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Intro; Preface; Chapter 1. The Processes of Short-Term Interest Rates and Their Probability Densities [1-4]; Chapter 2. The Term Structure of Interest Rates [5]; Chapter 3. The Vasiček Model [5, 6]; Chapter 4. The Cox-Ingersoll-Ross Model [7, 8]; Chapter 5. The Duffie-Kan One-Factor Model [9]; Chapter 6. The Duffie-Kan Two-Factor Model [10, 11]; Chapter 7. The Three-Factor Models [12]; Chapter 8. Another Term to Maturity Variable [13]; Chapter 9. The Nelson-Siegel-Svensson No-Arbitrage Yield Curve Models [14-16]; Chapter 10. Quadratic Models of Yield in a Risk-Neutral World [17, 18]
Chapter 11. Polynomial Models of Yield Term Structures [19, 20]Contents; 1 The Processes of Short-Term Interest Rates and Their Probability Densities; 1.1 Introduction; 1.2 The Vasiček Model; 1.3 The CIR Model; 1.4 The Duffie-Kan Model; 1.5 The Longstaff Model; 1.6 The Ahn-Gao Model; 1.7 The Brennan-Schwartz Model; 1.8 The BDT Model; 1.9 The Aït-Sahalia Model; 1.10 The CKLS Model; 1.11 The Unrestricted Model I; 1.12 The Unrestricted Model II; 1.13 The CEV Model; 1.14 The CIR (1980) Model; 1.15 The Merton Model; 1.16 The Dothan Model; 1.17 The GBM Model; 1.18 Conclusion; References
2 The Term Structure of Interest Rates2.1 Introduction; 2.2 The Term Structure Equation; 2.3 The Affine Models; 2.4 Conclusion; References; 3 The Vasiček Model; 3.1 Introduction; 3.2 The Vasiček Model and Its Generalization to the Multifactor Case; 3.3 Yield Curves in Two-Factor Vasiček Models; 3.4 Conclusion; References; 4 The Cox-Ingersoll-Ross Model; 4.1 Introduction; 4.2 The Single-Factor Cox-Ingersoll-Ross Model; 4.3 Generalization of the CIR Model for a Multifactorial Case; 4.4 The Two-Factor Cox-Ingersoll-Ross Model; 4.5 The Longstaff-Schwartz Model
4.6 Extension of the Longstaff-Schwartz Model4.7 Numerical Example; 4.8 Conclusion; References; 5 The Duffie-Kan One-Factor Model; 5.1 Introduction; 5.2 The Forward Curve and Yield Curve in the Duffie-Kan Model; 5.3 Properties of the Yield Curve and Forward Curves; 5.4 Conclusion; References; 6 The Duffie-Kan Two-Factor Models; 6.1 Introduction; 6.2 The Two-Factor Model "Rate and Its Local Average" (Small Parameter Method); 6.3 The Two-Factor Model "Rate and Its Instantaneous Variance" (Small Parameter Method); 6.4 The Two-Factor Model "Rate and Its Local Average" (Numerical Approach)
6.5 The Two-Factor Model "Rate and Its Instantaneous Variance" (Numerical Approach)6.6 Conclusion; References; 7 The Three Factor Models; 7.1 Introduction; 7.2 Stochastic Volatility of the Process of Level Local Mathematical Expectation; 7.3 The Process of Level Local Mathematical Expectation with Square Root; 7.4 The Gaussian Process of Level Local Mathematical Expectation; 7.5 Conclusion; References; 8 Another Version of the Term to Maturity Variable; 8.1 Introduction; 8.2 The One-Factor Duffie-Kan Model; 8.3 The Two-Factor Models; 8.4 The Three-Factor Models; 8.5 Conclusion; References
Chapter 11. Polynomial Models of Yield Term Structures [19, 20]Contents; 1 The Processes of Short-Term Interest Rates and Their Probability Densities; 1.1 Introduction; 1.2 The Vasiček Model; 1.3 The CIR Model; 1.4 The Duffie-Kan Model; 1.5 The Longstaff Model; 1.6 The Ahn-Gao Model; 1.7 The Brennan-Schwartz Model; 1.8 The BDT Model; 1.9 The Aït-Sahalia Model; 1.10 The CKLS Model; 1.11 The Unrestricted Model I; 1.12 The Unrestricted Model II; 1.13 The CEV Model; 1.14 The CIR (1980) Model; 1.15 The Merton Model; 1.16 The Dothan Model; 1.17 The GBM Model; 1.18 Conclusion; References
2 The Term Structure of Interest Rates2.1 Introduction; 2.2 The Term Structure Equation; 2.3 The Affine Models; 2.4 Conclusion; References; 3 The Vasiček Model; 3.1 Introduction; 3.2 The Vasiček Model and Its Generalization to the Multifactor Case; 3.3 Yield Curves in Two-Factor Vasiček Models; 3.4 Conclusion; References; 4 The Cox-Ingersoll-Ross Model; 4.1 Introduction; 4.2 The Single-Factor Cox-Ingersoll-Ross Model; 4.3 Generalization of the CIR Model for a Multifactorial Case; 4.4 The Two-Factor Cox-Ingersoll-Ross Model; 4.5 The Longstaff-Schwartz Model
4.6 Extension of the Longstaff-Schwartz Model4.7 Numerical Example; 4.8 Conclusion; References; 5 The Duffie-Kan One-Factor Model; 5.1 Introduction; 5.2 The Forward Curve and Yield Curve in the Duffie-Kan Model; 5.3 Properties of the Yield Curve and Forward Curves; 5.4 Conclusion; References; 6 The Duffie-Kan Two-Factor Models; 6.1 Introduction; 6.2 The Two-Factor Model "Rate and Its Local Average" (Small Parameter Method); 6.3 The Two-Factor Model "Rate and Its Instantaneous Variance" (Small Parameter Method); 6.4 The Two-Factor Model "Rate and Its Local Average" (Numerical Approach)
6.5 The Two-Factor Model "Rate and Its Instantaneous Variance" (Numerical Approach)6.6 Conclusion; References; 7 The Three Factor Models; 7.1 Introduction; 7.2 Stochastic Volatility of the Process of Level Local Mathematical Expectation; 7.3 The Process of Level Local Mathematical Expectation with Square Root; 7.4 The Gaussian Process of Level Local Mathematical Expectation; 7.5 Conclusion; References; 8 Another Version of the Term to Maturity Variable; 8.1 Introduction; 8.2 The One-Factor Duffie-Kan Model; 8.3 The Two-Factor Models; 8.4 The Three-Factor Models; 8.5 Conclusion; References