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Term Structure Modeling and Estimation in a State Space Framework 2006 ed. [Pehme köide]

  • Formaat: Paperback / softback, 226 pages, kõrgus x laius: 235x155 mm, kaal: 750 g, X, 226 p., 1 Paperback / softback
  • Sari: Lecture Notes in Economics and Mathematical Systems 565
  • Ilmumisaeg: 23-Sep-2005
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540283420
  • ISBN-13: 9783540283423
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  • Formaat: Paperback / softback, 226 pages, kõrgus x laius: 235x155 mm, kaal: 750 g, X, 226 p., 1 Paperback / softback
  • Sari: Lecture Notes in Economics and Mathematical Systems 565
  • Ilmumisaeg: 23-Sep-2005
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540283420
  • ISBN-13: 9783540283423
This book has been prepared during my work as a research assistant at the Institute for Statistics and Econometrics of the Economics Department at the University of Bielefeld, Germany. It was accepted as a Ph.D. thesis titled "Term Structure Modeling and Estimation in a State Space Framework" at the Department of Economics of the University of Bielefeld in November 2004. It is a pleasure for me to thank all those people who have been helpful in one way or another during the completion of this work. First of all, I would like to express my gratitude to my advisor Professor Joachim Frohn, not only for his guidance and advice throughout the com­ pletion of my thesis but also for letting me have four very enjoyable years teaching and researching at the Institute for Statistics and Econometrics. I am also grateful to my second advisor Professor Willi Semmler. The project I worked on in one of his seminars in 1999 can really be seen as a starting point for my research on state space models. I thank Professor Thomas Braun for joining the committee for my oral examination.

Arvustused

From the reviews:









"The author introduces the AMGM models and gives the exact form for the yields and their moment structures. the book is well-presented with sufficient references, and can serve as a reference for researchers in macroeconomics and financial mathematics. It can also be studied because it presents an important class of hidden Markov models." (Yanhong Wu, Mathematical Reviews, Issue 2006 h)

1 Introduction
1(4)
2 The Term Structure of Interest Rates
5(8)
2.1 Notation and Basic Interest Rate Relationships
5(2)
2.2 Data Set and Some Stylized Facts
7(6)
3 Discrete-Time Models of the Term Structure
13(42)
3.1 Arbitrage, the Pricing Kernel and the Term Structure
13(8)
3.2 One-Factor Models
21(18)
3.2.1 The One-Factor Vasicek Model
21(4)
3.2.2 The Gaussian Mixture Distribution
25(6)
3.2.3 A One-Factor Model with Mixture Innovations
31(3)
3.2.4 Comparison of the One-Factor Models
34(2)
3.2.5 Moments of the One-Factor Models
36(3)
3.3 Affine Multifactor Gaussian Mixture Models
39(16)
3.3.1 Model Structure and Derivation of Arbitrage-Free Yields
40(4)
3.3.2 Canonical Representation
44(6)
3.3.3 Moments of Yields
50(5)
4 Continuous-Time Models of the Term Structure
55(14)
4.1 The Martingale Approach to Bond Pricing
55(7)
4.1.1 One-Factor Models of the Short Rate
58(2)
4.1.2 Comments on the Market Price of Risk
60(1)
4.1.3 Multifactor Models of the Short Rate
61(1)
4.1.4 Martingale Modeling
62(1)
4.2 The Exponential-Affine Class
62(4)
4.2.1 Model Structure
62(2)
4.2.2 Specific Models
64(2)
4.3 The Heath-Jarrow-Morton Class
66(3)
5 State Space Models
69(14)
5.1 Structure of the Model
69(2)
5.2 Filtering, Prediction, Smoothing, and Parameter Estimation
71(3)
5.3 Linear Gaussian Models
74(9)
5.3.1 Model Structure
74(1)
5.3.2 The Kalman Filter
74(5)
5.3.3 Maximum Likelihood Estimation
79(4)
6 State Space Models with a Gaussian Mixture
83(18)
6.1 The Model
83(3)
6.2 The Exact Filter
86(7)
6.3 The Approximate Filter AMF(k)
93(4)
6.4 Related Literature
97(4)
7 Simulation Results for the Mixture Model
101(34)
7.1 Sampling from a Unimodal Gaussian Mixture
102(15)
7.1.1 Data Generating Process
102(2)
7.1.2 Filtering and Prediction for Short Time Series
104(3)
7.1.3 Filtering and Prediction for Longer Time Series
107(5)
7.1.4 Estimation of Hyperparameters
112(5)
7.2 Sampling from a Bimodal Gaussian Mixture
117(9)
7.2.1 Data Generating Process
117(1)
7.2.2 Filtering and Prediction for Short Time Series
118(2)
7.2.3 Filtering and Prediction for Longer Time Series
120(1)
7.2.4 Estimation of Hyperparameters
121(5)
7.3 Sampling from a Student t Distribution
126(5)
7.3.1 Data Generating Process
126(1)
7.3.2 Estimation of Hyperparameters
127(4)
7.4 Summary and Discussion of Simulation Results
131(4)
8 Estimation of Term Structure Models in a State Space Framework
135(18)
8.1 Setting up the State Space Model
137(7)
8.1.1 Discrete-Time Models from the AMGM Class
137(2)
8.1.2 Continuous-Time Models
139(4)
8.1.3 General Form of the Measurement Equation
143(1)
8.2 A Survey of the Literature
144(2)
8.3 Estimation Techniques
146(3)
8.4 Model Adequacy and Interpretation of Results
149(4)
9 An Empirical Application
153(26)
9.1 Models and Estimation Approach
153(7)
9.2 Estimation Results
160(14)
9.3 Conclusion and Extensions
174(5)
10 Summary and Outlook 179(36)
A Properties of the Normal Distribution
181(4)
B Higher Order Stationarity of a VAR(1)
185(4)
C Derivations for the One-Factor Models in Discrete Time
189(8)
C.1 Sharpe Ratios for the One-Factor Models
189(2)
C.2 The Kurtosis Increases in the Variance Ratio
191(1)
C.3 Derivation of Formula (3.53)
192(1)
C.4 Moments of Factors
192(1)
C.5 Skewness and Kurtosis of Yields
193(1)
C.6 Moments of Differenced Factors
194(1)
C.7 Moments of Differenced Yields
195(2)
D A Note on Scaling
197(4)
E Derivations for the Multifactor Models in Discrete Time
201(8)
E.1 Properties of Factor Innovations
201(1)
E.2 Moments of Factors
202(2)
E.3 Moments of Differenced Factors
204(1)
E.4 Moments of Differenced Yields
205(4)
F Proof of Theorem 6.3
209(4)
G Random Draws from a Gaussian Mixture Distribution
213(2)
References 215(6)
List of Figures 221(2)
List of Tables 223