Casualty Actuarial Society Dynamic Financial Analysis 1998 Special Interest Seminar Basic Track - Session 4 A Basic Model for DFA Stephen P. D’Arcy University of Illinois at Urbana-Champaign Charles C. Emma Miller, Rapp, Herbers & Terry, Inc.

Overview 1Description of Model - me 2Demonstration of Model - Chuck 3Use of Model - You (the audience)

Objectives of this DFA Model Develop a financial model for a U. S. property-liability insurer that is: Realistic enough to be useable Simple enough to be understood

Caveats Any model is a simplified version of reality This model deals with quantifiable risk only –Examples of excluded items: A line of business being socialized Management fraud Devastating meteor strike

Key Risks for U.S. Property- Liability Insurers Underwriting –Aging Phenomenon –Jurisdictional Risk –Loss Development Catastrophes Investment –Asset Value –Investment Income

Specifics Provisions of Model Six separate, but interrelated modules InvestmentsCatastrophes UnderwritingTaxation Interest rate generatorLoss reserve development Ten lines of business For each line of business –New business –1st renewals –2nd and subsequent renewals

What Does This Model Do? Simulates results for the next 5 years Generates financial statements Balance sheet Operating statement IRIS results Indicates expected values and distribution of results for any value selected

What Information is Required? Underwriting data Premiums and exposures, by line, state and age Renewal patterns Projected growth rates Loss development patterns Loss frequency and severity Reinsurance program Investment data Statutory and market asset values by asset class Maturity and coupon rates for bonds Beta for equity portfolio

Primary Risks Reflected Pricing Loss reserve development Catastrophe Investment

Components of Pricing Risk Random variation –Loss frequency and severity Inflation affects severity –Correlated with short term interest rates –Line of business specific Jurisdictional risk Underwriting cycle

Jurisdictional Risk State specific Range of rate changes established Narrower range in more restrictive states Time lag for implementing rate change Longer in more restrictive states Increases take longer to implement than decreases

Underwriting Cycle Four phases Immature hardMature hard Immature softMature soft Each phase has different supply-demand function Probability distribution for moving to different phase next period

Loss Development Risk Initial reserve levels based on actuarial analysis, not statement values Still subject to random variation Inflation also affects reserve development –Initial reserves reflect specific inflation rate –Changes in inflation rate affect development

Catastrophe Risk Poisson distribution for number of catastrophes Each catastrophe assigned to a geographic focal point Based on focal point, size of catastrophe is determined based on a lognormal distribution Contagion factor is used to distribute catastrophe to nearby states Losses distributed based on market share by state

Investment Risk Bonds Market values calculated based on term structure of interest rates Includes provision for default Equities - 3 step approach 1Initial market return: Short term interest rate + market risk premium of 8.5% 2Adjusted market return: Initial market return - 4 times change in short term rates 3Final return includes random component (mean = 0, standard deviation = 15%)

Interest Rate Generator Cox-Ingersoll-Ross one factor model

How to Obtain this Model Access the Miller, Rapp, Herbers & Terry, Inc. homepage ( Click on DFA Model to obtain DynaMo You need to have Excel to run this model You should in order to run full version of the model

How to Learn More about this Model CAS Limited Attendance Seminar on DFA October 1-2, 1998 Chicago, Illinois Explanation of types and history of DFA Discussion of common DFA issues Hands-on workshop using DynaMo Supervised use of model on participant provided data