Interest rate option models: understanding, analysing and using models for exotic interest rate options
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1998
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in financial engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 521 S. graph. Darst. |
| ISBN: | 0471979589 |
Internformat
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| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1998 | |
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Datensatz im Suchindex
| _version_ | 1804128174315929600 |
|---|---|
| adam_text | Contents
Preface to the Second Edition xiii
Preface to the First Edition xv
Acknowledgements xix
List of symbols and abbreviations xxi
PART ONE THE NEED FOR YIELD CURVE OPTION PRICING
MODELS 1
1 Definition and valuation of the underlying instruments 3
1.1 Introduction 3
1.2 Definition of spot rates, forward rates, swap rates and par coupon
rates 5
1.3 The valuation of plain vanilla swaps and FRAs 8
1.4 Obtaining the discount function from a set of spanning forward or
swap rates 14
1.5 The valuation of caps, floors and European swaptions 15
1.6 Determination of the discount function: the case of bonds — linear
models 21
1.7 Determination of the discount function: the case of bonds — non linear
models 25
1.8 Determination of the discount function: the case of the LIBOR
curve 27
2 Exotic interest rate instruments: description and valuation issues 29
2.1 Introduction 29
2.2 LIBOR in arrears swaps 30
viii Contents
2.3 American (Bermudan) swaptions 36
2.4 Trigger swaps 41
2.5 One way floaters 44
2.6 Captions 47
3 A statistical approach to yield curve models 51
3.1 Statistical analysis of the evolution of rates 51
3.2 The effects of model dimensionality on option pricing 63
3.3 A framework for option pricing 72
4 Correlation, average and instantaneous volatilities, and their impact on
the pricing of LIBOR options 75
4.1 Introduction and motivation 75
4.2 Instantaneous and average volatilities 77
4.3 Pricing European swaptions with instantaneous volatilities 80
4.4 Term decorrelation 83
4.5 Relationships between average, instantaneous and term structure of
volatilities 91
4.6 Conclusions 100
Appendix 4.1 101
Appendix 4.2 102
5 A motivation for yield curve models 105
5.1 Introduction 105
5.2 Hedging a bond option with the underlying forward contract 106
5.3 Hedging a path dependent bond option with forward contracts 109
PART TWO THE THEORETICAL TOOLS 117
6 Establishing a pricing framework 119
6.1 Introduction and motivation 119
6.2 First approach — Replication Strategy 121
6.3 Second approach — Naive Expectation 123
6.4 Third approach — Market Price of Risk 125
6.5 Fourth approach — Risk neutral valuation 129
6.6 Pseudo probabilities 130
6.7 A pricing framework 134
6.8 Evaluation of a contingent claim in a multi period setting 136
6.9 Self financing trading strategies 139
6.10 Fair prices as expectations 141
Contents ix
6.11 Switching numeraires and relating expectations under different
measures 144
6.12 Justifying the two state branching procedure 150
6.13 The nature of the transformation between measures — Girsanov s
theorem 153
7 The conditions of no arbitrage 157
7.1 First no arbitrage condition: the Vasicek approach 157
7.2 Second no arbitrage condition: the martingale approach 160
7.3 The case of a deterministic interest rates economy 162
7.4 First choice of numeraire: the money market account 165
7.5 Second choice of numeraire: discount bonds 170
7.6 An intuitive discussion 174
7.7 A worked out example: valuing a LIBOR in arrears swap 176
7.8 Switching between measures — the Vaillant brackets 179
PART THREE THE IMPLEMENTATION TOOLS 185
8 Lattice methods 187
8.1 Justification of lattice models 187
8.2 Implementation of lattice models: backward induction 194
8.3 Implementation of lattice models: forward induction 197
9 The partial differential equation (PDE) approach 201
9.1 The underlying parabolic equation and the calibration issues 201
9.2 Finite differences (FD) approximations to parabolic PDEs 205
9.3 The explicit finite differences scheme 208
9.4 The implicit finite differences scheme 212
10 Monte Carlo methods 215
10.1 Introduction 215
10.2 The method 216
10.3 Variance reduction techniques 222
10.4 Handling American options 227
PART FOUR ANALYSIS OF SPECIFIC MODELS 231
11 The CIR and Vasicek models 233
11.1 General features of desirable interest rate processes 233
11.2 Derivation of the CIR and Vasicek models 239
x Contents
11.3 Analytic properties of the CIR discount function 243
11.4 Bond options in the CIR model 246
11.5 Parametrisation of the CIR model 249
11.6 The CIR model: empirical results 251
12 The Black Derman and Toy model 259
