Catastrophe Modeling Session Reinsurance Boot Camp August 10, 2009 Catastrophe Modeling Session Reinsurance Boot Camp Intro: -who I am -work I for -what I do Aleeza Cooperman Serafin Guy Carpenter & Co, LLC

The Black Box Why are you here: to better understand the concept, process and components of cat modeling and break down common perceptions of models as “the black box”. Another common perception of cat modeling….

Cat Modeling Personal anecdote

Presentation Outline What are catastrophe models? How do catastrophe models work? Cat modeling process Understanding model output How is model output used? Questions - throughout We’ll save some time for questions at the end but please feel free to ask questions throughout the presentation.

What are Cat Models?

Catastrophe Modeling and Model Vendors What? A tool that quantifies risk How? Examines insured values that are exposed to catastrophic perils such as hurricanes, earthquakes and terrorism Why? Aids management decision making on Pricing and underwriting Reinsurance buying Rating Agencies Portfolio management One way your management values risk

Catastrophe Model Vendors Founded at Stanford University in 1988 World's leading provider of products and services for the quantification and management of catastrophe risks. Grew in the 1990s, expanding services and perils covered. Founded in 1987 Pioneered the probabilistic catastrophe modeling technology Founded in 1980s One of first catastrophe models in industry Popularized after Hurricane Andrew as w way to measure risk using probabilistic software. Other models Most large reinsurers and other risk management companies have developed their own in-house models

Modeled Perils Hurricane Wind and rain Demand Surge (Loss Amplification) and Storm Surge Earthquake Shake Fire Following Demand Surge and Sprinkler Leakage Other wind Winter storm Terrorism Flood (Europe) Wildfire Define demand surge and storm surge Define Fire Following Terrorism popularized after 911

Modeling using a single discrete event Types of Models Deterministic Model Modeling using a single discrete event The event is assumed to happen without regard to probability Commonly seen as recreations of historic events or single- hypothetical analysis Probabilistic Model Uses a series of simulated events and accounts for the probability of those events over time Deterministic models: Scenario Approach- very limited application for Reinsurance buying decisions or pricing Probabilistic Models: -OEP: Occurrence Exceeding Probabilty is the Probability that any one occurrence within a certain year will be greater than a certain amount. -AEP: Annual Exceeding Probability: the probability of the sum of all losses from all events in one year. -PML: Probable Maximum Loss- subjective; The exact return period associated with a PML can vary based on the Company’s policies, objectives and Risk Aversion. Can be 100 year losses 250 year losses etc.

Modeled Lines of Business Personal lines property Commercial lines property Industrial property Builders Risk Marine Auto physical damage (Personal Auto) Workers compensation Lives at risk – Accident and Health

Modeled Coverages Building/Vessel/Vehicle Other structures Contents Stock Machinery Inland marine Marine Time Element Business Interruption Loss of Use Head Count Payroll

Catastrophe Modeling Terminology FTP Site – used to transfer files to clients & markets Transmittal Document – includes instructions for accessing the FTP site, lists what files are posted and explains what’s in them EDM – RMS-specific database containing exposures RDM – RMS-specific database containing analysis results CEDE – AIR-specific database containing exposures CLF – AIR-specific file containing detailed analysis results. Can be loaded into CATRADER in order to apply cat treaties. Unicede – Text file containing aggregate (by county) exposure information by line of business, includes TIVs by county, no individual location detail. Used in AIR CATRADER (can be used in RMS) to perform aggregate analysis. Post Import Summary (PISR) – RMS report summarizing exposures in a portfolio (TIV, count, geocoding, etc.) Read over on your own time

How do Cat Models work? Understanding the Black Box

Portfolio Definition Hazard Module Engineering Module Financial Module The Four Catastrophe Model Components The Black Box Insurer Location and Policy Inputs 1 Portfolio Definition Defines the Event Hazard Module 2 Vulnerability of the Structure Engineering Module 3 Loss Calculation 4 Financial Module

Module 1 – Portfolio Definition Inputs 2 Hazard 3 Engineering 4 Financial Formatted exposure data Coverages Terms Risk characteristics Reinsurance Spatial Lookups Geocoding Hazard Hurricane: Distance to Coast, Elevation Earthquake: Soil type

