Hedging with multi-factor interest rate models:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2005
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 140 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Hedging with multi-factor interest rate models |c by Carsten Vocke |
| 264 | 1 | |c 2005 | |
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| 502 | |a St. Gallen, Univ., Diss., 2005 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Motivation 1
1.2 Overview 3
2 Hedging Methods 7
2.1 Sensitivity based hedging 7
2.2 Measures of risk 8
2.2.1 Coherent risk measures 9
2.2.2 Asymmetrie risk measures 11
2.2.3 Symmetrie risk measures 12
2.3 Minimizing asymmetric risk measures 15
2.3.1 Super replication 15
2.3.2 Neyman Pearson hedging 16
2.4 Quadratic hedging 20
2.4.1 Regression method 21
2.4.2 Discounted markets 21
2.4.3 Risk minimization 23
2.4.4 Mean variance hedging 29
2.4.5 Applications 31
3 Interest Rate Models 37
3.1 Overview 37
3.2 Interest rate produets 38
iii
I
]
iv CONTENTS
3.2.1 Caps and floors 39
3.2.2 Swaptions 39
3.3 Forward rate models: The HJM framework 40
3.3.1 Definition 40
3.3.2 Pricing derivatives 41
3.3.3 Discrete time approximation 43
3.4 Market models 44
3.4.1 Definition 45
3.4.2 Pricing derivatives 46
3.4.3 Discrete time approximation 47
3.5 String models 47 ;
3.5.1 Definition 48 j
3.5.2 Approximating finite factor models 51
3.5.3 Derivation of the string models 55 ;
3.5.4 Pricing derivatives 55
3.5.5 Observational equivalence 59 I
3.5.6 Asymptotics for stochastic covariance extensions 67
3.5.7 Hedging interest rate securities 74
4 Monte Carlo Methods 79
4.1 Overview 79
4.2 Risk neutral direct methods 80
4.2.1 Pathwise differentiation 80
4.2.2 Likelihood ratio method 81
4.3 Local risk minimization 82
4.3.1 Payoff depending on a single underlying 83
4.3.2 Multidimensional extension 88 ,
4.3.3 Convergence 93 ,
4.3.4 Computational costs 102
4.3.5 Relationship to other concepts *03
CONTENTS v
5 Applications 109
5.1 Measuring the hedging performance 109
5.2 Calibration 112
5.3 Different number of factors 114
6 Conclusion 119
6.1 Contributions 119
6.2 Outlook 120
A Additional Proofs 121
A.I Lattice formulation of the HJM model 121
A.2 Piecewise linear base functions 123
A.3 Convergence of the regression hedging method 125
B Notation 131
B.I Abbreviations 131
B.2 Symbols 131
List of Figures
1.1 Schematic diagram of the parts contributing to the hedging accuracy meas¬
urement 2
3.1 Exponential correlation structure with approximations for one, two and
three factors 54
3.2 Absolute errors for hedging a zero coupon bond with zero coupon bonds of
different maturities in a string model 77
4.1 Convergence diagrams of price and hedge ratio estimates for risk neutral
Monte Carlo methods and regression hedging in the case of the Margrabe
exchange option 100
4.2 Dependence of price and hedge ratio estimates for risk neutral Monte Carlo
methods and regression hedging on computation time 104
5.1 Hedge errors of the regression method as a function of the hedge instrument
prices shown for two different numbers of base functions Ill
5.2 First three Heath Jarrow Morton volatility functions for a Gaussian string
model and their approximations used 116
vii
List of Tables
4.1 Comparison of price estimates for risk neutral Monte Carlo methods and
regression hedging in the case of European options on a single underlying
with level dependent volatility. 97
4.2 Comparison of hedge ratio estimates for risk neutral Monte Carlo meth¬
ods and regression hedging in the case of European options on a single
underlying with level dependent volatility. 98
4.3 Comparison of price and hedge ratio estimates for risk neutral Monte Carlo
methods and regression hedging in the case of the exchange option for
different correlations of the underlying processes 101
4.4 Computation time of the regression hedging method for different numbers
of hedged items 105
5.1 Simulated hedging accuracy test using two factor models for a Gaussian
string model 115
5.2 Simulated hedging accuracy test using one to three factor models for a
string model with stochastic volatility. 118
be
|
| adam_txt |
Contents
1 Introduction 1
1.1 Motivation 1
1.2 Overview 3
2 Hedging Methods 7
2.1 Sensitivity based hedging 7
2.2 Measures of risk 8
2.2.1 Coherent risk measures 9
2.2.2 Asymmetrie risk measures 11
2.2.3 Symmetrie risk measures 12
2.3 Minimizing asymmetric risk measures 15
2.3.1 Super replication 15
2.3.2 Neyman Pearson hedging 16
2.4 Quadratic hedging 20
2.4.1 Regression method 21
2.4.2 Discounted markets 21
2.4.3 Risk minimization 23
2.4.4 Mean variance hedging 29
2.4.5 Applications 31
3 Interest Rate Models 37
3.1 Overview 37
3.2 Interest rate produets 38
iii
I
]
iv CONTENTS
3.2.1 Caps and floors 39
3.2.2 Swaptions 39
3.3 Forward rate models: The HJM framework 40
3.3.1 Definition 40
3.3.2 Pricing derivatives 41
3.3.3 Discrete time approximation 43
3.4 Market models 44
3.4.1 Definition 45
3.4.2 Pricing derivatives 46