12.1 Introduction 259
12.2 Analytic characterisation 260
12.3 Assessing the realism of the BDT model 262
12.4 Derivatives in one factor models: the BDT case 268
12.5 Calibrating the BDT model: pricing FRAs, caps and swaptions using
lattice models 270
13 The Hull and White approach 281
13.1 Introduction and motivation 281
13.2 Specification of the one factor version of the model 283
13.3 Exact fitting of the model to the term structure of volatilities 288
13.4 Constructing the HW tree for constant reversion speed and
volatility 289
13.5 Best fit calibration of the one dimensional HW model to market
data 295
13.6 The two dimensional formulation of the HW model 301
13.7 Calibrating a two factor HW model 306
13.8 Numerical implementation 308
13.9 Conclusions 311
Appendix 13.1 312
14 The Longstaff and Schwartz model 313
14.1 Motivation 313
14.2 The LS economy 314
14.3 The PDE obeyed by contingent claims 315
14.4 The dynamics of the transformed variables r and V 316
14.5 The equilibrium term structure 320
14.6 Term structure of volatilities 321
14.7 Correlation between rates 323
14.8 Option pricing 325
14.9 Calibrating the LS model 327
14.10 Fitting the yield curve using the implied approach 328
14.11 Tests of the joint dynamics using the implied approach 332
14.12 Calibration to the yield curve using the historical approach 337
14.13 Conclusions 339
Contents xi
15 The Brennan and Schwartz model 341
15.1 Introduction 341
15.2 The condition of no arbitrage and the market price of long yield
risk 342
15.3 The specific model 345
15.4 Conclusions 351
16 A class of arbitrage free log normal short rate two factor
models 353
16.1 Introduction and motivation 353
16.2 Description of the model 355
16.3 Implementation and numerical issues 358
16.4 Calibration and parametrisation 361
16.5 Computational results 364
16.6 Conclusions 367
Appendix 16.1 368
17 The Heath Jarrow and Morton approach 371
17.1 Introduction 371
17.2 The HJM approach 373
17.3 Specifications of the HJM model consistent with log normal bond
prices or forward rates 378
17.4 General constraints on the volatilities of discount bond prices 380
17.5 The process for the short rate 384
17.6 Conclusions 389
18 The Brace Gatarek Musiela/Jamshidian approach 393
18.1 Observable and unobservable state variables 393
18.2 The discretely compounded money market account — forward
rates 395
18.3 The discretely compounded money market account — swap
rates 399
18.4 The choice of the most suitable pricing framework 402
18.5 Do models still exist? 406
PART FIVE GENERAL TOPICS 411
19 Affine models 413
19.1 Definition of affine models 413
19.2 Time homogeneous affine models 414
xii Contents
19.3 Time inhomogeneous affine models 418
19.4 General considerations 420
20 Markovian and non Markovian interest rate models 423
20.1 Definition of Markovian rate processes 423
20.2 Conditions for the rate process to be Markovian 425
20.3 Non Markovian models on recombining trees 428
20.4 Implications for the choice of interest rate models 429
21 Calibration to cap prices of mean reverting log normal short rate
models 435
21.1 Introduction 435
21.2 Statement of the problem 436
21.3 The unconditional variance of the short rate in BDT — the discrete
case 437
21.4 The unconditional variance of the short rate in BDT — the continuous
time equivalent 440
21.5 Extension to two factor approaches 441
21.6 Conclusions 443
Appendix 21.1 444
Appendix A Elements of probability and stochastic calculus 447
A.I Fundamental results and definitions about set theory 447
A.2 Fundamental probabilistic definitions 448
A.3 Representing the flow of information 452
A.4 Brownian motions and random walks 466
A.5 Martingales and Ito integrals 474
A.6 Ito s lemma and the rules of stochastic differentiation 481
A.7 The link between stochastic differential equations (SDEs) and
parabolic partial differential equations (PDEs) 485
A.8 Switching between measures — the Radon Nikodym derivative and
Girsanov s theorem 486
Appendix B The securities market 491
B.I Prices and strategies 491
B.2 Definition of arbitrage in a discrete complete market 496
B.3 Replication of contingent claims 502
Bibliography 509
Index 515
|
| any_adam_object | 1 |
| author | Rebonato, Riccardo |
| author_GND | (DE-588)142802816 |
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| building | Verbundindex |
| bvnumber | BV013392496 |
| callnumber-first | H - Social Science |
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| callnumber-raw | HG6024.5 |
| callnumber-search | HG6024.5 |
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| callnumber-subject | HG - Finance |
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| ctrlnum | (OCoLC)38002568 (DE-599)BVBBV013392496 |
