A comparison of actuarial financial scenario generators cas soa vs aaa rbc c3
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A Comparison of Actuarial Financial Scenario Generators: CAS/SOA vs. AAA RBC C3. Kevin Ahlgrim, ASA, PhD, Illinois State University Steve D’Arcy, FCAS, PhD, University of Illinois Rick Gorvett, FCAS, ARM, FRM, PhD, University of Illinois 14th AFIR Colloquium Boston November 2004.

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A Comparison of Actuarial Financial Scenario Generators: CAS/SOA vs. AAA RBC C3

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A comparison of actuarial financial scenario generators cas soa vs aaa rbc c3

A Comparison of Actuarial Financial Scenario Generators:CAS/SOA vs.AAA RBC C3

Kevin Ahlgrim, ASA, PhD, Illinois State University

Steve D’Arcy, FCAS, PhD, University of Illinois

Rick Gorvett, FCAS, ARM, FRM, PhD, University of Illinois

14th AFIR Colloquium

Boston

November 2004


Outline of presentation

Outline of Presentation

  • Motivation for Financial Scenario Generators

  • Description of economic variables

  • Structure of each model

  • Comparison of output

  • Conclusion


Motivation

CAS/SOA

Motivation

  • Provide public access model for use in

    • DFA

    • Regulatory

    • Rating agency

    • Internal management tests

  • Conduct literature review

    • From finance, economics, and actuarial science

  • Develop financial scenario generator model

    • Generate scenarios over a 50 year time horizon

  • Facilitate use of model

    http://casact.org/research/econ/


Relationships among modeled economic series

CAS/SOA

Relationships Among Modeled Economic Series

Inflation

Real Interest Rates

Unemployment

Nominal Interest

Real Estate

Stock Dividends

Lg. Stock Returns

Sm. Stock Returns


Inflation q

CAS/SOA

Inflation (q)

  • Modeled as an Ornstein-Uhlenbeck process

    • One-factor, mean-reverting

      dqt = kq(mq – qt) dt + sq dBq


A comparison of actuarial financial scenario generators cas soa vs aaa rbc c3

CAS/SOA

Real Interest Rates (r)

  • Two-factor Vasicek term structure model

  • Short-term rate (r) and long-term mean (l) are both stochastic variables

    drt = kr (lt – rt) dt + sr dBr

    dlt = kl (ml – lt) dt + sl dBl


Nominal interest rates

CAS/SOA

Nominal Interest Rates

  • Combines inflation and real interest rates

    i = {(1+q) x (1+r)} - 1

    where i = nominal interest rate

    q = inflation

    r = real interest rate

  • Restriction against negative interest rates


Motivation1

AAA

Motivation

  • Provide guidance for setting Risk-Based Capital (RBC) requirements for variable products with guarantees

  • Focus is on

    • Interest rate risk

    • Equity risk

  • Recommend use of models

  • Also provide 10,000 Pre-packaged scenarios

  • Available at:

    http://www.actuary.org/life/phase2.htm


Relationships among modeled economic series1

AAA

Relationships Among Modeled Economic Series

10-year

U.S. Treasury yields

3-month

U.S. Treasury yields

U.S. Long Term

Corporate Bonds

U.S. Intermediate Term

Government Bonds

7-year

U.S. Treasury yields

Money Market

Diversified Fixed Income

Diversified U.S. Equity

Diversified

International Equity

Risk-free rate r = 5.5% (effective) for all markets,

roughly equal to the average 6-month U.S. Treasury yield

over the past 50 years

Diversified Balanced

Intermediate Risk Equity

Aggressive or

Specialized Equity


Nominal interest rates three processes for three time scales

AAA

Nominal Interest Rates Three Processes For Three Time Scales

  • Long term, 10-Year Treasury Yield

  • Short term, 3-Month Treasury Yield

  • Medium-term, 7 year Treasury Yield


Properties of the interest rate model

AAA

Properties of the Interest Rate Model

  • Where

  • Z1, Z2, Z3 are normal distributions with mean 0;

  • α, Φ are mean-reversion strengths;

  • λ, τ, ξt are regression parameters.

  • Lognormal distribution at time t

  • Avoid negative nominal interest rates.

  • Make the Kurtosis positive all the time

  • Funnel of Doubt Graphs shift to the upper side.

  • Variance increases faster as t increases


A comparison of actuarial financial scenario generators cas soa vs aaa rbc c3

CAS/SOA

AAA RBC C3

f (t, i)

f (t, i)

i

i

0

0

t

t


Funnel of doubt graphs 3 month nominal interest rates u s treasury bills

Funnel of Doubt Graphs3 Month Nominal Interest Rates (U. S. Treasury Bills)


Histogram of 3 month nominal interest rates model values and actual data 01 34 05 04

Histogram of 3 Month Nominal Interest RatesModel Values and Actual Data (01/34-05-04)


Funnel of doubt graphs 10 year nominal interest rates u s treasury bonds

Funnel of Doubt Graphs 10 Year Nominal Interest Rates (U. S. Treasury Bonds)


Histogram of 10 year nominal interest rates model values and actual data 04 53 05 04

Histogram of 10 Year Nominal Interest RatesModel Values and Actual Data (04/53-05/04)


Equity returns

CAS/SOA

AAA

Equity Returns

  • Both models use Regime Switching Lognormal Model with monthly data and 2 regimes (RSLN2)

  • Model equity returns as an excess return (xt) over the nominal interest rate

    st = it + xt

  • Two Regimes

    • High return, low volatility regime

    • Low return, high volatility regime

  • Six parametersμ1, σ1; μ2, σ2; P12, P21

    Within Volatility Regimes μ1, σ1; μ2, σ2

    Transition Matrix


Parameter differences

Parameter Differences

  • Data Sources for Maximum likelihood estimates

  • Parameter Differences (AAA Pre-packaged scenarios)


Funnel of doubt graphs large stock return us equity

Funnel of Doubt Graphs Large Stock Return (US Equity)


Histogram of large stock return model values and actual data 1872 2004

Histogram of Large Stock ReturnModel Values and Actual Data (1872-2004)


Funnel of doubt graphs small stock return intermediate risk equity

Funnel of Doubt Graphs Small Stock Return (Intermediate Risk Equity)


Histogram of small stock return model values and actual data 1926 2003

Histogram of Small Stock ReturnModel Values and Actual Data (1926-2003)


Conclusion

Conclusion

  • Financial models are assuming greater importance for actuaries

  • Actuaries need to understand how to apply these models

  • CAS/SOA model generates greater variance

  • AAA RBC C3 model provides returns on more types of investments

  • Try out these models

  • Suggest additions or improvements

  • Questions?


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