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

222 MODELING FINANCIAL SCENARIOSlevant. Therefore, three-month interest rates are used for in Figure11.) Figures 11 through 13 show the distribution of nominalinterest rates one year into the projection period.Significant differences exist between the modeled and historicaldistributions for interest rates. In Figure 11, the modeledthree-month nominal interest rates are 0.0% in almost 20% ofthe cases, whereas actual three-month interest rates have neverbeen below 0.5 percent (the column reflecting the 1% bin representsvalues between 0.5 and 1.5 percent). However, combiningthe model values for 0 and 1 percent indicates a total in line withactual values. In addition, the model distributions are smootherthan the actual values, which is natural since the model resultsare based on 5,000 iterations, whereas the actual results, eventhough derived from 845 (monthly) or 614 (one- and 10-year)observations, are not at nearly as smooth, indicating that the systemthat generates interest rates is not as straightforward as themodel.At first glance, modeled interest rates are generally lower thanthe historical rates. It is important to note that the modeled interestrates are influenced by the starting values for the initial realinterest rate (rinit1), the initial mean reversion level for the realinterest rate (rinit2), and the initial inflation level (qinit1), whichare lower than historical averages.The comparison between the 10-year modeled rates and the10-year historical rates, Figure 13, indicates a few differences.The modeled interest rates are more compact than actual 10-yearinterest rates have been. If the user feels that the variance of themodel values should be closer to the historical distribution, thenthe strength of the mean reversion factor in the interest rate modelcan be reduced, but this would increase the incidence of negativeinterest rates unless the user selects to avoid negative nominalinterest rates. The other significant difference is the skewness.The historical rates exhibit positive skewness, but the modeledrates have a slight negative skewness. Finally, the model rates