Fixed income securities: dynamic methods for interest rate risk pricing and hedging
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2001
|
| Schriftenreihe: | Wiley finance series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 254 S. graph. Darst. |
| ISBN: | 0471495026 |
Internformat
MARC
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| 246 | 1 | 3 | |a Fixed-income securities |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2001 | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Fixed-income securities |x Mathematical models | |
| 650 | 4 | |a Hedging (Finance) |x Mathematical models | |
| 650 | 4 | |a Pricing |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804128602495647744 |
|---|---|
| adam_text | Contents
INTRODUCTION ix
ACKNOWLEDGMENTS xü
STANDARD NOTATION xiii
PART I: PRICING AND HEDGING CERTAIN
CASH FLOWS 1
1: DERIVING THE CURRENT ZERO COUPON RATE
CURVE 3
1.1 The Direct Method 3
1.2 Indirect Methods 5
1.2.1 Parameterization of the Discount Function as a
Spline Function 6
1.2.2 Parameterization of the Zero Coupon Curve as a
Function of Different Parameters 18
1.2.3 Discussion and Comparison of the Methods 27
1.2.4 Fitting the Zero Coupon Yield Curve using Data
from the Swap Market 28
2: BASIC ASSETS PRICING AND HEDGING 31
2.1 General Principle 41
2.1.1 Qualification of Interest Rate Risk 41
2.1.2 Quantification of Interest Rate Risk 42
vi CONTENTS
2.2 Specific Applications 49
2.2.1 A Simplified Framework: Assuming a Fiat
Zero Coupon Yield Curve 49
2.2.2 More Realistic Frameworks: Accounting for
Non Flat Zero Coupon Yield Curves 61
PART II: PRICING AND HEDGING UNCERTAIN
CASH FLOWS 89
3: MODELLING THE ZERO COUPON YIELD CURVE
DYNAMICS 91
3.1 Equilibrium Models 93
3.1.1 Single Factor Models 93
3.1.2 Multi Factor Models 109
3.2 Arbitrage Models 117
3.2.1 General Framework 118
3.2.2 Markov Models 124
3.2.3 Market Models: The BGM/Jamshidian Approach 156
3.3 A Classic Example: The Two Factor Extended Vasicek
Model 166
3.3.1 Presentation ofthe Model 167
3.3.2 Reconciling the Model with the Results of a PCA on
the Yield Curve Variation 170
3.3.3 Yield Curve Transformations Allowed by the Model 172
3.3.4 Shortcomings of the Model 173
4: PRICING AND HEDGING FIXED INCOME
DERIVATIVES 175
4.1 The Black Model: A Market Standard 175
4.1.1 Pricing and Hedging Caps 176
4.1.2 Pricing and Hedging Swaptions 180
4.1.3 Inconsistency in the Market Pricing of Caps and
Swaptions 183
CONTENTS vii
4.2 The Two Factor Extended Vasicek Model: Calibration Of
The Model 183
4.2.1 UsingaPCA 183
4.2.2 Using Market Prices 185
4.3 The Two Factor Extended Vasicek Model: Pricing and
Hedging 189
4.3.1 Standard Derivative Pricing 189
4.3.2 Derivative Hedging 204
4.3.3 Pricing Defaultable Fixed Income Claims 207
PART III: MATHEMATICAL APPENDICES 215
APPENDIX A: AN INTRODUCTION TO STOCHASTIC
PROCESSES IN CONTINUOUS TIME 217
A.l Brownian Motion 217
A.l.l Standard Brownian Motion 218
A.l.2 Generalization 221
A.2 Stochastic Integrals 222
A.2.1 Construction and Properties 222
A.2.2 Itö Process 223
A.3 Stochastic Differential Equations (SDEs) 224
A.4 Asset Price Process 225
A.5 Representation Of Brownian Martingales 226
A.6 Continuous Time Asset Pricing 226
A.6.1 Unidimensional Itö s Lemma 226
A.6.2 A Multidimensional Version of Itö s Lemma 229
A.6.3 Integration by Parts 230
A.6.4 Girsanov s Theorem 231
A.6.5 Application to Finance 232
A.7 Feynman Kac Formula 233
APPENDIX B: NUMERICAL METHODS 235
B.l Monte Carlo Simulations 235
B.l.l Principle 235
B. 1.2 Generating Asset Paths 236
viii CONTENTS
B.1.3 Application to Fixed Income Securities 236
B.1.4 Generating Multidimensional Processes 237
B.2 Finite Difference Methods 238
B.2.1 General Presentation 238
B.2.2 Explicit Schemes 239
B.2.3 Implicit Schemes 240