| dewey-full | 332.63/23 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
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| dewey-search | 332.63/23 |
| dewey-sort | 3332.63 223 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013392496 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:45:03Z |
| institution | BVB |
| isbn | 0471979589 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009135996 |
| oclc_num | 38002568 |
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| owner_facet | DE-91G DE-BY-TUM DE-83 DE-11 DE-188 DE-473 DE-BY-UBG |
| physical | XXIII, 521 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in financial engineering |
| spelling | Rebonato, Riccardo Verfasser (DE-588)142802816 aut Interest rate option models understanding, analysing and using models for exotic interest rate options Riccardo Rebonato 2. ed. Chichester [u.a.] Wiley 1998 XXIII, 521 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in financial engineering Futures gtt Marchés à terme de taux d'intérêt - Modèles mathématiques ram Optiehandel gtt Options (finances) - Modèles mathématiques ram Taux d'intérêt - Modèles mathématiques ram Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Options (Finance) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Entwicklung (DE-588)4113450-3 gnd rswk-swf Kapitalmarkt (DE-588)4029578-3 gnd rswk-swf Zinsoption (DE-588)4234822-5 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Zins (DE-588)4067845-3 gnd rswk-swf Zinsoption (DE-588)4234822-5 s Derivat Wertpapier (DE-588)4381572-8 s Optionspreistheorie (DE-588)4135346-8 s DE-188 Kapitalmarkt (DE-588)4029578-3 s Zins (DE-588)4067845-3 s Entwicklung (DE-588)4113450-3 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009135996&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rebonato, Riccardo Interest rate option models understanding, analysing and using models for exotic interest rate options Futures gtt Marchés à terme de taux d'intérêt - Modèles mathématiques ram Optiehandel gtt Options (finances) - Modèles mathématiques ram Taux d'intérêt - Modèles mathématiques ram Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Options (Finance) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Entwicklung (DE-588)4113450-3 gnd Kapitalmarkt (DE-588)4029578-3 gnd Zinsoption (DE-588)4234822-5 gnd Optionspreistheorie (DE-588)4135346-8 gnd Zins (DE-588)4067845-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4381572-8 (DE-588)4113450-3 (DE-588)4029578-3 (DE-588)4234822-5 (DE-588)4135346-8 (DE-588)4067845-3 |
| title | Interest rate option models understanding, analysing and using models for exotic interest rate options |
| title_auth | Interest rate option models understanding, analysing and using models for exotic interest rate options |
| title_exact_search | Interest rate option models understanding, analysing and using models for exotic interest rate options |
| title_full | Interest rate option models understanding, analysing and using models for exotic interest rate options Riccardo Rebonato |
| title_fullStr | Interest rate option models understanding, analysing and using models for exotic interest rate options Riccardo Rebonato |
| title_full_unstemmed | Interest rate option models understanding, analysing and using models for exotic interest rate options Riccardo Rebonato |
| title_short | Interest rate option models |
| title_sort | interest rate option models understanding analysing and using models for exotic interest rate options |
| title_sub | understanding, analysing and using models for exotic interest rate options |
| topic | Futures gtt Marchés à terme de taux d'intérêt - Modèles mathématiques ram Optiehandel gtt Options (finances) - Modèles mathématiques ram Taux d'intérêt - Modèles mathématiques ram Wiskundige modellen gtt Mathematisches Modell Interest rate futures Mathematical models Options (Finance) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Entwicklung (DE-588)4113450-3 gnd Kapitalmarkt (DE-588)4029578-3 gnd Zinsoption (DE-588)4234822-5 gnd Optionspreistheorie (DE-588)4135346-8 gnd Zins (DE-588)4067845-3 gnd |
| topic_facet | Futures Marchés à terme de taux d'intérêt - Modèles mathématiques Optiehandel Options (finances) - Modèles mathématiques Taux d'intérêt - Modèles mathématiques Wiskundige modellen Mathematisches Modell Interest rate futures Mathematical models Options (Finance) Mathematical models Derivat Wertpapier Entwicklung Kapitalmarkt Zinsoption Optionspreistheorie Zins |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009135996&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rebonatoriccardo interestrateoptionmodelsunderstandinganalysingandusingmodelsforexoticinterestrateoptions |