Defensible Space

• Clearing vegetation away from home is crucial

Development Factors

Wildlife Urban Interface (WUI)

natural, undeveloped areas meet human development

Urban Configuration

Spread of a fire in a neighborhood, homes become fuel