Module 1 – Portfolio Definition Data Quality 2 Hazard 3 Engineering Completeness Correctness Construction, occupancy, etc Location information Values Valuation date Current Reflecting growth or reduction Sources of uncertainty Entry errors Old records Miscoding 4 Financial Is the data Complete? Are all risk included in the data set? Is the data Correct? Is it coded correctly to reflect all risk characteristics Address information accurate for highest possible level of geocoding Limits and deductibles appropriate for the peril being modeled? Shortfall due to Insurance To Value?

Module 1 – Portfolio Definition Geocoding 2 Hazard 3 Engineering 4 Financial Individual risk locations 2 1 3 Geocoding – geographic recognition 4

1 Portfolio Definition Module 2 – Hazard 2 Hazard 3 Engineering Generates the physical disturbance that is produced by an event Hurricane: Site Wind Speed Earthquake: Ground Motion Tornado/ Hail: Event Intensity 4 Financial Requirements Geocoding: latitude and longitude coordinates Based on address information Geospatial information: environmental and/or physical factors that can influence an event’s intensity at the site Soil conditions Topography and surface roughness Adjacent buildings Important client data element for Hazard Component is physical location of risks in the portfolio. Ideal is latitude and longitude. Next best is street address. Estimates physical damage to structures and contents Takes physical intensity field, along with site specific information pertaining to all structures in the insurance inventory, and calculates damage rates for each structure and coverage type Should account for initial quality of construction as well as the age and maintenance of the building Need different damage functions for buildings, contents and time element Models vary on: Classifications of structures Functional forms of vulnerability curves Distributions around mean damage Correlations between damages to similar constructions at neighboring sites

Module 2 – Hazard Definition Hurricane Example 1 Portfolio Definition Module 2 – Hazard Definition Hurricane Example 2 Hazard 3 Engineering 4 Financial 18

Module 2 – Hazard Definition Hurricane Example - Stochastic Database 1 Portfolio Definition Module 2 – Hazard Definition Hurricane Example - Stochastic Database 2 Hazard 3 Engineering Thousands of hypothetical events 4 Financial Windstorm Parameters Central Pressure Radius to Max. Wind Translational Speed Wind Profile Fill Rate Terrain, etc.

Module 2 – Hazard Definition Hurricane Example - Event Rates 1 Portfolio Definition Module 2 – Hazard Definition Hurricane Example - Event Rates 2 Hazard 3 Engineering Each stochastic event is assigned a rate – an annual frequency 4 Financial Last 100 years of historical data averages about 2.4 landfalling events per year Traditional event probabilities distributed among thousands of storms – why not just use historical data? - Relatively few historical events are insufficient to predict the future

Module 2 – Hazard Definition Hurricane Example - Event Rates 1 Portfolio Definition Module 2 – Hazard Definition Hurricane Example - Event Rates 2 Hazard 3 Engineering Near-term hurricane frequency Five year view (RMS) More than three landfalling events per year 4 Financial After the frequency of landfalling storms in 2004 and 2005, the modeling firms (particularly RMS), released new event probabilities that reflected a nearer term view of frequency on 5 year cycle of landfall probabilities.

Compute wind speed at each risk location 1 Portfolio Definition Module 2 – Hazard Definition Hurricane Example - Calculate Site Windspeed 2 Hazard 3 Engineering 4 Financial Path 2 Distance (d) Compute wind speed at each risk location Vw = f(Pc, d, regional topography) 1 3 4 Hurricane

Module 2 – Hazard Definition Earthquake Example - Site Ground Motion 1 Portfolio Definition Module 2 – Hazard Definition Earthquake Example - Site Ground Motion 2 Hazard 3 Engineering 4 Financial Frequency of earthquakes Fault location Fault geometry: length depth strike angle dip angle Magnitude-recurrence Soil type Epicenter Rupture length Fault

