Lecture 2 The Use of Interest Rate Models in Insurance

1. Lecture 2The 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

2. 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

3. 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

4. Interest Rate Generator in the Public Access Model - 1998 Cox-Ingersoll-Ross one factor model

5. 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 • Effective duration relaxes these assumptions • Requires interest rate model • Effective duration of assets • Effective duration of liabilities

6. 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

7. 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

8. Investment Valuation • Callable bonds • Mortgage backed securities • Options on bonds • Interest rate options • Interest rate caps/floors • Swaps • Swaptions

9. Conclusion • Actuaries use interest rates for a variety of situations • Different interest rate models may be appropriate depending on the application