Casualty Actuarial Society Dynamic Financial Analysis 1998 Special Interest Seminar Basic Track - Session 4 A Basic Model for DFA Stephen P. D

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Casualty Actuarial Society Dynamic Financial
Analysis1998 Special Interest SeminarBasic
Track - Session 4A Basic Model for DFAStephen
P. DArcyUniversity of Illinois at
Urbana-ChampaignCharles C. EmmaMiller, Rapp,
Herbers Terry, Inc.
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Overview

• Description of Model - me
• Demonstration of Model - Chuck
• Use of Model - You (the audience)

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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

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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

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Key Risks for U.S. Property-Liability Insurers

• Underwriting
• Aging Phenomenon
• Jurisdictional Risk
• Loss Development
• Catastrophes
• Investment
• Asset Value
• Investment Income

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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

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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

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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

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Primary Risks Reflected

• Pricing
• Loss reserve development
• Catastrophe
• Investment

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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

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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

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Underwriting Cycle

• Four phases
• Immature hard Mature hard
• Immature soft Mature soft
• Each phase has different supply-demand function
• Probability distribution for moving to different
  phase next period

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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

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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

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Investment Risk

• Bonds
• Market values calculated based on term structure
  of interest rates
• Includes provision for default
• Equities - 3 step approach
• 1 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 rates
• 3 Final return includes random component (mean
  0, standard deviation 15)

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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 _at_Risk in order to run full
  version of the model

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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