Spanning rates as factors in derivative term structure models: theory, empirical analysis and implementation
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| Format: | Book |
| Language: | English |
| Published: |
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | St. Gallen, Univ., Diss., 2000 |
| Physical Description: | VIII, 228 S. graph. Darst. |
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MARC
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| 100 | 1 | |a Haab, Stefan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spanning rates as factors in derivative term structure models |b theory, empirical analysis and implementation |c Stefan Haab |
| 264 | 1 | |c 2000 | |
| 300 | |a VIII, 228 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Table of Contents
I Introduction 1
1 Outline 3
2 Summary of the Thesis 9
2.1 Objective of Research 9
2.2 Part II: Nature of Term Structure Movements 10
2.3 Part III: Theory 11
2.4 Part IV: Estimation 13
2.5 Part V: Implementation 14
II Nature of Term Structure Movements 17
3 The Data 21
3.1 Selection Criteria 21
3.2 Data Description 23
3.2.1 McCulloch, Kwon Term Structure Database 23
3.2.2 Federal Reserve H.15 Data 24
3.2.3 Swiss Government Bond Market 25
3.3 Descriptive Statistics 25
3.3.1 Averages 26
3.3.2 Distribution and Dispersion 27
3.3.3 Co Movement 30
3.3.4 Orthogonality of Spread and Long Rate 31
4 Parameters of Diffusion 35
4.1 Theory 35
4.2 Results of the GMM Estimation 39
4.2.1 Drift Volatility Parameters 40
4.2.2 Prediction Errors Residuals 44
4.2.3 Correlation of Spread and Long Rate 45
5 Common Dynamics of Term Structure 51
5.1 Theory 52
5.2 Results of the Principal Components Analysis 53
6 Summary and Conclusion 59
iv Contents
III Spanning Rates as Factors in Derivative Term Structure
Models Theory 63
7 Introduction 65
7.1 Modern Theory of Valuation 65
7.1.1 Diffusion Process 65
7.1.2 Ito s Lemma 67
7.1.3 Fundamental Partial Differential Equation 68
7.1.4 The Risk neutral Valuation Principle 70
7.1.5 Lattice Representation 73
7.1.6 Summary 74
7.2 Classification 74
7.2.1 No Arbitrage, Partial Equilibrium or Equilibrium Models 75
7.2.2 Single or Multi Factor Models 78
7.2.3 Markovian or non Markovian Process 79
7.2.4 Model in Risk neutral or Realistic Probabilities 80
7.3 Summary and Conclusion 80
8 The Brennan and Schwartz Model 85
8.1 Description of the Model 86
8.2 Critique 90
8.2.1 Hogan s Critique 91
8.2.2 Black s Consol Rate Conjecture 91
8.2.3 Long Rates Never Fall 93
8.2.4 Modeling Prices of Coupon Bonds 93
8.3 BeyondtheBS Model 93
8.3.1 Adaptations of the BS Model 94
8.3.2 Escaping Black s Consol Rate Conjecture 95
9 A Basic Spread Long Rate Model 97
9.1 Realistic Probability Measure 98
9.1.1 Setting up the FPDE 98
9.1.2 The FPDE and Process Modifications 102
9.1.3 Solving the FPDE for Bond Prices 104
9.2 Risk neutral Probability Measure 106
9.2.1 The Set up forthe RNVP 107
9.2.2 Valuation of a General Contingent Claim 108
9.2.3 Valuation of a European Call on a Discount Bond 112
9.2.4 Valuation of a Put on a Discount Bond 114
Contents v
9.2.5 Valuation of Further Contingent Claims 115
9.3 Model Analysis 115
9.3.1 Comparative Statics 115
9.3.2 Probability of Negative Interest Rates 116
9.3.3 Forward Rates and Bias 116
9.3.4 Spanning Rates 118
9.3.5 Bias of Spot Rate Curve 119
9.3.6 Instantaneous Term Premium 119
9.4 Summary 120
10 Model Endogenous Consistency 121
10.1 Two Necessary Conditions 123
10.1.1 Condition I: Independence of Spread Long Rate 123
10.1.2 Condition II: Empirically Valid Factor Definitions 124
10.2 Further Enhancements 127
10.2.1 Correlation 127
10.2.2 Mean Reversion Speed 128
10.3 The New Model: Summary Conclusion 129
11 Variations 131
11.1 Curvature as a Third Factor 131
11.1.1 The Model 131
11.1.2 Model Endogenous Consistency 132
11.2 The Square Root Volatility Case 133
11.2.1 Independence of Spread Long Rate 135
11.2.2 Empirical Valid Factor Definitions 135
11.3 Summary and Conclusion 135
12 Appendix Part III: Generalized Duration 139
12.1 Introduction 139
12.2 Conventional Duration Measures 139
12.3 Generalized Duration Measures 144
12.4 Theoretical Comparison 145
IV Spanning Rates as Factors in Derivative Term Structure
Models Empirical Analysis 147
13 Introduction 149
14 Theory to Estimation 153
14.1 Diffusion Parameters (1st step) 153
14.2 Cross sectional Parameters (2nd step) 155
vi Contents
15 Estimation Results 161
15.1 Data 162
15.2 Time Series Parameters (1st step) 162
15.3 Basic Model (2nd step) 164
15.3.1 Whole Sample 164
15.3.2 Moving Sample Window 166
15.4 Condition I Model (2nd step) 169
15.4.1 Whole Sample 169
15.4.2 Moving Sample Window 171
15.5 Conditions Ha lib Model (2nd step) 173
15.5.1 Whole Sample 173
15.5.2 Moving Sample Window 176
15.6 Summary and Conclusion 177
16 Appendix to Part IV: Sensitivity Analysis 179
V Spanning Rates as Factors in Derivative Term Structure
Models Implementation 183
17 Introduction 185
18 Pensions, Wage Growth Interest Rates 187
18.1 The Model 187
18.2 Results 192
19 Summary 201
VI Appendix 203
20 Part II: U.S. Interest Rates 205
21 Part II: Swiss Interest Rates 211
22 Part IV: Estimation with Swiss Data 217
Bibliography 219
List of Figures
3.1 Short Rate and Moving Averages 27
3.2 Quantiles of first differences of several interest rates 29
3.3 Standard deviation of long rate 29
3.4 Correlations between spread and long rate 32
3.5 Spread and long rate: levels 33
3.6 Spread and long rate: first differences 33
4.1 Diffusion coefficients of long rate: unnested UC model 42
4.2 P values of diffusion coefficients of long rate: unnested UC
model 43
4.3 Correlations between prediction errors of spread and long rate 46
