Exotic option pricing and advanced Lévy models:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2005
|
| Schriftenreihe: | Wilmott collection
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 320 S. graph. Darst. |
| ISBN: | 9780470016848 |
Internformat
MARC
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| 245 | 1 | 0 | |a Exotic option pricing and advanced Lévy models |c ed. by Andreas Kyprianou ... |
| 264 | 1 | |a Chichester |b Wiley |c 2005 | |
| 300 | |a XXII, 320 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wilmott collection | |
| 650 | 4 | |a Optionspreistheorie - Lévy-Prozess | |
| 650 | 4 | |a Optionspreistheorie / Statistische Methode | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Lévy processes | |
| 650 | 4 | |a Options (Finance) |x Prices |x Mathematical models | |
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| 700 | 1 | |a Kyprianou, Andreas E. |e Sonstige |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015677218 | ||
Datensatz im Suchindex
| _version_ | 1804136556382912512 |
|---|---|
| adam_text | Contents Contributors xi
Preface xiii
About the Editors xvii
About the Contributors xix
1 Levy Processes in Finance Distinguished by their Coarse and Fine Path
Properties 1
Andreas E. Kyprianou andR. Loeffen
1.1 Introduction 1
1.2 L6vy processes 2
1.3 Examples of Le vy processes in finance 4
1.3.1 Compound Poisson processes and jump-diffusions 5
1.3.2 Spectrally one-sided processes 6
1.3.3 Meixner processes 6
1.3.4 Generalized tempered stable processes and subclasses 7
1.3.5 Generalized hyperbolic processes and subclasses 9
1.4 Path properties 10
1.4.1 Path variation 10
1.4.2 Hitting points 12
1.4.3 Creeping 14
1.4.4 Regularity of the half line 16
1.5 Examples revisited 17
1.5.1 Compound Poisson processes and jump-diffusions 17
1.5.2 Spectrally negative processes 17
1.5.3 Meixner process 17
1.5.4 Generalized tempered stable process 19
1.5.5 Generalized hyperbolic process 23
1.6 Conclusions 24
References 26
vi Contents ^___ 2 Simulation Methods with Levy Processes 29
Nick Webber
2.1 Introduction 29
2.2 Modelling price and rate movements 30
2.2.1 Modelling with L6vy processes 30
2.2.2 Lattice methods 31
2.2.3 Simulation methods 32
2.3 A basis for a numerical approach 33
2.3.1 The subordinator approach to simulation 34
2.3.2 Applying the subordinator approach 35
2.4 Constructing bridges for Levy processes 36
2.4.1 Stratified sampling and bridge methods 36
2.4.2 Bridge sampling and the subordinator representation 37
2.5 Valuing discretely reset path-dependent options 39
2.6 Valuing continuously reset path-dependent options 40
2.6.1 Options on extreme values and simulation bias 42
2.6.2 Bias correction for Levy processes 43
2.6.3 Variation: exceedence probabilities 44
2.6.4 Application of the bias correction algorithm 45
2.7 Conclusions 48
References 48
3 Risks in Returns: A Pure Jump Perspective 51
Helyette Geman and Dilip B. Madan
3.1 Introduction 51
3.2 CGMY model details 54
3.3 Estimation details 57
3.3.1 Statistical estimation 58
3.3.2 Risk neutral estimation 59
3.3.3 Gap risk expectation and price 60
3.4 Estimation results 60
3.4.1 Statistical estimation results 61
3.4.2 Risk neutral estimation results 61
3.4.3 Results on gap risk expectation and price 61
3.5 Conclusions 63
References 65
4 Model Risk for Exotic and Moment Derivatives 67
Wim Schoutens, Erwin Simons andJurgen Tistaert
4.1 Introduction 67
4.2 The models 68
4.2.1 The Heston stochastic volatility model 69
4.2.2 The Heston stochastic volatility model with jumps 69
___ Contents vii
4.2.3 The Barndorff-Nielsen-Shephard model 70
4.2.4 L6 y models with stochastic time 71
4.3 Calibration 74
4.4 Simulation 78
4.4.1 NIG Le vy process 78
4.4.2 VG Levy process 79
4.4.3 CIR stochastic clock 79
4.4.4 Gamma-OU stochastic clock 79
