Term structure modeling and estimation in a state space framework:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
2006
|
| Series: | Lecture notes in economics and mathematical systems
565 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Bielefeld, Univ., Diss., 2004 |
| Physical Description: | IX, 223 S. graph. Darst. |
| ISBN: | 3540283420 9783540283423 |
Staff View
MARC
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| 100 | 1 | |a Lemke, Wolfgang |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Term structure modeling and estimation in a state space framework |c Wolfgang Lemke |
| 264 | 1 | |a Berlin u.a. |b Springer |c 2006 | |
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| 500 | |a Zugl.: Bielefeld, Univ., Diss., 2004 | ||
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Record in the Search Index
| _version_ | 1804134155325276160 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTIO
N 1
2 TH
E TERM STRUCTUR
E O
F INTERES
T RATE
S
5
2.1 NOTATION AND BASIC INTEREST RAT
E RELATIONSHIPS 5
2.2 DAT
A SET AND SOME STYLIZED FACTS 7
3 DISCRETE-TIM
E MODEL
S O
F TH
E TER
M STRUCTUR
E
1
3
3.1
ARBITRAGE, THE PRICING KERNEL AND TH
E TERM STRUCTURE 13
3.2 ONE-FACTOR MODELS 21
3.2.1 THE ONE-FACTOR VASICEK MODEL 21
3.2.2 THE GAUSSIAN MIXTURE DISTRIBUTION 25
3.2.3 A ONE-FACTOR MODEL WITH MIXTURE INNOVATIONS 31
3.2.4 COMPARISON OF TH
E ONE-FACTOR MODELS 34
3.2.5 MOMENTS OF TH
E ONE-FACTOR MODELS 36
3.3 AFFINE MULTIFACTOR GAUSSIAN MIXTURE MODELS 39
3.3.1 MODEL STRUCTURE AND DERIVATION OF ARBITRAGE-FREE YIELDS 40
3.3.2 CANONICAL REPRESENTATION 44
3.3.3 MOMENTS OF YIELDS 50
4 CONTINUOUS-TIM
E MODEL
S O
F TH
E
TER
M
STRUCTUR
E
5
5
4.1 THE MARTINGALE APPROACH TO BOND PRICING 55
4.1.1 ONE-FACTOR MODELS OF TH
E SHORT RATE 58
4.1.2 COMMENTS ON TH
E MARKET PRICE OF RISK 60
4.1.3 MULTIFACTOR MODELS OF TH
E SHORT RATE 61
4.1.4 MARTINGALE MODELING 62
4.2 THE EXPONENTIAL-AFFINE CLASS 62
4.2.1 MODEL STRUCTURE 62
4.2.2 SPECIFIC MODELS 64
4.3 THE HEATH-JARROW-MORTON CLASS 66
VIII CONTENTS
5 STAT
E SPAC
E
MODEL
S
6
9
5.1 STRUCTURE OF THE MODEL 69
5.2 FILTERING, PREDICTION, SMOOTHING, AND PARAMETER ESTIMATION . . 71
5.3 LINEAR GAUSSIAN MODELS 74
5.3.1 MODEL STRUCTURE 74
5.3.2 THE KALMAN FILTER 74
5.3.3 MAXIMUM LIKELIHOOD ESTIMATION 79
6 STAT
E SPAC
E
MODEL
S WIT
H A GAUSSIA
N MIXTUR
E
8
3
6.1 THE MODEL 83
6.2 THE EXACT FILTER 86
6.3 THE APPROXIMATE FILTER
AMF(K)
93
6.4 RELATED LITERATURE 97
7 SIMULATIO
N RESULT
S FOR TH
E MIXTUR
E MODE
L
101
7.1 SAMPLING FROM A UNIMODAL GAUSSIAN MIXTURE 102
7.1.1 DAT
A GENERATING PROCESS 102
7.1.2 FILTERING AND PREDICTION FOR SHORT TIME SERIES 104
7.1.3 FILTERING AND PREDICTION FOR LONGER TIME SERIES 107
7.1.4 ESTIMATION OF HYPERPARAMETERS 112
7.2 SAMPLING FROM A BIMODAL GAUSSIAN MIXTURE 117
7.2.1 DAT
A GENERATING PROCESS 117
7.2.2 FILTERING AND PREDICTION FOR SHORT TIME SERIES 118
7.2.3 FILTERING AND PREDICTION FOR LONGER TIME SERIES 120
7.2.4 ESTIMATION OF HYPERPARAMETERS 121
7.3 SAMPLING FROM A STUDENT
T
DISTRIBUTION 126
7.3.1 DAT
A GENERATING PROCESS 126
7.3.2 ESTIMATION OF HYPERPARAMETERS 127
7.4 SUMMARY AND DISCUSSION OF SIMULATION RESULTS 131
8 ESTIMATIO
N O
F TERM STRUCTUR
E MODEL
S I
N A STAT
E SPACE
FRAMEWOR
K 135
8.1 SETTING UP THE STATE SPACE MODEL 137
8.1.1 DISCRETE-TIME MODELS FROM THE AMGM CLASS 137
8.1.2 CONTINUOUS-TIME MODELS 139
8.1.3 GENERAL FORM OF TH
E MEASUREMENT EQUATION 143
8.2 A SURVEY OF THE LITERATURE 144
8.3 ESTIMATION TECHNIQUES 146
8.4 MODEL ADEQUACY AND INTERPRETATION OF RESULTS 149
9 AN EMPIRICA
L APPLICATIO
N
153
9.1 MODELS AND ESTIMATION APPROACH 153
9.2 ESTIMATION RESULTS 160
9.3 CONCLUSION AND EXTENSIONS 174
10 SUMMAR
Y AN
D OUTLOO
K
179
CONTENTS IX
A PROPERTIES OF THE
NORMA
L
DISTRIBUTION 181
B HIGHER ORDER STATIONARITY OF A VAR(L
) 185
C DERIVATIONS FOR TH
E ONE-FACTOR MODELS IN DISCRETE
TIM
E . . . 189
C.
