Catastrophe Modeling and Actuarial Applications Jonathan Evans FCAS

Catastrophe Modeling and Actuarial Applications Jonathan Evans, FCAS, MAAA Actuary Iowa Actuarial Club February 23, 2007 National Council on Compensation Insurance, Inc. 1

What Are Catastrophes ? • Single events that produce such a large number of claims – that it is very highly improbable such an event would actually occur (assuming risk exposures are independent) • Usually resulting from a special type of peril: hurricane, earthquake, terrorist attack, asbestos, etc. • More rarely, sometimes extremely large single claims are called “catastrophes” 2 Source: 2007 National Council on Compensation Insurance, Inc.

What Applications Make Actuaries Care About Catastrophes ? • Ratemaking for policies exposed to catastrophes, such as homeowners in Florida • Reserving for long tail catastrophic losses, such as asbestos in general liability • Analyses of reinsurance programs • Analyses of insurer catastrophe risk, such as catastrophic return period loss estimates 3 Source: 2007 National Council on Compensation Insurance, Inc.

Why Model Catastrophes ? • For non-catastrophic perils (such as an automobile accident that independently affects risk exposures or only a few risk exposures simultaneously) it is easy to gather a credible volume of experience • For catastrophic perils (such as hurricanes) even nationwide experience over many years may not be credible 4 Source: 2007 National Council on Compensation Insurance, Inc.

Catastrophic Versus Non-Catastrophic Experience 5 Source: 2007 National Council on Compensation Insurance, Inc.

Who Builds Catastrophe Models ? • Prior to the 1980 s most models were built by insurers for underwriting purposes • From the 1980 s to present most models were built by specialized modeling firms and sold as software, that allows users to input exposure information • Event databases and estimated frequencies are often prepared by scientists: geophysical for earthquake, atmospheric for hurricanes, social/behavioral for terrorism, etc. • Loss functions are often determined by engineers • Actuaries are mostly end users of models; except for reserving models for mass liability, such as asbestos/environmental, where actuaries have compiled databases and built their own models 6 Source: 2007 National Council on Compensation Insurance, Inc.

How Are Catastrophes Modeled ? Catastrophe models generally consist of: 1. A database of individual exposures, such as homeowners policies by location and insured value 2. A database of potential catastrophic events, such as hurricanes by landfall location and wind speed 3. A loss function that uses as input the characteristics of a single exposure from #1 and a single catastrophic event from #2 4. Estimates for the frequency of each catastrophic event in #2 7 Source: 2007 National Council on Compensation Insurance, Inc.

Simplified Hypothetical Example Of A Catastrophe Model 1 2 3 4 8 Source: 2007 National Council on Compensation Insurance, Inc.

Example Of Calculating Loss For Policy A and Event U the loss is calculated as: 9 Source: 2007 National Council on Compensation Insurance, Inc.

Example Model Loss Output 10 Source: 2007 National Council on Compensation Insurance, Inc.

Example Ratemaking Application For Policy A 11 Source: 2007 National Council on Compensation Insurance, Inc.

Example Portfolio Risk Application 12 Source: 2007 National Council on Compensation Insurance, Inc.

Questions 13 Source: 2007 National Council on Compensation Insurance, Inc.

Further Reading -Bouska, Amy, “From Disability Income to Mega-Risks: Policy-Event Based Loss Estimation”, CAS Forum, Summer 1996. -Grossi, Patricia and Kunreuther, Howard, Catastrophe Modeling: A New Approach to Managing Risk (Huebner International Series on Risk, Insurance and Economic Security), Springer, 2005. -Kozlowski, Ronald T. and Mathewson, Stuart B. , “Measuring and Managing Catastrophic Risk”, CAS Discussion Paper Program, 1995. -Woo, Gordon, The Mathematics of Natural Catastrophes, World Scientific Publishing Company, 1999. 14 Source: 2007 National Council on Compensation Insurance, Inc.