Transcript Lecture 2

Lecture 2
The Use of Interest Rate Models
in Insurance
Ratemaking
DFA
Asset-Liability Management
Life insurance policies
Minimum guarantee contracts
Credited interest rate
Lapse rates
Investment valuation
Ratemaking
• Expected investment returns
– Risk free interest rate
• Discounting cash flows
– Term structure of interest rates
• Based on U.S. government bonds
• Based on STRIPS
DFA
• Simulating potential future developments
for underwriting and investments
• Key element is an interest rate generator
• Examines the evolution of the term
structure of interest rates
• Other factors related to interest rates
– Inflation
– Equity investment performance
Interest Rate Generator in the Public
Access Model - 1998
Cox-Ingersoll-Ross one factor model
r  a(b  r )t  s r 
r  short term interest rate
a  speed of reversion  .2339
b  long run mean interest rate  .05
s  volatility of interest rate process  .0854
r  annual change in r
t  one year
  random sampling from a standard normal distributi on
Asset-Liability Management
• Assumptions under Macaulay or modified
duration
– Yield curve is flat
– Parallel shift in yield curve
– Cash flows do not change as interest rates change
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Effective duration relaxes these assumptions
Requires interest rate model
Effective duration of assets
Effective duration of liabilities
Minimum Guarantee Contracts
• Life insurance policies often provide a
minimum interest rate guarantee
• Essentially an interest rate floor
• Valuing an interest rate floor requires an
assumption about possible interest rate
movements
Other Life Insurance Issues
• Lapse rates
– Likely to be a function of interest rates
– Path dependent factor
• Interest rate crediting approach
– What interest rate will an insurer credit on cash
value policies
– Depends on interest rate movements
Investment Valuation
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Callable bonds
Mortgage backed securities
Options on bonds
Interest rate options
Interest rate caps/floors
Swaps
Swaptions
Conclusion
• Actuaries use interest rates for a variety of
situations
• Different interest rate models may be
appropriate depending on the application