4.4.5 Path generation for time-changed LeVy process 79
4.5 Pricing of exotic options 80
4.5.1 Exotic options 80
4.5.2 Exotic option prices 82
4.6 Pricing of moment derivatives 86
4.6.1 Moment swaps 89
4.6.2 Moment options 89
4.6.3 Hedging moment swaps 90
4.6.4 Pricing of moments swaps 91
4.6.5 Pricing of moments options 93
4.7 Conclusions 93
References 95
5 Symmetries and Pricing of Exotic Options in Levy Models 99
Ernst Eberlein andAntonis Papapantoleon
5.1 Introduction 99
5.2 Model and assumptions 100
5.3 General description of the method 105
5.4 Vanilla options 106
5.4.1 Symmetry 106
5.4.2 Valuation of European options 111
5.4.3 Valuation of American options 113
5.5 Exotic options 114
5.5.1 Symmetry 114
5.5.2 Valuation of barrier and lookback options 115
5.5.3 Valuation of Asian and basket options 117
5.6 Margrabe-type options 119
References 124
6 Static Hedging of Asian Options under Stochastic Volatility Models using
Fast Fourier Transform 129
Hansjorg Albrecher and Wim Schoutens
6.1 Introduction 129
6.2 Stochastic volatility models 131
6.2.1 The Heston stochastic volatility model 131
6.2.2 The Barndorff-Nielsen-Shephard model 132
6.2.3 Le y models with stochastic time 133
i
viii Contents 6.3 Static hedging of Asian options 136
6.4 Numerical implementation 138
6.4.1 Characteristic function inversion using FFT 138
6.4.2 Static hedging algorithm 140
6.5 Numerical illustration 140
6.5.1 Calibration of the model parameters 140
6.5.2 Performance of the hedging strategy 140
6.6 A model-independent static super-hedge 145
6.7 Conclusions 145
References 145
7 Impact of Market Crises on Real Options 149
Pauline Barrieu andNadine Bellamy
7.1 Introduction 149
7.2 The model 151
7.2.1 Notation 151
7.2.2 Consequence of the modelling choice 153
7.3 The real option characteristics 155
7.4 Optimal discount rate and average waiting time 156
7.4.1 Optimal discount rate 156
7.4.2 Average waiting time 157
7.5 Robustness of the investment decision characteristics 158
7.5.1 Robustness of the optimal time to invest 159
7.5.2 Random jump size 160
7.6 Continuous model versus discontinuous model 161
7.6.1 Error in the optimal profit-cost ratio 161
7.6.2 Error in the investment opportunity value 163
7.7 Conclusions 165
Appendix 165
References 167
8 Moment Derivatives and Levy-type Market Completion 169
Jose Manuel Corcuera, David Nualart and Wim Schoutens
8.1 Introduction 169
8.2 Market completion in the discrete-time setting 170
8.2.1 One-step trinomial market 170
8.2.2 One-step finite markets 172
8.2.3 Multi-step finite markets 173
8.2.4 Multi-step markets with general returns 174
8.2.5 Power-return assets 174
8.3 The Le y market 177
8.3.1 LeVy processes 177
8.3.2 The geometric L6vy model 178
8.3.3 Power-jump processes 178
Contents ix
8.4 Enlarging the L6vy market model 179
8.4.1 Martingale representation property 180
8.5 Arbitrage 183
8.5.1 Equivalent martingale measures 183
8.5.2 Example: a Brownian motion plus a finite number of Poisson pro¬
cesses 185
8.6 Optimal portfolios 186
8.6.1 Optimal wealth 187
8.6.2 Examples 188
References 192
9 Pricing Perpetual American Options Driven by Spectrally One-sided Levy
Processes 195
Terence Chan
9.1 Introduction 195
9.2 First-passage distributions and other results for spectrally positive LeVy
processes 198
9.3 Description of the model, basic definitions and notations 202
9.4 A renewal equation approach to pricing 204
9.5 Explicit pricing formulae for American puts 207
9.6 Some specific examples 209
Appendix: use of fast Fourier transform 213
References 214
Epilogue 215
Further references 215
10 On Asian Options of American Type 217
Goran Peskir and Nadia Uys
10.1 Introduction 217
10.2 Formulation of the problem 218
10.3 The result and proof 220
10.4 Remarks on numerics . 231
Appendix 233
References 234
11 Why be Backward? Forward Equations for American Options 237
