An introduction to exotic option pricing:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
CRC Press
2012
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| Series: | Chapman & Hall/CRC financial mathematics series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 269 - 273 |
| Physical Description: | XVII, 278 S. graph. Darst. |
| ISBN: | 9781420091007 142009100X |
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MARC
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| 245 | 1 | 0 | |a An introduction to exotic option pricing |c Peter Buchen |
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| adam_text | Titel: An introduction to exotic option pricing
Autor: Buchen, Peter W
Jahr: 2012
Contents
List of Figures xi
Symbols and Abbreviations xiii
Preface xv
Part I Technical Background 1
1 Financial Preliminaries 3
1.1 European Derivative Securities ........................................4
1.2 Exotic Options ..........................................................5
1.3 Binary Options ..........................................................6
1.4 No-Arbitrage ............................................................7
1.4.1 The Law of One Price..........................................8
1.4.2 The Principle of Static Replication............................8
1.4.3 Parity Relations..................................................11
1.5 Pricing Methods ........................................................12
1.6 The Black-Scholes PDE Method ......................................12
1.7 Derivation of Black-Scholes PDE ......................................15
1.8 Meaning of the Black-Scholes PDE....................................16
1.8.1 Other Derivatives and the BS-PDE............................18
1.9 The Fundamental Theorem of Asset Pricing ..........................19
1.10 The EMM Pricing Method..............................................24
1.10.1 The Martingale Restriction ....................................25
1.11 Black-Scholes and the FTAP ..........................................27
1.12 Effect of Dividends ......................................................29
1.13 Summary ................................................................31
Exercise Problems..............................................................31
2 Mathematical Preliminaries 35
2.1 Probability Spaces ......................................................35
2.2 Brownian Motion ........................................................36
2.3 Stochastic DE s ..........................................................38
2.3.1 Arithmetic Brownian Motion ..................................39
2.4 Stochastic Integrals......................................................40
2.5 Itô s Lemma..............................................................41
2.5.1 Geometrical Brownian Motion..................................41
2.5.2 Itô s Product and Quotient Rules..............................42
2.6 Martingales ..............................................................42
2.6.1 Martingale Representation Theorem ..........................43
2.7 Feynman-Kac Formula..................................................44
2.8 Girsanov s Theorem ....................................................45
2.9 Time Varying Parameters ..............................................46
2.10 The Black-Scholes PDE ................................................47
2.11 The BS Green s Function ..............................................49
2.12 Log-Volutions ............................................................50
2.12.1 The Mellin Transform..........................................52
2.13 Summary ................................................................55
Exercise Problems..............................................................56
3 Gaussian Random Variables 61
3.1 Univariate Gaussian Random Variables................................61
3.2 Gaussian Shift Theorem ................................................63
3.3 Rescaled Gaussians ......................................................64
3.4 Gaussian Moments ......................................................65
3.4.1 Sums of Independent Gaussians................................65
3.5 Central Limit Theorem..................................................66
3.6 Log-Normal Distribution................................................66
3.7 Bivariate Normal ........................................................68
3.7.1 Gaussian Shift Theorem (Bivariate Case)......................69
3.8 Multi-Variate Gaussian Statistics ......................................70
3.9 Multi-Variate Gaussian Shift Theorem ................................71
3.10 Multi-Variate Itô s Lemma and BS-PDE ..............................72
3.11 Linear Transformations of Gaussian RVs..............................74
3.12 Summary ................................................................74
Exercise Problems..............................................................75
Part II Applications to Exotic Option Pricing 79
4 Simple Exotic Options 81
4.1 First-Order Binaries ....................................................82
4.2 BS-Prices for First-Order Asset and Bond Binaries ..................83
4.3 Parity Relation ..........................................................84
4.4 European Calls and Puts................................................85
4.5 Gap and Q-Options......................................................86
4.6 Capped Calls and Puts..................................................87
4.7 Range Forward Contracts ..............................................88
4.8 Turbo Binary ............................................................89
4.9 The Log-Contract........................................................89
4.10 Pay-at-Expiry and Money-Back Options ..............................91
4.11 Corporate Bonds ........................................................92
4.12 Binomial Trees ..........................................................95
4.13 Options on a Traded Account ..........................................101
4.14 Summary ................................................................103
Exercise Problems..............................................................104
5 Dual Expiry Options 107
5.1 Forward Start Calls and Puts ..........................................107
5.2 Second-Order Binaries ..................................................109
5.3 Second-Order Asset and Bond Binaries................................110
5.4 Second-Order Q-Options................................................112
5.5 Compound Options......................................................114