REFERENCES 243
INDEX 253
|
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| indexdate | 2024-07-09T18:51:51Z |
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| isbn | 0471495026 |
| language | English |
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| spelling | Martellini, Lionel Verfasser aut Fixed income securities dynamic methods for interest rate risk pricing and hedging Lionel Martellini ; Philippe Priaulet Fixed-income securities Chichester [u.a.] Wiley 2001 XV, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Couverture (Finances) - Modèles mathématiques Prix - Fixation - Modèles mathématiques Valeurs mobilières à revenus fixes - Modèles mathématiques Mathematisches Modell Fixed-income securities Mathematical models Hedging (Finance) Mathematical models Pricing Mathematical models Preisbildung (DE-588)4047103-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Einkommenssicherung (DE-588)4113389-4 gnd rswk-swf Hedging (DE-588)4123357-8 gnd rswk-swf Hedging (DE-588)4123357-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Einkommenssicherung (DE-588)4113389-4 s Preisbildung (DE-588)4047103-2 s Priaulet, Philippe Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009420485&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martellini, Lionel Priaulet, Philippe Fixed income securities dynamic methods for interest rate risk pricing and hedging Couverture (Finances) - Modèles mathématiques Prix - Fixation - Modèles mathématiques Valeurs mobilières à revenus fixes - Modèles mathématiques Mathematisches Modell Fixed-income securities Mathematical models Hedging (Finance) Mathematical models Pricing Mathematical models Preisbildung (DE-588)4047103-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Einkommenssicherung (DE-588)4113389-4 gnd Hedging (DE-588)4123357-8 gnd |
| subject_GND | (DE-588)4047103-2 (DE-588)4114528-8 (DE-588)4113389-4 (DE-588)4123357-8 |
| title | Fixed income securities dynamic methods for interest rate risk pricing and hedging |
| title_alt | Fixed-income securities |
| title_auth | Fixed income securities dynamic methods for interest rate risk pricing and hedging |
| title_exact_search | Fixed income securities dynamic methods for interest rate risk pricing and hedging |
| title_full | Fixed income securities dynamic methods for interest rate risk pricing and hedging Lionel Martellini ; Philippe Priaulet |
| title_fullStr | Fixed income securities dynamic methods for interest rate risk pricing and hedging Lionel Martellini ; Philippe Priaulet |
| title_full_unstemmed | Fixed income securities dynamic methods for interest rate risk pricing and hedging Lionel Martellini ; Philippe Priaulet |
| title_short | Fixed income securities |
| title_sort | fixed income securities dynamic methods for interest rate risk pricing and hedging |
| title_sub | dynamic methods for interest rate risk pricing and hedging |
| topic | Couverture (Finances) - Modèles mathématiques Prix - Fixation - Modèles mathématiques Valeurs mobilières à revenus fixes - Modèles mathématiques Mathematisches Modell Fixed-income securities Mathematical models Hedging (Finance) Mathematical models Pricing Mathematical models Preisbildung (DE-588)4047103-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Einkommenssicherung (DE-588)4113389-4 gnd Hedging (DE-588)4123357-8 gnd |
| topic_facet | Couverture (Finances) - Modèles mathématiques Prix - Fixation - Modèles mathématiques Valeurs mobilières à revenus fixes - Modèles mathématiques Mathematisches Modell Fixed-income securities Mathematical models Hedging (Finance) Mathematical models Pricing Mathematical models Preisbildung Einkommenssicherung Hedging |
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