1. 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

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