Tools for computational finance:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 240 S. graph. Darst. |
| ISBN: | 3540406042 |
Staff View
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Record in the Search Index
| _version_ | 1804130290240585728 |
|---|---|
| adam_text | Riidiger Seydel
Tools for
Computational Finance
Second Edition
Springer
Contents
Prefaces V
Contents XI
Notation XV
Chapter 1 Modeling Tools for Financial Options 1
1 1 Options 1
1 2 Model of the Financial Market 7
1 3 Numerical Methods 10
1 4 The Binomial Method 12
1 5 Risk-Neutral Valuation 21
1 6 Stochastic Processes 24
161 Wiener Process 26
162 Stochastic Integral 28
1 7 Stochastic Differential Equations 31
171 Ito Process 31
172 Application to the Stock Market 34
1 8 Ito Lemma and Implications 38
1 9 Jump Processes 42
Notes and Comments 46
Exercises 49
Chapter 2 Generating Random Numbers with Specified
Distributions 57
2 1 Pseudo-Random Numbers 57
211 Linear Congruential Generators 58
212 Random Vectors 59
213 Fibonacci Generators 62
2 2 Transformed Random Variables 63
221 Inversion 64
222 Transformation in R1 66
223 Transformation in R n 67
2 3 Normally Distributed Random Variables 68
231 Method of Box and Muller 68
232 Variant of Marsaglia 69
XII Contents
233 Correlated Random Variables 70
2 4 Sequences of Numbers with Low Discrepancy 72
241 Monte Carlo Integration 72
242 Discrepancy 73
243 Examples of Low-Discrepancy Sequences 76
Notes and Comments 78
Exercises 80
Chapter 3 Numerical Integration of Stochastic Differential
Equations 85
3 1 Approximation Error 86
3 2 Stochastic Taylor Expansion 89
3 3 Examples of Numerical Methods 92
3 4 Intermediate Values 95
3 5 Monte Carlo Simulation 96
351 The Basic Version 96
352 Variance Reduction 99
Notes and Comments 104
Exercises • 105
Chapter 4 Finite Differences and Standard Options 109
4 1 Preparations 110
4 2 Foundations of Finite-Difference Methods 112
421 Difference Approximation 112
422 The Grid 113
423 Explicit Method 114
424 Stability 116
425 Implicit Method 119
4 3 Crank-Nicolson Method 120
4 4 Boundary Conditions 123
4 5 American Options as Free Boundary-Value Problems 126
451 Free Boundary-Value Problems 126
452 Black-Scholes Inequality 130
453 Obstacle Problems 130
454 Linear Complementarity for American Put Options 133
4 6 Computation of American Options 134
461 Discretization with Finite Differences 135
462 Iterative Solution 136
463 Algorithm for Calculating American Options 138
4 7 On the Accuracy 142
Notes and Comments 146
Exercises 148
Contents XIII
Chapter 5 Finite-Element Methods 151
5 1 Weighted Residuals 152
511 The Principle of Weighted Residuals 153
512 Examples of Weighting Functions 154
513 Examples of Basis Functions 155
5 2 Galerkin Approach with Hat Functions 156
521 Hat Functions 157
522A Simple Application 159
5 3 Application to Standard Options 162
5 4 Error Estimates 166
541 Classical and Weak Solutions 166
542 Approximation on Finite-Dimensional Subspaces 168
543 Cea s Lemma 170
Notes and Comments 172
Exercises 173
Chapter 6 Pricing of Exotic Options 175
6 1 Exotic Options 176
6 2 Asian Options 178
621 The Payoff 178
622 Modeling in the Black-Scholes Framework 180
623 Reduction to a One-Dimensional Equation 181
624 Discrete Monitoring 183
6 3 Numerical Aspects 186
631 Convection-Diffusion Problems 187
632 Von Neumann Stability Analysis 189
6 4 Upwind Schemes and Other Methods 191
641 Upwind Scheme 191
642 Dispersion 194
6 5 High-Resolution Methods 195
651 The Lax-Wendroff Method 196
652 Total Variation Diminishing 197
653 Numerical Dissipation 198
Notes and Comments 199
Exercises 201
Appendices 203
Al Financial Derivatives 203
A2 Essentials of Stochastics 206
A3 The Black-Scholes Equation 210
A4 Numerical Methods 214
A5 Iterative Methods for Ax = b 218
A6 Function Spaces 220
A7 Complementary Formula 223
XIV Contents
References 227
Index 235
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| language | German |
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| spelling | Seydel, Rüdiger 1947- Verfasser (DE-588)13662782X aut Tools for computational finance Rüdiger Seydel 2. ed. Berlin [u.a.] Springer 2004 XVI, 240 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Black-Scholes-Modell - Optionspreistheorie Deutschland Finanzmathematik / Optionspreistheorie / Wertpapieranalyse / Stochastischer Prozess / Simulation / Theorie Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Wertpapieranalyse (DE-588)4124458-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Wertpapieranalyse (DE-588)4124458-8 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Finanzmathematik (DE-588)4017195-4 s Derivat Wertpapier (DE-588)4381572-8 s Optionspreistheorie (DE-588)4135346-8 s Black-Scholes-Modell (DE-588)4206283-4 s HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537601&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Seydel, Rüdiger 1947- Tools for computational finance Black-Scholes-Modell - Optionspreistheorie Deutschland Finanzmathematik / Optionspreistheorie / Wertpapieranalyse / Stochastischer Prozess / Simulation / Theorie Stochastisches Modell (DE-588)4057633-4 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
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| title | Tools for computational finance |
| title_auth | Tools for computational finance |
| title_exact_search | Tools for computational finance |
| title_full | Tools for computational finance Rüdiger Seydel |
| title_fullStr | Tools for computational finance Rüdiger Seydel |
| title_full_unstemmed | Tools for computational finance Rüdiger Seydel |
| title_short | Tools for computational finance |
| title_sort | tools for computational finance |
| topic | Black-Scholes-Modell - Optionspreistheorie Deutschland Finanzmathematik / Optionspreistheorie / Wertpapieranalyse / Stochastischer Prozess / Simulation / Theorie Stochastisches Modell (DE-588)4057633-4 gnd Wertpapieranalyse (DE-588)4124458-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Optionspreistheorie (DE-588)4135346-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd |
| topic_facet | Black-Scholes-Modell - Optionspreistheorie Deutschland Finanzmathematik / Optionspreistheorie / Wertpapieranalyse / Stochastischer Prozess / Simulation / Theorie Stochastisches Modell Wertpapieranalyse Finanzmathematik Optionspreistheorie Black-Scholes-Modell Derivat Wertpapier |
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