Peter Carr and AH Hirsa
11.1 Introduction 237
11.2 Review of the backward free boundary problem 239
11.3 Stationarity and domain extension in the maturity direction 242
11.4 Additivity and domain extension in the strike direction 245
11.5 The forward free boundary problem 247
11.6 Summary and future research 250
x Contents Appendix: Discretization of forward equation for American options 251
References 257
12 Numerical Valuation of American Options Under the CGMY Process 259
Ariel Almendral
12.1 Introduction 259
12.2 The CGMY process as a L£vy process 260
12.2.1 Options in a L6vy market 261
12.3 Numerical valuation of the American CGMY price 263
12.3.1 Discretization and solution algorithm 263
12.4 Numerical experiments 270
Appendix: Analytic formula for European option prices 271
References 275
13 Convertible Bonds: Financial Derivatives of Game Type 277
Jan Kallsen and Christoph Kiihn
13.1 Introduction 277
13.2 No-arbitrage pricing for game contingent claims 279
13.2.1 Static no-arbitrage prices 279
13.2.2 No-arbitrage price processes 282
13.3 Convertible bonds 286
13.4 Conclusions 289
References 289
14 The Spread Option Optimal Stopping Game 293
Pavel V. Gapeev
14.1 Introduction 293
14.2 Formulation of the problem 294
14.3 Solution of the free-boundary problem 296
14.4 Main result and proof 299
14.5 Conclusions 302
References 304
Index 307
|
| adam_txt |
Contents Contributors xi
Preface xiii
About the Editors xvii
About the Contributors xix
1 Levy Processes in Finance Distinguished by their Coarse and Fine Path
Properties 1
Andreas E. Kyprianou andR. Loeffen
1.1 Introduction 1
1.2 L6vy processes 2
1.3 Examples of Le"vy processes in finance 4
1.3.1 Compound Poisson processes and jump-diffusions 5
1.3.2 Spectrally one-sided processes 6
1.3.3 Meixner processes 6
1.3.4 Generalized tempered stable processes and subclasses 7
1.3.5 Generalized hyperbolic processes and subclasses 9
1.4 Path properties 10
1.4.1 Path variation 10
1.4.2 Hitting points 12
1.4.3 Creeping 14
1.4.4 Regularity of the half line 16
1.5 Examples revisited 17
1.5.1 Compound Poisson processes and jump-diffusions 17
1.5.2 Spectrally negative processes 17
1.5.3 Meixner process 17
1.5.4 Generalized tempered stable process 19
1.5.5 Generalized hyperbolic process 23
1.6 Conclusions 24
References 26
vi Contents ^_ 2 Simulation Methods with Levy Processes 29
Nick Webber
2.1 Introduction 29
2.2 Modelling price and rate movements 30
2.2.1 Modelling with L6vy processes 30
2.2.2 Lattice methods 31
2.2.3 Simulation methods 32
2.3 A basis for a numerical approach 33
2.3.1 The subordinator approach to simulation 34
2.3.2 Applying the subordinator approach 35
2.4 Constructing bridges for Levy processes 36
2.4.1 Stratified sampling and bridge methods 36
2.4.2 Bridge sampling and the subordinator representation 37
2.5 Valuing discretely reset path-dependent options 39
2.6 Valuing continuously reset path-dependent options 40
2.6.1 Options on extreme values and simulation bias 42
2.6.2 Bias correction for Levy processes 43
2.6.3 Variation: exceedence probabilities 44
2.6.4 Application of the bias correction algorithm 45
2.7 Conclusions 48
References 48
3 Risks in Returns: A Pure Jump Perspective 51
Helyette Geman and Dilip B. Madan
3.1 Introduction 51
3.2 CGMY model details 54
3.3 Estimation details 57
3.3.1 Statistical estimation 58
3.3.2 Risk neutral estimation 59
3.3.3 Gap risk expectation and price 60
3.4 Estimation results 60
3.4.1 Statistical estimation results 61
3.4.2 Risk neutral estimation results 61
3.4.3 Results on gap risk expectation and price 61
3.5 Conclusions 63
References 65
4 Model Risk for Exotic and Moment Derivatives 67
Wim Schoutens, Erwin Simons andJurgen Tistaert
4.1 Introduction 67
4.2 The models 68
4.2.1 The Heston stochastic volatility model 69
4.2.2 The Heston stochastic volatility model with jumps 69
