PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

MODELING FINANCIAL SCENARIOS 199equation in stage 2, we first obtain fitted estimates for the longrate ˆl t , based on the parameter estimates from stage 1:Stage 1: l t+1 = ¯1 + ¯2l t + " 0 lt ,Stage 2: r t+1 = ® 1ˆlt + ® 2 r t + " 0 rt : (3.14)The resulting parameters were generated from the regression results.Real Interest Rate Process Estimated from 1982to 2001·r ¹ r ¾ r·l ¾ l6.1 2.8% 10.0% 5.1 10.0%These parameters indicate a very high level of volatility that istempered by strong levels of mean reversion. See the discussionof the nominal interest rates below for the parameters that areused in the simulation illustration in section five.Nominal Interest RatesFisher [20] provides a thorough presentation of the interactionof real interest rates and inflation and their effects on nominalinterest rates. He argues that nominal interest rates compensateinvestors not only for the time value of money but also for theerosion of purchasing power that results from inflation. In themodel presented here, the underlying movements in inflation andreal interest rates generate the process for nominal interest rates.If bonds are priced using expectations of inflation and real interestrates until the bond’s maturity, then nominal interest ratesare implied by combining the term structure of inflation and theterm structure of real interest rates. Therefore,P i (t,T)=P r (t,T) ¢ P q (t,T), (3.15)where i refers to nominal interest rates and the superscripts onthe bond prices correspond to the underlying stochastic variables.