Yield Curves and Forward Curves for Diffusion Models of Short Rates

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 Rates
	2.1 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 Model
	4.7 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 
orward 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
9 The Nelson–Siegel–Svensson No-Arbitrage Yield Curve Model
	9.1 Introduction
	9.2 The Nelson–Siegel–Svensson Model
	9.3 Latent Factors
	9.4 The No-Arbitrage Conditions for the Nelson–Siegel–Svensson Model
	9.5 The No-Arbitrage Conditions for 
the Svensson Expansion
	9.6 On Yield Curves of the 
European Central Bank
	9.7 The Nelson–Siegel–Svensson Yields
	9.8 Probability Properties
	9.9 Estimation
	9.10 Conclusion
	References
10 Quadratic Models of Yield in a 
Risk-Neutral World
	10.1 Introduction
	10.2 Quadratic Models of the 
Term Structure
	10.3 Equations for 
Term Structure Functions
	10.4 A 
Risk-Neutral Setting
	10.5 Features of 
Yield Curves in Quadratic Models
	10.6 Numerical Example
	10.7 On a Particular Case of 
a Quadratic Model
	10.8 Numerical Comparison of Duffie–Kan and Quadratic Models
	10.9 Conclusion
	References
11 Polynomial Models of 
Yield Term Structure
	11.1 Introduction
	11.2 The Term Structure as 
a Polynomial
	11.3 The Term Structure as 
a Power Series
	11.4 Testing Known Models
	11.5 A Family of Non-affine Models of 
Yield Term Structure
	11.6 Conclusion
	References
Index