5.6 Chooser Options ........................................................116
5.7 Reset Options............................................................117
5.8 Simple Cliquet Option ..................................................119
5.9 Summary ................................................................121
Exercise Problems..............................................................122
6 Two-Asset Rainbow Options 125
6.1 Two-Asset Binaries......................................................126
6.2 The Exchange Option ..................................................129
6.3 Options on the Minimum/Maximum of Two Assets..................131
6.4 Product and Quotient Options ........................................133
6.5 ICIAM Option Competition ............................................135
6.6 Executive Stock Option ................................................138
6.7 Summary ................................................................139
Exercise Problems..............................................................140
7 Barrier Options 143
7.1 Introduction..............................................................143
7.2 Method of Images........................................................144
7.3 Barrier Parity Relations ................................................148
7.4 Equivalent Payoffs for Barrier Options ................................149
7.5 Call and Put Barrier Options ..........................................150
7.6 Barrier Option Rebates..................................................152
7.7 Barrier Option Extensions ..............................................154
7.8 Binomial Model for Barrier Options....................................155
7.9 Partial Time Barrier Options ..........................................157
7.9.1 Start-out, Partial Time Barrier Options......................157
7.9.2 End-out, Partial Time Barrier Options........................159
7.10 Double Barriers..........................................................160
7.10.1 Proof of Mol for Double Barrier Options......................162
7.10.2 Double Barrier Calls and Puts..................................166
7.11 Sequential Barrier Options..............................................168
7.12 Compound Barrier Options ............................................172
7.13 Outside Barrier Options ................................................177
7.14 Reflecting Barriers ......................................................179
7.15 Summary ................................................................185
Exercise Problems..............................................................187
8 Lookback Options 191
8.1 Introduction..............................................................191
8.2 Equivalent Payoffs for Lookback Options...............193
8.3 The Generic Lookback Options m(x,y,t) and M(x,z,t) ......196
8.4 The Standard Lookback Calls and Puts ...............198
8.5 Partial Price Lookback Options ........................................202
8.6 Partial Time Lookback Options ........................................203
8.7 Extreme Spread Options................................................206
8.8 Look-Barrier Options....................................................208
8.9 Summary ................................................................211
Exercise Problems..............................................................212
9 Asian Options 217
9.1 Introduction..............................................................217
9.2 Pricing Framework ......................................................218
9.3 Geometric Mean Asian Options ........................................220
9.4 FTAP Method for GM Asian Options ................221
9.4.1 GM Asian Calls and Puts...................223
9.5 PDE Method for GM Asian Options .................225
9.5.1 Fixed Strike GM Asian Calls .................225
9.5.2 Floating Strike GM Asian Calls................227
9.6 Discrete GM Asian Options ......................229
9.7 Summary ................................231
Exercise Problems...............................232
10 Exotic Multi-Options 235
10.1 Introduction...............................235
10.2 Matrix and Vector Notation ......................236
10.3 The M-Binary Payoff..........................240
10.4 Valuation of the M-Binary.......................243
10.5 Previous Results Revisited.......................247
10.6 Multi-Asset, 1-Period Asset and Bond Binaries ...........250
10.7 Quality Options.............................251
10.8 Compound Exchange Option .....................254
10.9 Multi-Asset Barrier Options ......................257
10.10 Summary ................................264
Exercise Problems...............................266
References 269
Index 275
|
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| author | Buchen, Peter W. |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV036477080 |
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| isbn | 9781420091007 142009100X |
| language | English |
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| physical | XVII, 278 S. graph. Darst. |
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| spelling | Buchen, Peter W. Verfasser (DE-588)171574109 aut An introduction to exotic option pricing Peter Buchen Boca Raton, FL [u.a.] CRC Press 2012 XVII, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Literaturverz.: S. 269 - 273 Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionsgeschäft (DE-588)4043670-6 gnd rswk-swf Optionsgeschäft (DE-588)4043670-6 s Finanzmathematik (DE-588)4017195-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020348665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchen, Peter W. An introduction to exotic option pricing Finanzmathematik (DE-588)4017195-4 gnd Optionsgeschäft (DE-588)4043670-6 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4043670-6 |
| title | An introduction to exotic option pricing |
| title_auth | An introduction to exotic option pricing |
| title_exact_search | An introduction to exotic option pricing |
| title_full | An introduction to exotic option pricing Peter Buchen |
| title_fullStr | An introduction to exotic option pricing Peter Buchen |
| title_full_unstemmed | An introduction to exotic option pricing Peter Buchen |
| title_short | An introduction to exotic option pricing |
| title_sort | an introduction to exotic option pricing |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Optionsgeschäft (DE-588)4043670-6 gnd |
| topic_facet | Finanzmathematik Optionsgeschäft |
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