Property liability insurance loss reserve ranges based on economic value
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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value PowerPoint PPT Presentation


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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value. Alfred Au and Liang Zhang. Overview. Background of research Methodologies Results Feedback. Background. Traditional loss reserving methods Nominal, undiscounted, for statutory requirements

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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value

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Property liability insurance loss reserve ranges based on economic value

Property-Liability Insurance Loss Reserve Ranges Based on Economic Value

Alfred Au and Liang Zhang


Overview

Overview

  • Background of research

  • Methodologies

  • Results

  • Feedback


Background

Background

  • Traditional loss reserving methods

    • Nominal, undiscounted, for statutory requirements

    • Impacts of inflation on traditional methods


Background1

Background

  • Recent Developments

    • ALM

    • FASB & IASC: “Fair Value”

    • CEA: Solvency II

    • S&P criticism


Trends in inflation

Trends in Inflation


Trends in inflation1

Trends in Inflation

  • Increasing oil prices

  • Depreciation of the dollar

  • Sub-prime mortgage, credit crunch

  • Fed lowered discount rate


Trends in inflation2

Trends in Inflation


Methodologies

Methodologies

  • Loss generation model

  • Loss decay model

  • Inflation model

    • Ornstein-Uhlenbeck

  • Real interest rate model

    • 2 factor Hull-White

  • Fixed claim model

    • D’Arcy & Gorvett


Loss generation model

Loss Generation Model

  • Nominal values:

    • Normally generated losses compounded by the nominal interest rate

  • Economic values:

    • Nominal losses discounted by the inflation rate


Fixed claim model

Fixed Claim Model


Fixed claim model1

Fixed Claim Model

  • Discrete approximation of continuous function

  • Impact of inflation on fixed claim model

  • ICA


Demonstration

Demonstration

  • Demo of model


Results

Results

  • Constant (Case A) vs. stochastic real interest rate (Case B)


Results1

Results

  • Taylor method (Case B) vs. Fixed claim model (Case C, base case)


Results2

Results

  • Impact of time step: monthly (Case D)


Results3

Results

  • Periods of high & volatile inflation (Case E)


Summary

Summary

  • Traditional loss reserving methods do not reflect the economic value of loss reserves

  • Economic value ranges are smaller than the nominal value ranges


Sensitivity analysis

Sensitivity Analysis

  • Sensitivity of results from adjusting the number of claims and number of simulations


Feedback

Feedback

  • Decoupling of nominal interest rate and inflation

    • Observed correlation was ~80-90%

    • From assignment 1…

    • Correlation between nominal interest rate and inflation was ~40%

    • New model controls for correlation


Feedback1

Feedback

  • ALM

    • Companies do not fully duration match their liabilities

    • Duration matching sacrifices yield

    • Impact of duration-mismatch on reserves

    • Outside scope of research


Feedback2

Feedback

  • Fisher Formula in a short-rate, stochastic modeling context

    • Found it to be appropriate

  • CPI as a proxy for claims inflation not appropriate

    • Masterson claims cost index


Feedback3

Feedback

  • Discrepancies in results with different time steps

    • Indication of improper discretization

    • Use monthly time step


Ongoing work

Ongoing work…

  • Incorporation of suggestions

    • Changes the results

    • Economic value CI becomes larger than nominal value CI

    • Changes supporting motivation of smaller reserve ranges


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