Module 2 – Hazard Definition Limitations 1 Portfolio Definition Module 2 – Hazard Definition Limitations 2 Hazard Major sources of uncertainty: Limited historical data on events Unknown atmospheric elements may not be recognized e.g. Hurricane cycles 3 Engineering 4 Financial

Module 3 – Vulnerability Definition 1 Portfolio Definition Module 3 – Vulnerability Definition 2 Hazard 3 Engineering Data Required: Value What is the value of the insured property? Occupancy How is the property used? Residential Single or Multi-Family Commercial Mercantile or Industrial Construction How is the property constructed? Frame, Masonry, Metal, etc. Lowrise or Highrise Age When was the property built? What building codes apply? 4 Financial Important client data elements for vulnerability component are value of risk; construction; occupancy; year built; number of stories.

Module 3 – Vulnerability 1 Portfolio Definition Module 3 – Vulnerability 2 Hazard 3 Engineering Building Damageability 0% 20% 40% 60% 80% 100% 70 90 110 130 150 Wind Speed Damage Const 1 Const 2 Const 3 4 Financial Frame Construction 50% 1 4 Damaged Properties Hurricane Damage Rates are for illustration only and are not selected from any particular model

Module 3 – Vulnerability Limitations 1 Portfolio Definition Module 3 – Vulnerability Limitations 2 Hazard 3 Engineering Major sources of uncertainty: Limited claims data Improper coding of risk characteristics Lack of understanding of structural behavior under severe loads 4 Financial Limited claims data on catastrophic events

Decreasing loss levels 1 Portfolio Definition Module 4 –Financial Perspectives 2 Hazard 3 Engineering Calculates insured losses given the damage level and user risk inputs 4 Financial Evaluates multiple financial perspectives Ground up: damage prior to coverage limits and deductibles Gross: loss after deductibles, limits, attachment points Net: loss after treaty cessions, facultative, etc. Decreasing loss levels Evaluates insured loss given structural and values as well as the applicable insurance and reinsurance structures Important client data elements for financial component are limits, deductibles, reinsurance. Damage: Any economic loss or destruction caused by an earthquake, windstorm, or other peril. Ground Up Loss: amount of loss occurring to an insured and subject to the insured's insurance policy, beginning with the first dollar of loss and prior to the application to the deductible or deduction, if any, required by the policy. Gross Loss: The amount of a ceding company's loss irrespective of any reinsurance recoveries due. It is calculated by taking the ground-up loss less any deductibles. Net Loss: The amount of loss which an insurer keeps for its own account and does not pass on to another insurer (or reinsurer).

Module 4 – Financial Perspectives Limitations 1 Portfolio Definition Module 4 – Financial Perspectives Limitations 2 Hazard 3 Engineering Major sources of uncertainty: Limits versus Value at Risk Insurance and reinsurance structures are applied to loss distribution differently: Site-level loss Policy-level loss 4 Financial Portfolio exposure data is interpreted differently – limis vs value at risk

Catastrophe Modeling Process 30

The Catastrophe Modeling Process Overview Determine project scope Gather relevant data Evaluate, verify and format data Data quality checklist Data assumptions document Import Run the model Review the output Extract detailed losses Present results Post analysis portfolio management Most time consuming is evaluating data and post analysis works. Value added.

Understanding Model Output

Model Output Terminology Average Annual Loss (aka Pure Premium, aka Expected Loss): Long term average loss expected in any one year OEP - Occurrence Exceeding Probability: Probability that a single occurrence will exceed a certain threshold AEP - Aggregate Exceeding Probability: Probability that one or more occurrences will combine in a year to exceed the threshold. Return Period: Level of loss and the expected amount of time between recurrences. Critical Prob. Return Period AEP Loss OEP Loss 0.10% 1,000 160 147 0.20% 500 144 134 0.40% 250 126 118 0.50% 200 120 112 1.00% 100 97 90 Pure Premium 8 Standard Deviation 18 AAL: Represents the loss cost or pure premium for the book of business for the peril being modeled. EP (Exceeding Probability): The probability of exceeding specified loss thresholds. RP: e.g. a $100 million loss in this territory has a return period of 50 years

