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

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

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

7. .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

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

11. Figure 4.5: One Factor State Space Tree Diagram

13. 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

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

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

20. 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

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

22. 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)

25. 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.

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

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