Figure 4.1: Forward Rate Curve Evolutions over January 1973 - March 1997

Figure 4.2: Histogram of Monthly Changes in Forward Rates from January 1973 - March 1997.

Figure 4.2 (continued): Histogram of Monthly Changes in Forward Rates from January 1973 - March 1997.

.05 1/2 Probability  1/2 - .05 .1 .1 1/2 .05 Probability  1/2 - 1/4 - .075 .05 .075 .1 .1 1/2 .025 Probability .05  3/8 - 1/8 - .075 .025 .05 .075 .1 .1 1/2 ... True Distribution  . . . .3 Figure 4.3: Example of A Binomial Approximation to the True Distribution--A Normal Distribution

Figure 4.4: An Example of a One-Factor State Space Tree Diagram

Figure 4.5: One Factor State Space Tree Diagram

time 1 2 3 4 Figure 4.6: An Example of a One-Factor Bond Price Curve Evolution. Actual Probabilities Along Each Branch of the Tree

Figure 4.7: One Factor Bond Price Curve Evolution time 1 2 Figure 4.7: One Factor Bond Price Curve Evolution

Figure 4.7: One Factor Bond Price Curve Evolution (continued) ... t t+1 -1  Figure 4.7: One Factor Bond Price Curve Evolution (continued)

Figure 4. 8: An Example of a One-Factor Forward Rate Curve Figure 4.8: An Example of a One-Factor Forward Rate Curve. Actual Probabilities Along Each Branch of the Tree

Figure 4.9: One Factor Forward Rate Curve Evolution time 1 Figure 4.9: One Factor Forward Rate Curve Evolution

Figure 4.9: One Factor Forward Rate Curve Evolution (continued) N/A t t+1 -1  Figure 4.9: One Factor Forward Rate Curve Evolution (continued)

Figure 4. 10: An Example of a One-Factor Spot Rate Process Figure 4.10: An Example of a One-Factor Spot Rate Process. Actual Probabilities Along Each Branch of the Tree.

Figure 4.11: One Factor Spot Rate Process time 1 2 Figure 4.11: One Factor Spot Rate Process

Figure 4.11: One Factor Spot Rate Process (continued) -2 -1 Figure 4.11: One Factor Spot Rate Process (continued)