عنوان

Yield curves and forward curves for diffusion models of short rates /

3030154998

3030155005

3030155013

3030155021

9783030154998

9783030155001

9783030155018

9783030155025

9783030154998

Yield curves and forward curves for diffusion models of short rates /

[Book]

Gennady A. Medvedev.

Cham :

Springer,

[2019]

©2019

1 online resource :

illustrations

Includes bibliographical references and index.

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]

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

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This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.

Springer Nature

com.springer.onix.9783030155001

9783030154998

9783030155018

9783030155025

Rate of return.

Zero coupon securities.

BUSINESS & ECONOMICS-- Finance.

Rate of return.

Zero coupon securities.

BUS-- 027000

KF

KF

Medvedev, Gennady A.

20200823084520.0

pn

[Book]

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