_ Contents vii
4.2.3 The Barndorff-Nielsen-Shephard model 70
4.2.4 L6\y models with stochastic time 71
4.3 Calibration 74
4.4 Simulation 78
4.4.1 NIG Le"vy process 78
4.4.2 VG Levy process 79
4.4.3 CIR stochastic clock 79
4.4.4 Gamma-OU stochastic clock 79
4.4.5 Path generation for time-changed LeVy process 79
4.5 Pricing of exotic options 80
4.5.1 Exotic options 80
4.5.2 Exotic option prices 82
4.6 Pricing of moment derivatives 86
4.6.1 Moment swaps 89
4.6.2 Moment options 89
4.6.3 Hedging moment swaps 90
4.6.4 Pricing of moments swaps 91
4.6.5 Pricing of moments options 93
4.7 Conclusions 93
References 95
5 Symmetries and Pricing of Exotic Options in Levy Models 99
Ernst Eberlein andAntonis Papapantoleon
5.1 Introduction 99
5.2 Model and assumptions 100
5.3 General description of the method 105
5.4 Vanilla options 106
5.4.1 Symmetry 106
5.4.2 Valuation of European options 111
5.4.3 Valuation of American options 113
5.5 Exotic options 114
5.5.1 Symmetry 114
5.5.2 Valuation of barrier and lookback options 115
5.5.3 Valuation of Asian and basket options 117
5.6 Margrabe-type options 119
References 124
6 Static Hedging of Asian Options under Stochastic Volatility Models using
Fast Fourier Transform 129
Hansjorg Albrecher and Wim Schoutens
6.1 Introduction 129
6.2 Stochastic volatility models 131
6.2.1 The Heston stochastic volatility model 131
6.2.2 The Barndorff-Nielsen-Shephard model 132
6.2.3 Le y models with stochastic time 133
i
viii Contents 6.3 Static hedging of Asian options 136
6.4 Numerical implementation 138
6.4.1 Characteristic function inversion using FFT 138
6.4.2 Static hedging algorithm 140
6.5 Numerical illustration 140
6.5.1 Calibration of the model parameters 140
6.5.2 Performance of the hedging strategy 140
6.6 A model-independent static super-hedge 145
6.7 Conclusions 145
References 145
7 Impact of Market Crises on Real Options 149
Pauline Barrieu andNadine Bellamy
7.1 Introduction 149
7.2 The model 151
7.2.1 Notation 151
7.2.2 Consequence of the modelling choice 153
7.3 The real option characteristics 155
7.4 Optimal discount rate and average waiting time 156
7.4.1 Optimal discount rate 156
7.4.2 Average waiting time 157
7.5 Robustness of the investment decision characteristics 158
7.5.1 Robustness of the optimal time to invest 159
7.5.2 Random jump size 160
7.6 Continuous model versus discontinuous model 161
7.6.1 Error in the optimal profit-cost ratio 161
7.6.2 Error in the investment opportunity value 163
7.7 Conclusions 165
Appendix 165
References 167
8 Moment Derivatives and Levy-type Market Completion 169
Jose Manuel Corcuera, David Nualart and Wim Schoutens
8.1 Introduction 169
8.2 Market completion in the discrete-time setting 170
8.2.1 One-step trinomial market 170
8.2.2 One-step finite markets 172
8.2.3 Multi-step finite markets 173
8.2.4 Multi-step markets with general returns 174
8.2.5 Power-return assets 174
8.3 The Le y market 177
8.3.1 LeVy processes 177
8.3.2 The geometric L6vy model 178
8.3.3 Power-jump processes 178
Contents ix
8.4 Enlarging the L6vy market model 179
8.4.1 Martingale representation property 180
8.5 Arbitrage 183
8.5.1 Equivalent martingale measures 183
8.5.2 Example: a Brownian motion plus a finite number of Poisson pro¬
cesses 185
8.6 Optimal portfolios 186
8.6.1 Optimal wealth 187
8.6.2 Examples 188
References 192
9 Pricing Perpetual American Options Driven by Spectrally One-sided Levy
Processes 195
Terence Chan
9.1 Introduction 195
9.2 First-passage distributions and other results for spectrally positive LeVy
processes 198
9.3 Description of the model, basic definitions and notations 202
9.4 A renewal equation approach to pricing 204
9.5 Explicit pricing formulae for American puts 207
9.6 Some specific examples 209
Appendix: use of fast Fourier transform 213
References 214
