Introduction to option pricing theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
[2000]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 268 Seiten |
| ISBN: | 3764341084 0817641084 |
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| 100 | 1 | |a Kallianpur, Gopinath |d 1925- |0 (DE-588)119075547 |4 aut | |
| 245 | 1 | 0 | |a Introduction to option pricing theory |c Gopinath Kallianpur ; Rajeeva L. Karandikar |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c [2000] | |
| 264 | 4 | |c © 2000 | |
| 300 | |a x, 268 Seiten | ||
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| 650 | 4 | |a Optionspreistheorie - Stochastische Analysis | |
| 650 | 4 | |a Optionspreistheorie / Theorie | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Options (Finance) -- Prices -- Mathematical models | |
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Record in the Search Index
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Contents
Preface ix
1 Stochastic Integration 1
1.1 Notation and definitions 1
1.2 The predictable a field 5
1.3 The Ito integral 6
1.4 Quadratic variation of a continuous martingale 19
1.5 The stochastic integral w.r.t. continuous local martingales 26
1.6 Stochastic integral w.r.t. continuous semimartingales 32
1.7 Integration w.r.t. semimartingales 38
2 Ito's Formula and its Applications 47
2.1 Preliminaries 47
2.2 Ito's formula for continuous semimartingales 51
2.3 Ito's formula for r.c.1.1. semimartingales 54
2.4 Applications 56
2.5 Application to geometric Brownian motion 62
2.6 Local time and the Tanaka formula 62
2.7 Brownian motion and the heat equation 63
3 Representation of Square Integrable Martingales 71
3.1 The Ito representation 71
3.2 The Kunita Watanabe representation 74
vi Contents
4 Stochastic Differential Equations 79
4.1 Preliminaries 79
4.2 Existence and uniqueness of solutions 81
4.3 The Feynman Kac formula 91
4.4 The Ornstein Uhlenbeck process (O.U.P) 93
5 Girsanov's Theorem 95
5.1 Auxiliary results 95
5.2 Girsanov's Theorem 98
6 Option Pricing in Discrete Time 103
6.1 Arbitrage opportunities 103
6.2 Option pricing: an example 109
6.3 European call option Ill
6.4 Complete markets 114
6.5 The American option 117
7 Introduction to Continuous Time Trading 123
7.1 Introduction 123
7.2 A general model 125
7.3 Trading strategies and arbitrage opportunities 126
7.4 Examples 133
7.5 Contingent claims and complete markets 134
8 Arbitrage and Equivalent Martingale Measures 137
8.1 Introduction 137
8.2 Necessary and sufficient conditions for NA 139
8.3 A general model of stock prices 147
8.4 The separation theorem 151
8.5 Orlicz spaces 155
8.6 No arbitrage with controlled risk 157
8.7 Fractional Brownian motion (1/2 H 1)
and existence of arbitrage opportunities 161
8.8 Extension to geometric Gladyshev processes 165
9 Complete Markets 169
9.1 Definition 169
9.2 Representation of martingales 172
9.3 Examples of complete markets 177
9.3.1 Geometric Brownian motion (GBM) 177
9.3.2 Diffusion model for stock prices 179
9.4 Equivalent martingale measures 180
9.5 Incomplete markets 183
9.6 Completeness and underlying filtration 187
Contents vii
10 Black and Scholes Theory 191
10.1 Preliminaries 191
10.2 The Black Scholes PDE 194
10.3 Explicit solution of the Black Scholes PDE 195
10.4 The Black Scholes formula 199
10.5 Diffusion model 201
11 Discrete Approximations 205
11.1 The binomial model 205
11.2 A binomial Feynman Kac formula 207
11.3 Approximation of the Black Scholes PDE 208
11.4 Approximation to the Black Scholes formula 211
12 The American Options 215
12.1 Model 215
12.2 Upper and lower bounds 217
12.3 American claims in complete markets 220
13 Asset Pricing with Stochastic Volatility 225
13.1 Introduction 225
13.2 Incompleteness of the market 226
13.3 Asymptotic analysis for models with two scales 232
13.4 Filtering of the stochastic volatility 235
13.5 PDE when 5 is observed 239
14 The Russian Options 241
14.1 Introduction and background 241
14.2 The Russian put option 243
14.3 A free boundary problem for the put option 243
14.4 Proofs of the lemmas 250
14.5 The Russian call option (or the option for selling short) 255
14.6 The F.B.P. for the call option 255
References 265
Index 269 |
| any_adam_object | 1 |
| author | Kallianpur, Gopinath 1925- Karandikar, Rajeeva L. 1956- |
| author_GND | (DE-588)119075547 (DE-588)121730425 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Kallianpur, Gopinath 1925- (DE-588)119075547 aut Introduction to option pricing theory Gopinath Kallianpur ; Rajeeva L. Karandikar Boston [u.a.] Birkhäuser [2000] © 2000 x, 268 Seiten txt rdacontent n rdamedia nc rdacarrier Optionspreistheorie - Stochastische Analysis Optionspreistheorie / Theorie Mathematisches Modell Options (Finance) -- Prices -- Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Preistheorie (DE-588)4115623-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Preistheorie (DE-588)4115623-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Optionspreistheorie (DE-588)4135346-8 s Stochastische Analysis (DE-588)4132272-1 s DE-188 Karandikar, Rajeeva L. 1956- (DE-588)121730425 aut Erscheint auch als Online-Ausgabe 978-1-4612-0511-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008673953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kallianpur, Gopinath 1925- Karandikar, Rajeeva L. 1956- Introduction to option pricing theory Optionspreistheorie - Stochastische Analysis Optionspreistheorie / Theorie Mathematisches Modell Options (Finance) -- Prices -- Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd Optionspreistheorie (DE-588)4135346-8 gnd Preistheorie (DE-588)4115623-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4135346-8 (DE-588)4115623-7 (DE-588)4114528-8 |
| title | Introduction to option pricing theory |
| title_auth | Introduction to option pricing theory |
| title_exact_search | Introduction to option pricing theory |
| title_full | Introduction to option pricing theory Gopinath Kallianpur ; Rajeeva L. Karandikar |
| title_fullStr | Introduction to option pricing theory Gopinath Kallianpur ; Rajeeva L. Karandikar |
| title_full_unstemmed | Introduction to option pricing theory Gopinath Kallianpur ; Rajeeva L. Karandikar |
| title_short | Introduction to option pricing theory |
| title_sort | introduction to option pricing theory |
| topic | Optionspreistheorie - Stochastische Analysis Optionspreistheorie / Theorie Mathematisches Modell Options (Finance) -- Prices -- Mathematical models Stochastische Analysis (DE-588)4132272-1 gnd Optionspreistheorie (DE-588)4135346-8 gnd Preistheorie (DE-588)4115623-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Optionspreistheorie - Stochastische Analysis Optionspreistheorie / Theorie Mathematisches Modell Options (Finance) -- Prices -- Mathematical models Stochastische Analysis Optionspreistheorie Preistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008673953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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