1. The document discusses various term structure models for interest rates, including Black-Scholes, Vasicek, Cox-Ingersoll-Ross (CIR), Hull-White, and Ho-Lee models. 2. A key concept is that term structure models describe the evolution of the entire yield curve over time, while short rate models only describe the probability distribution of interest rates at single points in time. 3. The models make different assumptions about the behavior of interest rates through time, such as mean-reversion or following stochastic processes, and can be used to price fixed income securities and derivatives.

1. Interest Rate Derivatives: Models of the Short Rate Chapter 28

4. Equilibrium Models

5. Mean Reversion (Figure 28.1, page 651) Interest rate HIGH interest rate has negative trend LOW interest rate has positive trend Reversion Level

6. Alternative Term Structures in Vasicek & CIR (Figure 28.2, page 652) Zero Rate Maturity Zero Rate Maturity Zero Rate Maturity

10. Initial Forward Curve Short Rate r r r r Time Diagrammatic Representation of Ho and Lee (Figure 28.3, page 655)

12. Diagrammatic Representation of Hull and White (Figure 28.4, page 656) Short Rate r r r r Time Forward Rate Curve

18. Alternative Branching Processes in a Trinomial Tree (Figure 28.7, page 661) (a) (b) (c)

22. The Initial Tree (Figure 28.8, page 663) Node A R 0.000% 1.732% 0.000% -1.732% 3.464% 1.732% 0.000% -1.732% -3.464% p u 0.1667 0.1217 0.1667 0.2217 0.8867 0.1217 0.1667 0.2217 0.0867 p m 0.6666 0.6566 0.6666 0.6566 0.0266 0.6566 0.6666 0.6566 0.0266 p d 0.1667 0.2217 0.1667 0.1217 0.0867 0.2217 0.1667 0.1217 0.8867 A B C D E F G H I B C D E F G H I

24. The Final Tree (Figure 28.9, Page 665) Node A B C D E F G H I R 3.824% 6.937% 5.205% 3.473% 9.716% 7.984% 6.252% 4.520% 2.788% p u 0.1667 0.1217 0.1667 0.2217 0.8867 0.1217 0.1667 0.2217 0.0867 p m 0.6666 0.6566 0.6666 0.6566 0.0266 0.6566 0.6666 0.6566 0.0266 p d 0.1667 0.2217 0.1667 0.1217 0.0867 0.2217 0.1667 0.1217 0.8867 A B C D E F G H I