Tools for computational finance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 283 - 292 |
| Beschreibung: | XXI, 332 S. graph. Darst. |
| ISBN: | 9783540929284 |
Internformat
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| 245 | 1 | 0 | |a Tools for computational finance |c Rüdiger U. Seydel |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XXI, 332 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. 283 - 292 | ||
| 650 | 4 | |a Black-Scholes-Modell - Optionspreistheorie | |
| 650 | 7 | |a Finanzmathematik |2 stw | |
| 650 | 7 | |a Optionspreistheorie |2 stw | |
| 650 | 7 | |a Simulation |2 stw | |
| 650 | 7 | |a Stochastischer Prozess |2 stw | |
| 650 | 7 | |a Theorie |2 stw | |
| 650 | 7 | |a Wertpapieranalyse |2 stw | |
| 650 | 0 | 7 | |a Optionspreistheorie |0 (DE-588)4135346-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804138697793208320 |
|---|---|
| adam_text | Contents
Prefaces
....................................................
V
Contents
....................................................
XV
Notations
...................................................
XIX
Chapter
1
Modeling Tools for Financial Options
.......... 1
1.1
Options
............................................. 1
1.2
Model of the Financial Market
......................... 8
1.3
Numerical Methods
................................... 11
1.4
The Binomial Method
................................. 14
1.5
Risk-Neutral Valuation
................................ 23
1.6
Stochastic Processes
.................................. 26
1.6.1
Wiener Process
................................. 28
1.6.2
Stochastic Integral
.............................. 30
1.7
Diffusion Models
...................................... 33
1.7.1
Ito
Process
.................................... 33
1.7.2
Geometric Brownian Motion
..................... 36
1.7.3
Risk-Neutral Valuation
.......................... 37
1.7.4
Mean Reversion
................................ 39
1.7.5
Vector-Valued SDEs
............................ 41
1.8
Ito
Lemma and Applications
........................... 42
1.8.1
Ito
Lemma
.................................... 42
1.8.2
Consequences for Stocks and Options
............. 43
1.8.3
Integral Representation
.......................... 45
1.8.4
Bermudán
Options
.............................. 46
1.8.5
Empirical Tests
................................ 47
1.9
Jump Models
........................................ 49
1.10
Calibration
.......................................... 53
Notes and Comments
...................................... 56
Exercises
................................................. 60
Chapter
2
Generating Random Numbers with Specified
Distributions
............................................... 69
2.1
Uniform Deviates
..................................... 70
2.1.1
Linear Congruential Generators
.................. 70
XV
XVI Contents
2.1.2
Quality of Generators
........................... 71
2.1.3
Random Vectors and Lattice Structure
............ 72
2.1.4
Fibonacci Generators
........................... 75
2.2
Extending to Random Variables From Other Distributions
. 77
2.2.1
Inversion
...................................... 77
2.2.2
Transformations in H1
.......................... 78
2.2.3
Transformation in
Ж™
........................... 80
2.3
Normally Distributed Random Variables
................. 80
2.3.1
Method of Box and
Muller
....................... 80
2.3.2
Variant of Marsaglia
............................ 82
2.3.3
Correlated Random Variables
.................... 83
2.4
Monte Carlo Integration
............................... 85
2.5
Sequences of Numbers with Low Discrepancy
............. 88
2.5.1
Discrepancy
.................................... 88
2.5.2
Examples of Low-Discrepancy Sequences
.......... 90
Notes and Comments
...................................... 93
Exercises
................................................. 95
Chapter
3
Monte Carlo Simulation with Stochastic
Differential Equations
...................................... 101
3.1
Approximation Error
.................................. 102
3.2
Stochastic Taylor Expansion
........................... 106
3.3
Examples of Numerical Methods
........................ 109
3.4
Intermediate Values
................................... 112
3.5
Monte Carlo Simulation
............................... 113
3.5.1
Integral Representation
.......................... 114
3.5.2
Basic Version for European Options
............... 115
3.5.3
Bias
.......................................... 118
3.5.4
Variance Reduction
............................. 119
3.5.5
Application to an Exotic Option
.................. 123
3.6
Monte Carlo Methods for American Options
............. 126
3.6.1
Stopping Time
................................. 126
3.6.2
Parametric Methods
............................ 128
3.6.3
Regression Methods
............................. 130
3.6.4
Other Methods, and Further Hints
................ 132
Notes and Comments
...................................... 134
Exercises
................................................. 137
Chapter
4
Standard Methods for Standard Options
....... 141
4.1
Preparations
......................................... 142
4.2
Foundations of Finite-Difference Methods
................ 144
4.2.1
Difference Approximation
................ 144
4.2.2
The Grid
.....................