Model Output The Event Loss Table Sample Event Output: The data underlying any cat model output is the event loss table Consists of each event simulated along with the resulting loss

Model Output The Event Loss Table – determining PMLs - OEP Different levels of severity based on company appetite Common to monitor portfolios “1-100 year” loss level In the example, “100 year loss level” is saying that there is a 1% chance that there will be a single occurrence of $2.5 billion or greater in any given year The term “PML” can mean different levels of severity to different companies Many companies monitor and manage their windstorm portfolios to a “1-100 year” loss level. In this example the “100 year loss level” is $2.5 billion. What this is saying is that there is a 1% chance that there will be a single occurrence of $2.5 billion or greater in any given year.

Model Output The Event Loss Table – AEP AEP reflects year’s worth of events rather than a single event i.e. “there is an X% chance that there will be a total of $XX billion or greater losses in total in any given year” While our previous example concluded that there is “a 1% chance that there will be a single occurrence of $2.5billion or greater in any given year.”, the AEP reflects years i.e. “there is an X% chance that there will be a total of $XX billion or greater losses in total in any given year” Reflects a year’s worth of events rather than a single event.

Model Output The Event Loss Table – determining average annual loss Average annual loss is the weighted average of the event losses and their likelihood of occurring A company should collect at least $91million in CAT premium to cover its average annual expected loss for the peril and portfolio being modeled Sum Product of Event Probability and Loss = $91M The event frequency can be used to determine the average annual loss. The average annual loss is simply the weighted average of the event losses and their likelihood of occurring. In this case the weighted average is around $91million This implies that for this portfolio, a company should collect at least $91million in CAT premium to cover its average annual expected loss for the peril and portfolio being modeled

Average Annual Loss Properties AAL used to determine loss drivers: Territory Zip code County State Rating territory Source Risk location Policy Product line Producer Characteristics Construction class Occupancy AAL is always additive

Understanding Model Uncertainty Primary Uncertainty - Uncertainty in the occurrence of an event Secondary Uncertainty - Uncertainty in the loss level Range of possible loss levels “Inherent” uncertainty Uncertainty in the vulnerability (damage) driven by: Insufficient historical data (infrequent) Poor quality data Translating data from one region to the next (San Francisco 1906)

How is Catastrophe Model Output Used? 40

How Is Catastrophe Model Output Used? Portfolio Management Monitor Exposure Growth / Geographic Spread Evaluate Impact of Portfolio Expansion / Contraction Underwriting on New/Renewal Books of Business Evaluate Reinsurance Needs Evaluate Reinsurance Program Effectiveness Pricing Insurance Policies Reinsurance Treaties Rating Agency (e.g. A.M. Best) Requirements Real-time Event Analysis

Catastrophe Model Output Portfolio Management - Monitoring Loss/Premium Ratio in RML Risk Managed Layer (RML): a range of loss levels from the EP Curve that the company wants to manage Excluding 685 policies from portfolio produces an optimal RML/Premium ratio

Catastrophe Model Output Gradient Map – Zip Code Index Index Range # ZipCodes Identifies how geographic areas are correlated to show growth/reduction opportunities Reveals the most critical geographic areas contributing loss to the RML Shows relative contribution to RML losses by Zip Code. Top 10 ZipCodes: ZipCode Index Measures the marginal impact of loss to the RML when adding a notional risk in a particular location RML loss is conditional, derived from the weighted average loss to the layer

Catastrophe Model Output Real-time event monitoring Wildfire Hurricane Severe Weather Flood Earthquake Tornado/Hail 44

Conclusions Catastrophe Model Benefits and Shortcomings Values Valuable risk measure Encourage better data tracking Create marketplace advantages Innovation Dangers Over-reliance Misuse Errors Extremely valuable as one of many information inputs - Models have improved risk quantification significantly – exposure and loss Extremely dangerous if used as the only information input Models can mislead if users do not understand shortcomings Applications can create significant marketplace advantages Inappropriate applications can create hidden dangers Models continue the tradition of innovation and progress Models are “not" perfect and need to improve

Questions? Why are you here: to better understand the concept, process and components of cat modeling and break down common perceptions of models as “the black box”.

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