Casualty Actuarial Society Dynamic Financial Analysis

1998 Special Interest Seminar

Basic Track - Session 4A Basic Model for DFA

Stephen P. D’ArcyUniversity of Illinois at Urbana-Champaign

Charles C. EmmaMiller, Rapp, Herbers & Terry, Inc.

Overview

1 Description of Model - me

2 Demonstration of Model - Chuck

3 Use 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 useableSimple 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

Investments Catastrophes

Underwriting Taxation

Interest rate generator Loss 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 ageRenewal patternsProjected growth ratesLoss development patternsLoss frequency and severityReinsurance program

Investment dataStatutory and market asset values by asset classMaturity and coupon rates for bondsBeta 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 specificRange of rate changes established

Narrower range in more restrictive states

Time lag for implementing rate changeLonger in more restrictive statesIncreases take longer to implement than decreases

Underwriting CycleFour phases

Immature hard Mature hardImmature soft Mature 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

BondsMarket values calculated based on term structure of interest ratesIncludes provision for default

Equities - 3 step approach1 Initial market return:

Short term interest rate + market risk premium of 8.5%2 Adjusted market return: Initial market return - 4 times change in short term rates3 Final return includes random component (mean = 0, standard

deviation = 15%)

Interest Rate Generator

Cox-Ingersoll-Ross one factor model

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How to Obtain this Model

Access the Miller, Rapp, Herbers & Terry, Inc. homepage (www.mrht.com)

Click on DFA Model to obtain DynaMo

You need to have Excel to run this model

You should have @Risk 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