Epilogue 215
Further references 215
10 On Asian Options of American Type 217
Goran Peskir and Nadia Uys
10.1 Introduction 217
10.2 Formulation of the problem 218
10.3 The result and proof 220
10.4 Remarks on numerics . 231
Appendix 233
References 234
11 Why be Backward? Forward Equations for American Options 237
Peter Carr and AH Hirsa
11.1 Introduction 237
11.2 Review of the backward free boundary problem 239
11.3 Stationarity and domain extension in the maturity direction 242
11.4 Additivity and domain extension in the strike direction 245
11.5 The forward free boundary problem 247
11.6 Summary and future research 250
x Contents Appendix: Discretization of forward equation for American options 251
References 257
12 Numerical Valuation of American Options Under the CGMY Process 259
Ariel Almendral
12.1 Introduction 259
12.2 The CGMY process as a L£vy process 260
12.2.1 Options in a L6vy market 261
12.3 Numerical valuation of the American CGMY price 263
12.3.1 Discretization and solution algorithm 263
12.4 Numerical experiments 270
Appendix: Analytic formula for European option prices 271
References 275
13 Convertible Bonds: Financial Derivatives of Game Type 277
Jan Kallsen and Christoph Kiihn
13.1 Introduction 277
13.2 No-arbitrage pricing for game contingent claims 279
13.2.1 Static no-arbitrage prices 279
13.2.2 No-arbitrage price processes 282
13.3 Convertible bonds 286
13.4 Conclusions 289
References 289
14 The Spread Option Optimal Stopping Game 293
Pavel V. Gapeev
14.1 Introduction 293
14.2 Formulation of the problem 294
14.3 Solution of the free-boundary problem 296
14.4 Main result and proof 299
14.5 Conclusions 302
References 304
Index 307 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:44:04Z |
| indexdate | 2024-07-09T20:58:17Z |
| institution | BVB |
| isbn | 9780470016848 |
| language | English |
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| record_format | marc |
| series2 | Wilmott collection |
| spelling | Exotic option pricing and advanced Lévy models ed. by Andreas Kyprianou ... Chichester Wiley 2005 XXII, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wilmott collection Optionspreistheorie - Lévy-Prozess Optionspreistheorie / Statistische Methode Mathematisches Modell Lévy processes Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 s DE-604 Kyprianou, Andreas E. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Exotic option pricing and advanced Lévy models Optionspreistheorie - Lévy-Prozess Optionspreistheorie / Statistische Methode Mathematisches Modell Lévy processes Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4135346-8 |
| title | Exotic option pricing and advanced Lévy models |
| title_auth | Exotic option pricing and advanced Lévy models |
| title_exact_search | Exotic option pricing and advanced Lévy models |
| title_exact_search_txtP | Exotic option pricing and advanced Lévy models |
| title_full | Exotic option pricing and advanced Lévy models ed. by Andreas Kyprianou ... |
| title_fullStr | Exotic option pricing and advanced Lévy models ed. by Andreas Kyprianou ... |
| title_full_unstemmed | Exotic option pricing and advanced Lévy models ed. by Andreas Kyprianou ... |
| title_short | Exotic option pricing and advanced Lévy models |
| title_sort | exotic option pricing and advanced levy models |
| topic | Optionspreistheorie - Lévy-Prozess Optionspreistheorie / Statistische Methode Mathematisches Modell Lévy processes Options (Finance) Prices Mathematical models Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Optionspreistheorie - Lévy-Prozess Optionspreistheorie / Statistische Methode Mathematisches Modell Lévy processes Options (Finance) Prices Mathematical models Optionspreistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kyprianouandrease exoticoptionpricingandadvancedlevymodels |