3.4.3 Discrete time approximation 47
3.5 String models 47 ;
3.5.1 Definition 48 j
3.5.2 Approximating finite factor models 51
3.5.3 Derivation of the string models 55 ;
3.5.4 Pricing derivatives 55
3.5.5 Observational equivalence 59 I
3.5.6 Asymptotics for stochastic covariance extensions 67
3.5.7 Hedging interest rate securities 74
4 Monte Carlo Methods 79
4.1 Overview 79
4.2 Risk neutral direct methods 80
4.2.1 Pathwise differentiation 80
4.2.2 Likelihood ratio method 81
4.3 Local risk minimization 82
4.3.1 Payoff depending on a single underlying 83
4.3.2 Multidimensional extension 88 ,
4.3.3 Convergence 93 ,
4.3.4 Computational costs 102
4.3.5 Relationship to other concepts *03
CONTENTS v
5 Applications 109
5.1 Measuring the hedging performance 109
5.2 Calibration 112
5.3 Different number of factors 114
6 Conclusion 119
6.1 Contributions 119
6.2 Outlook 120
A Additional Proofs 121
A.I Lattice formulation of the HJM model 121
A.2 Piecewise linear base functions 123
A.3 Convergence of the regression hedging method 125
B Notation 131
B.I Abbreviations 131
B.2 Symbols 131
List of Figures
1.1 Schematic diagram of the parts contributing to the hedging accuracy meas¬
urement 2
3.1 Exponential correlation structure with approximations for one, two and
three factors 54
3.2 Absolute errors for hedging a zero coupon bond with zero coupon bonds of
different maturities in a string model 77
4.1 Convergence diagrams of price and hedge ratio estimates for risk neutral
Monte Carlo methods and regression hedging in the case of the Margrabe
exchange option 100
4.2 Dependence of price and hedge ratio estimates for risk neutral Monte Carlo
methods and regression hedging on computation time 104
5.1 Hedge errors of the regression method as a function of the hedge instrument
prices shown for two different numbers of base functions Ill
5.2 First three Heath Jarrow Morton volatility functions for a Gaussian string
model and their approximations used 116
vii
List of Tables
4.1 Comparison of price estimates for risk neutral Monte Carlo methods and
regression hedging in the case of European options on a single underlying
with level dependent volatility. 97
4.2 Comparison of hedge ratio estimates for risk neutral Monte Carlo meth¬
ods and regression hedging in the case of European options on a single
underlying with level dependent volatility. 98
4.3 Comparison of price and hedge ratio estimates for risk neutral Monte Carlo
methods and regression hedging in the case of the exchange option for
different correlations of the underlying processes 101
4.4 Computation time of the regression hedging method for different numbers
of hedged items 105
5.1 Simulated hedging accuracy test using two factor models for a Gaussian
string model 115
5.2 Simulated hedging accuracy test using one to three factor models for a
string model with stochastic volatility. 118
be |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:30:27Z |
| indexdate | 2024-07-09T20:28:31Z |
| institution | BVB |
| language | English |
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| physical | X, 140 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| spelling | Vocke, Carsten Verfasser aut Hedging with multi-factor interest rate models by Carsten Vocke 2005 X, 140 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 2005 Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Zinsstrukturtheorie (DE-588)4117720-4 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zinsstrukturtheorie (DE-588)4117720-4 s Hedging (DE-588)4123357-8 s Monte-Carlo-Simulation (DE-588)4240945-7 s b DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014281060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vocke, Carsten Hedging with multi-factor interest rate models Monte-Carlo-Simulation (DE-588)4240945-7 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd Hedging (DE-588)4123357-8 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4117720-4 (DE-588)4123357-8 (DE-588)4113937-9 |
| title | Hedging with multi-factor interest rate models |
| title_auth | Hedging with multi-factor interest rate models |
| title_exact_search | Hedging with multi-factor interest rate models |
| title_exact_search_txtP | Hedging with multi-factor interest rate models |
| title_full | Hedging with multi-factor interest rate models by Carsten Vocke |
| title_fullStr | Hedging with multi-factor interest rate models by Carsten Vocke |
| title_full_unstemmed | Hedging with multi-factor interest rate models by Carsten Vocke |
| title_short | Hedging with multi-factor interest rate models |
| title_sort | hedging with multi factor interest rate models |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd Hedging (DE-588)4123357-8 gnd |
| topic_facet | Monte-Carlo-Simulation Zinsstrukturtheorie Hedging Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014281060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT vockecarsten hedgingwithmultifactorinterestratemodels |