. . . . . . . . . . .У. . . . .
145
4.2.3
Explicit Method
................................ 146
Contents XVII
4.2.4
Stability
....................................... 148
4.2.5
An Implicit Method
............................. 151
4.3
Crank-Nicolson Method
............................... 153
4.4
Boundary Conditions
.................................. 156
4.5
American Options as Free Boundary Problems
........... 158
4.5.1
Early-Exercise Curve
............................ 159
4.5.2
Free Boundary Problem
......................... 161
4.5.3
Black-Scholes Inequality
......................... 164
4.5.4
Obstacle Problem
............................... 166
4.5.5
Linear Complementarity for American Put Options
. 167
4.6
Computation of American Options
...................... 168
4.6.1
Discretization with Finite Differences
............. 169
4.6.2
Reformulation and Analysis of the LCP
........... 171
4.6.3
An Algorithm for Calculating American Options
.... 174
4.7
On the Accuracy
..................................... 178
4.7.1
Elementary Error Control
....................... 179
4.7.2
Extrapolation
.................................. 182
4.8
Analytic Methods
..................................... 184
4.8.1
Approximation Based on Interpolation
............ 185
4.8.2
Quadratic Approximation
........................ 188
4.8.3
Analytic Method of Lines
........................ 190
Notes and Comments
...................................... 192
Exercises
................................................. 197
Chapter
5
Finite-Element Methods
....................... 203
5.1
Weighted Residuals
................................... 204
5.1.1
The Principle of Weighted Residuals
.............. 205
5.1.2
Examples of Weighting Functions
................. 207
5.1.3
Examples of Basis Functions
..................... 208
5.2
Galerkin Approach with Hat Functions
.................. 209
5.2.1
Hat Functions
.................................. 209
5.2.2
Assembling
.................................... 211
5.2.3
A Simple Application
........................... 213
5.3
Application to Standard Options
....................... 214
5.3.1
European Options
.............................. 215
5.3.2
Variational Form of the Obstacle Problem
......... 216
5.3.3
American Options
.............................. 217
5.4
Application to an Exotic Call Option
.................... 222
5.5
Error Estimates
...................................... 225
5.5.1
Strong and Weak Solutions
...................... 226
5.5.2
Approximation on Finite-Dimensional Subspaces
. .. 228
5.5.3
Céa s
Lemma
.................................. 229
Notes and Comments
...................................... 232
Exercises
................................................. 233
XVIII
Contents
Chapter
6
Pricing of Exotic Options
...................... 235
6.1
Exotic Options
....................................... 236
6.2
Options Depending on Several Assets
................... 237
6.3
Asian Options
........................................ 240
6.3.1
The Payoff
..................................... 240
6.3.2
Modeling in the Black-Scholes Framework
......... 241
6.3.3
Reduction to a One-Dimensional Equation
......... 242
6.3.4
Discrete Monitoring
............................. 245
6.4
Numerical Aspects
.................................... 248
6.4.1
Convection-Diffusion Problems
................... 248
6.4.2 Von
Neumann Stability Analysis
................. 251
6.5
Upwind Schemes and Other Methods
.................... 253
6.5.1
Upwind Scheme
................................ 253
6.5.2
Dispersion
..................................... 256
6.6
High-Resolution Methods
.............................. 258
6.6.1
Lax-Wendroff Method
........................... 258
6.6.2
Total Variation Diminishing
...................... 259
6.6.3
Numerical Dissipation
........................... 260
Notes and Comments
...................................... 262
Exercises
................................................. 263
Appendices
................................................. 265
A Financial Derivatives
.................................. 265
Al
Investment and Risk
............................ 265
A2 Financial Derivatives
............................ 266
A3
Forwards and the No-Arbitrage Principle
.......... 269
A4
The Black-Scholes Equation
...................... 270
A5 Early-Exercise Curve
............................ 275
В
Stochastic Tools
...................................... 279
Bl Essentials of Stochastics
......................... 279
B2 Advanced Topics
............................... 283
