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

212 MODELING FINANCIAL SCENARIOS1st—99th percentile range after 10 years is ¡5:1% to +9:7%,reflecting a similar distribution for the full year as was observedfor the monthly values. For the 10-year real interest rates, themean after the first projection month is 1.1%, and in the lastprojection month, the mean is 2.6%, reflecting the strength ofthe mean reversion over this long a period of time. The 1st—99thpercentile range after 10 years is ¡3:3% to +7:6%, reflecting themore compact distribution for long-term (10-year) real interestrates, compared to shorter time horizons.Figures 1 through 3 depict the funnel of doubt graphs ofone-month, one-year and 10-year real interest rates. All reflectthe same shape, although the scaling differs. The “kink” in theearly portion of the graph occurs because the first 12 points representmonthly intervals, which have small changes in values, andthe latter steps are larger intervals, which lead to correspondinglylarger changes. The level of uncertainty increases over the entire50-year time frame, but the shifts toward the end of the simulationperiod are less pronounced. This shape occurs because of thestructure and parameterization of the model. The uncertainty inherentin the real interest rate process generates the initial spreadof the distribution, but the impact of mean reversion offsets thistendency, keeping the “funnel of doubt” from expanding further.InflationThe next variable of interest is the inflation rate. As shown inTable 1, the mean value of the (annualized) one-month inflationrate is 2.3% after the first projection year and 4.8% after 50years. Note that the initial inflation rate (qinit1) is set at 1.0%and 4.8% is the long-term mean (qm2). The 1st—99th percentilerange after 10 years is ¡5:3% to +14:5%, which is wider than thedistribution for real interest rates since the mean reversion speedfor inflation is lower (0.4 compared to 1.0). Negative inflation(or deflation) is not objectionable since small negative monthlyvalues have occurred in recent years. Also, monthly inflationvalues in excess of 14.5% did occur during the 1970s.