Interest Rate Dynamics, Derivatives Pricing, and Risk Management

1 A Three-Factor Model of the Term Structure of Interest Rates.- 1.1 Introduction.- 1.2 The Model.- 1.3 Benchmark Case.- 1.4 Green's Function.- 1.5 Derivatives Pricing.- 1.6 The Term Structure of Interest Rates.- 1.7 Expected Future Short Rate.- 1.8 Forward Rates.- 2 Pricing Interest Rate Derivatives.- 2.1 Introduction.- 2.2 Bond Options.- 2.3 Caps, Floors, and Collars.- 2.4 Futures Price and Forward Price.- 2.5 Swaps.- 2.6 Quality Delivery Options.- 2.7 Futures Options.- 2.8 American Options.- 3 Pricing Exotic Options.- 3.1 Introduction.- 3.2 Green's Function in the Presence of Boundaries.- 3.3 Derivatives with Payoffs at Random Times.- 3.4 Barrier Options.- 3.5 Lookback Options.- 3.6 Yield Options.- 4 Fitting to a Given Term Structure.- 4.1 Introduction.- 4.2 Merging to the Heath-Jarrow-Morton Framework.- 4.3 Whole-Yield Model.- 5 A Discrete-Time Version of the Model.- 5.1 Introduction.- 5.2 Construction of the Four-Dimensional Lattice.- 5.3 Applications.- 6 Estimation of the Model.- 6.1 Introduction.- 6.2 Kaiman Filter.- 6.3 Maximum Likelihood.- 6.4 Method of Moments.- 6.5 Simulated Moments.- 7 Managing Interest Rate Risk.- 7.1 Introduction.- 7.2 Generalized Duration and Convexity.- 7.3 Hedging Ratios.- 7.4 Hedging: General Approach.- 7.5 Hedging Yield Curve Risk.- 8 Extensions of the Model.- 8.1 Introduction.- 8.2 Extension I: Jumping Mean and Diffusing Volatility.- 8.3 Extension II: Jumping Mean and Jumping Volatility.- 9 Concluding Remarks.- A Proof of Lemma 1.- B Proof of Proposition 2.- C Proof of Lemma 2.- D Proof of Proposition 8.- E Integral Equation for Derivative Prices.