4.4 Correlation between OU process specifications for spread
and long rate and corresponding P value 46
4.5 Diffusion coefficients of long rate in a correlated OU
diffusion system of spread and long rate 47
4.6 P Values for coefficients of long rate in an OU diffusion
system of spread and long rate 47
4.7 Diffusion coefficients of spread in a correlated OU diffusion
system of spread and long rate 48
4.8 P values of coefficients of spread in a correlated OU
diffusion system of spread and long rate 49
5.1 Factor analysis: explanatory power of factors 54
5.2 Factor analysis: cumulative communality of the factors 55
5.3 Factor analysis: first three scaled factors. Influence on short
rate r is only approximated 56
15.1 Typical term structure under the basic model 165
15.2 Errors of basic model, whole sample 166
15.3 Basic model: market price of risk parameters, rolling
sub samples of 120 months 167
15.4 Basic model: P values to market price of risk parameters,
rolling sub samples of 120 months 168
15.5 Errors of the basic model, rolling sub samples of 120
months 168
viii List of Figures
15.6 Typical term structure under condition I model 170
15.7 Errors of condition I model, whole sample 170
15.8 Model under condition I: market price of risk parameters,
rolling sub samples of 120 months 171
15.9 P values to market price of risk parameters of the model
under condition I, rolling sub samples of 120 months 172
15.10 Errors of the model under condition I, rolling sub samples
of 120 months 172
15.11 Typical term structure for model under conditions Ha lib 174
15.12 Errors of model under conditions Ha lib, whole sample 175
15.13 Market price of risk parameter of the model under
conditions Ha and lib, rolling sub samples of 120 months 176
15.14 Errors of the model under conditions Ila and lib, rolling
sub samples of 120 months 177
16.1 Sensitivity of 2nd step estimate to changes in 1st step
estimates 180
16.2 Simultaneous sensitivity analysis of 2nd step estimate to
changes in 1st step estimates 180
18.1 Macro economy and wage growth 190
18.2 Relationship between the factors (long rate and spread) and
wage growth 190
18.3 Liability surface for different 9L and 9a as well as factor
starting values, 5 years to retirement 193
18.4 Liability surface for different 9L and 6S as well as factor
starting values, 20 years to retirement 194
18.5 Liability surface for different 9L and 9S but identical factor
starting values, 5 years to retirement 195
18.6 Liability surface for different 9L and 9a but identical factor
starting values, 20 years to retirement 195
18.7 Liability surface for different oL and a,, 5 years to
retirement 197
18.8 Liability surface for different aL and a», 20 years to
retirement 197
18.9 Time horizon effects and volatility. 198
18.10 Time horizon effects and factor starting points 198
List of Tables
3.1 Data Summary 23
3.2 Skewness, kurtosis and normality test (Jarque Bera) 28
3.3 Correlations between first differences of interest rates 31
4.1 Nested process specifications 36
4.2 P values to runs test on the residuals 44
4.3 Prediction errors of long rate time series models 45
7.1 Classification and Model Attributes 83
11.1 Overview to Processes, Factors, and Conditions 136
14.1 GMM estimates: instruments and moments 154
15.1 Step one estimates of diffusion parameters 163
15.2 Basic model: market prices of risk for whole sample 165
15.3 Model under condition I: market prices of risk for the whole
sample 169
15.4 Model under conditions Ha and lib: market price of risk 173
21.1 Swiss interest rates: Descriptive statistics of spread and long
rate 212
21.2 Swiss interest rates: Descriptive statistics of spread and long
rate 212
21.3 Swiss interest rates: Correlated system of OU processes for
spread and long rate 214
22.1 1st Step Estimation for Swiss Data 218
22.2 2nd Step Estimation for Swiss data: Model under conditions
Ila and lib 218
22.3 2nd Step Estimation for Swiss data: Model under conditions
Ila and lib 218
|
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| spelling | Haab, Stefan Verfasser aut Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation Stefan Haab 2000 VIII, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2000 Zinsstrukturtheorie (DE-588)4117720-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zinsstrukturtheorie (DE-588)4117720-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008940630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haab, Stefan Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| subject_GND | (DE-588)4117720-4 (DE-588)4113937-9 |
| title | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation |
| title_auth | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation |
| title_exact_search | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation |
| title_full | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation Stefan Haab |
| title_fullStr | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation Stefan Haab |
| title_full_unstemmed | Spanning rates as factors in derivative term structure models theory, empirical analysis and implementation Stefan Haab |
| title_short | Spanning rates as factors in derivative term structure models |
| title_sort | spanning rates as factors in derivative term structure models theory empirical analysis and implementation |
| title_sub | theory, empirical analysis and implementation |
| topic | Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| topic_facet | Zinsstrukturtheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008940630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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