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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

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

slide6

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
slide12

CAS/SOA

AAA RBC C3

f (t, i)

f (t, i)

i

i

0

0

t

t

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)
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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