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

MODELING FINANCIAL SCENARIOS 215strating that, over longer time horizons, the (geometric) averagerate of inflation is less variable.The funnel of doubt graphs of one-month, one-year, and 10-year inflation rates are shown in Figures 4 through 6. The uncertaintyof the 10-year inflation rate is much smaller than it isfor one-month and one-year rates, reflecting the strength of themean reversion term for this single-factor model. Although inflationvaries widely over shorter time horizons, in this model thelong-term inflation rate is much less variable. This pattern can bealtered by increasing the volatility of the inflation process (¾ q )or reducing the mean reversion speed (·q).The histograms for the one-year projected inflation rates andof actual one-year inflation rates from 1913 through 2003 (fromJanuary to January) are shown on Figure 7. It is readily apparentthat the modeled inflation rates generate a nice bell-shapedcurve, whereas the actual inflation rates are much less smooth.One reason for this difference is that the model results are basedon 5,000 iterations, while the actual data contain only 90 datapoints. More importantly, though, the projected values are derivedfrom a concise mathematical expression that will producea smooth distribution of results, but the actual inflation ratesdepend on the interactions of an almost unlimited number ofvariables. The key question is whether the model adequately expressesthe probability distribution of potential inflation rates.The actual inflation rates are more leptokurtic (fatter in the tailsthan a normal distribution) than the modeled values, but they reflectthe central portion of the graph fairly well. All of the largenegative inflation rates occurred prior to 1950. Many of the positiveoutliers are from years prior to 1980, when monetary policywas less focused on controlling inflation.Nominal Interest RatesNominal interest rates reflect the combination of the real interestrate and inflation. The mean values for one-month nominalinterest rates were 1.1% for the first month and 7.8% for the