B3 State-Price Process
............................. 286
B4 Levy Processes
................................. 289
С
Numerical Methods
................................... 291
Cl Basic Numerical Tools
........................... 291
C2 Iterative Methods for Ax
=
b
..................... 296
C3 Function Spaces
................................ 299
C4 Minimization
................................... 301
D
Complementary Material
.............................. 305
Dl Bounds for Options
............................. 305
D2 Approximation Formula
......................... 307
D3 Software
....................................... 309
References
.................................................. 311
Index
....................................................... 325
|
| any_adam_object | 1 |
| author | Seydel, Rüdiger 1947- |
| author_GND | (DE-588)13662782X |
| author_facet | Seydel, Rüdiger 1947- |
| author_role | aut |
| author_sort | Seydel, Rüdiger 1947- |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV035369915 |
| classification_rvk | QK 660 SK 980 |
| classification_tum | MAT 620f WIR 160f |
| ctrlnum | (OCoLC)309392354 (DE-599)BVBBV035369915 |
| dewey-full | 332.6322830285 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.6322830285 |
| dewey-search | 332.6322830285 |
| dewey-sort | 3332.6322830285 |
| dewey-tens | 330 - Economics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV035369915 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:32:19Z |
| institution | BVB |
| isbn | 9783540929284 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017173824 |
| oclc_num | 309392354 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-945 DE-29T DE-473 DE-BY-UBG DE-384 DE-91G DE-BY-TUM DE-11 DE-634 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-945 DE-29T DE-473 DE-BY-UBG DE-384 DE-91G DE-BY-TUM DE-11 DE-634 DE-188 |
| physical | XXI, 332 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Seydel, Rüdiger 1947- Verfasser (DE-588)13662782X aut Tools for computational finance Rüdiger U. Seydel 4. ed. Berlin [u.a.] Springer 2009 XXI, 332 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 283 - 292 Black-Scholes-Modell - Optionspreistheorie Finanzmathematik stw Optionspreistheorie stw Simulation stw Stochastischer Prozess stw Theorie stw Wertpapieranalyse stw Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Wertpapieranalyse (DE-588)4124458-8 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 s Optionspreistheorie (DE-588)4135346-8 s DE-604 Wertpapieranalyse (DE-588)4124458-8 s Stochastisches Modell (DE-588)4057633-4 s 1\p DE-604 Finanzmathematik (DE-588)4017195-4 s Derivat Wertpapier (DE-588)4381572-8 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-3-540-92929-1 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2789415&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173824&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Seydel, Rüdiger 1947- Tools for computational finance Black-Scholes-Modell - Optionspreistheorie Finanzmathematik stw Optionspreistheorie stw Simulation stw Stochastischer Prozess stw Theorie stw Wertpapieranalyse stw Optionspreistheorie (DE-588)4135346-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd Wertpapieranalyse (DE-588)4124458-8 gnd |
| subject_GND | (DE-588)4135346-8 (DE-588)4017195-4 (DE-588)4381572-8 (DE-588)4206283-4 (DE-588)4057633-4 (DE-588)4124458-8 |
| 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 U. Seydel |
| title_fullStr | Tools for computational finance Rüdiger U. Seydel |
| title_full_unstemmed | Tools for computational finance Rüdiger U. Seydel |
| title_short | Tools for computational finance |
| title_sort | tools for computational finance |
| topic | Black-Scholes-Modell - Optionspreistheorie Finanzmathematik stw Optionspreistheorie stw Simulation stw Stochastischer Prozess stw Theorie stw Wertpapieranalyse stw Optionspreistheorie (DE-588)4135346-8 gnd Finanzmathematik (DE-588)4017195-4 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Stochastisches Modell (DE-588)4057633-4 gnd Wertpapieranalyse (DE-588)4124458-8 gnd |
| topic_facet | Black-Scholes-Modell - Optionspreistheorie Finanzmathematik Optionspreistheorie Simulation Stochastischer Prozess Theorie Wertpapieranalyse Derivat Wertpapier Black-Scholes-Modell Stochastisches Modell |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2789415&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173824&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT seydelrudiger toolsforcomputationalfinance |