I SHARP
E RATIO
S FOR TH
E ONE-FACTO
R MODEL
S 189
C.2 TH
E KURTOSI
S INCREASE
S I
N TH
E VARIANC
E RATI
O 191
C.
3 DERIVATIO
N OF FORMUL
A (3.53) 192
C.4 MOMENT
S OF FACTOR
S 192
C.5 SKEWNES
S AN
D KURTOSI
S OF YIELD
S 193
C.
6 MOMENT
S OF DIFFERENCED FACTOR
S 194
C.
7 MOMENT
S OF DIFFERENCED YIELD
S 195
D A NOT
E ON SCALING 197
E DERIVATIONS FOR THE MULTIFACTOR MODELS IN DISCRETE TIME
. . 201
E.
I PROPERTIE
S O
F FACTO
R INNOVATION
S 20
1
E.
2 MOMENT
S O
F FACTOR
S 202
E.
3 MOMENT
S O
F DIFFERENCED FACTOR
S 204
E.
4 MOMENT
S OF DIFFERENCED YIELD
S 205
F PROOF OF THEOREM 6.3
209
G
RANDOM DRAWS FROM A GAUSSIAN MIXTURE DISTRIBUTION 213
REFERENCES 215
LIST OF FIGURES 221
LIST OF TABLES 223
|
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| id | DE-604.BV020825902 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:20:07Z |
| institution | BVB |
| isbn | 3540283420 9783540283423 |
| language | English |
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| physical | IX, 223 S. graph. Darst. |
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| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Lemke, Wolfgang Verfasser aut Term structure modeling and estimation in a state space framework Wolfgang Lemke Berlin u.a. Springer 2006 IX, 223 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 565 Zugl.: Bielefeld, Univ., Diss., 2004 Mathematisches Modell Interest rates Mathematical models Zinsstrukturtheorie (DE-588)4117720-4 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Zustandsraum (DE-588)4132647-7 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zinsstrukturtheorie (DE-588)4117720-4 s Zustandsraum (DE-588)4132647-7 s Schätzung (DE-588)4193791-0 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Lecture notes in economics and mathematical systems 565 (DE-604)BV000000036 565 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013831188&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lemke, Wolfgang Term structure modeling and estimation in a state space framework Lecture notes in economics and mathematical systems Mathematisches Modell Interest rates Mathematical models Zinsstrukturtheorie (DE-588)4117720-4 gnd Schätzung (DE-588)4193791-0 gnd Zustandsraum (DE-588)4132647-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4117720-4 (DE-588)4193791-0 (DE-588)4132647-7 (DE-588)4057633-4 (DE-588)4113937-9 |
| title | Term structure modeling and estimation in a state space framework |
| title_auth | Term structure modeling and estimation in a state space framework |
| title_exact_search | Term structure modeling and estimation in a state space framework |
| title_full | Term structure modeling and estimation in a state space framework Wolfgang Lemke |
| title_fullStr | Term structure modeling and estimation in a state space framework Wolfgang Lemke |
| title_full_unstemmed | Term structure modeling and estimation in a state space framework Wolfgang Lemke |
| title_short | Term structure modeling and estimation in a state space framework |
| title_sort | term structure modeling and estimation in a state space framework |
| topic | Mathematisches Modell Interest rates Mathematical models Zinsstrukturtheorie (DE-588)4117720-4 gnd Schätzung (DE-588)4193791-0 gnd Zustandsraum (DE-588)4132647-7 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Mathematisches Modell Interest rates Mathematical models Zinsstrukturtheorie Schätzung Zustandsraum Stochastisches Modell Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013831188&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT lemkewolfgang termstructuremodelingandestimationinastatespaceframework |