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

200 MODELING FINANCIAL SCENARIOSUnfortunately, the parameters for the real interest rate processshown above generate a distribution that severely restrictsthe range of potential future nominal interest rates. For example,using the regression results from Formulas (3.13) and (3.14), the1st percentile of the distribution for the 20-year nominal rate is5.9% and the 99th percentile is 8.2%. There are several candidatesfor problems with real interest rates that may lead to thisseemingly unrealistic distribution of future nominal rates: (1)the use of ex post real interest rate measures is unsuitable, (2)because of potential errors in monthly reporting of CPI mentionedabove, monthly measurements of real interest rates produceself-correcting errors that exaggerate mean reversion speed,or (3) the time period used to measure real interest rates is tooshort.As a result, the parameters for real interest rates were alteredto allow nominal interest rates to better reflect historical volatility.Specifically, mean reversion speed was dramatically reduced.Given that mean reversion speed and volatility work together toaffect the range of interest rate projections, volatility was alsoreduced. The following parameters are used as the “base case”in the model. These parameters are in line with what was usedin Hull [27].·r ¹ r ¾ r·l ¾ l1.0 2.8% 1.00% 0.1 1.65%An important consideration in the model is the correlationbetween interest rates and inflation. Risa [36] reviews the literatureon the relationship between inflation and interest rates.Pennacchi [33] finds evidence that the instantaneous real interestrates and expected inflation are significantly negatively correlated.Ang and Bekaert [5] develop a regime-switching modelfor inflation and real interest rates. They find that inflation is