Computational methods for option pricing:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
2005
|
| Series: | Frontiers in applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 297 S. Ill., graph. Darst. |
| ISBN: | 0898715733 9780898715736 |
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MARC
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| 100 | 1 | |a Achdou, Yves |e Verfasser |0 (DE-588)140964363 |4 aut | |
| 245 | 1 | 0 | |a Computational methods for option pricing |c Yves Achdou, Olivier Pironneau |
| 264 | 1 | |a Philadelphia |b Society for Industrial and Applied Mathematics |c 2005 | |
| 300 | |a XVIII, 297 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Frontiers in applied mathematics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Options (Finances) - Prix - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Options (Finance) |x Prices |x Mathematical models | |
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| 650 | 0 | 7 | |a Optionspreis |0 (DE-588)4115453-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
List of Algorithms xiii
Preface xv
1 Option Pricing 1
1.1 Orientation 1
1.2 A Brief Introduction to Options 1
1.3 Constant Coefficients. The Black Scholes Formula 6
1.4 Monte Carlo Methods 8
1.5 Other Options 15
1.6 Complement: Binomial Trees 17
2 The Black Scholes Equation: Mathematical Analysis 23
2.1 Orientation 23
2.2 The Partial Differential Equation 24
2.3 Mathematical Analysis of the Black Scholes Equation
with Local Volatility 27
2.4 Barrier Options 43
2.5 Levy Driven Assets 44
2.6 Options on a Basket of Assets 46
2.7 Stochastic Volatility 48
3 Finite Differences 57
3.1 Finite Differences in Logarithmic Prices 57
3.2 Upwinding 71
3.3 Finite Differences in the Primitive Variables 76
3.4 Numerical Results 81
3.5 Which Variable Is Better? 83
3.6 Options on a Basket of Two Assets 83
3.7 An Asian Put with Fixed Strike 85
4 The Finite Element Method 95
4.1 Orientation 95
4.2 A Generic Problem 96
4.3 The Black Scholes Equation with Local Volatility 104
ix
x Contents
4.4 A Black Scholes Equation Solver in C++ 107
4.5 A Transparent Boundary Condition 110
4.6 Levy Driven Assets 114
4.7 Programs for Two Dimensional Cases 126
4.8 Programming in Dimension d 2 141
4.9 High Dimensions: An Introduction to Galerkin Methods
with Sparse Tensor Product Spaces 142
4.10 Appendix: The Full Program for Two Dimensional Black Scholes .... 146
5 Adaptive Mesh Refinement 151
5.1 The Black Scholes Equation and Some Discretizations 152
5.2 Error Indicators for the Black Scholes Equation 156
5.3 Conclusion 159
5.4 A Taste of the Software 159
5.5 Results 165
5.6 Mesh Adaption for a Put on a Basket of Two Assets 172
5.7 Appendix: Proofs 174
6 American Options 185
6.1 Introduction 185
6.2 The Variational Inequality 186
6.3 The Exercise Boundary 189
6.4 Discrete Approximations to the Variational Inequality 192
6.5 Solution Procedures 198
6.6 Results 208
6.7 More Complex American Options 209
7 Sensitivities and Calibration 219
7.1 Introduction 219
7.2 Automatic Differentiation of Computer Programs 219
7.3 Computation of Greeks 223
7.4 An Introduction to the Calibration of Volatility 228
7.5 Finite Dimensional Differentiable Optimization 230
7.6 Application: Calibration on a Basis of Solutions 234
7.7 Appendix 236
8 Calibration of Local Volatility with European Options 243
8.1 The Least Squares Problem 243
8.2 Which Space for r and Which Tychonoff Functional? 245
8.3 Existence of a Minimizer 247
8.4 The Gradient of J 248
8.5 The Discrete Problem 249
8.6 A Taste of the Program 251
8.7 Results 254
8.8 A Stochastic Control Approach 257
Contents xi
9 Calibration of Local Volatility with American Options 263
9.1 The Calibration Problem 263
9.2 A Penalized Problem 265
9.3 Necessary Optimality Conditions 268
9.4 Differentiability 274
9.5 Algorithm 275
9.6 Results 277
Bibliography 287
Index 295
xiv List of Algorithms
Algorithm 6.2 Free boundary localization 204
Algorithm 6.3 Primal dual active set algorithm 207
Algorithm 7.1 Automatic differentiation 220
Algorithm 7.2 AD 221
Algorithm 7.3 AD++ 221
Algorithm 7.4 A class for an unconstrained minimization problem 232
Algorithm 7.5 Computation of the gradient by automatic differentiation 232
Algorithm 7.6 Armijo s rule 233
Algorithm 7.7 Auxiliary function for Armijo s rule 233
Algorithm 7.8 Conjugate gradient with Armijo s rule 233
Algorithm 7.9 The ddouble library for automatic differentiation 236
Algorithm 7.10 The file ddouble.cpp 238
Algorithm 7.11 An example of automatic differentiation 241
Algorithm 8.1 Gradient 252
Algorithm 8.2 Backward loop: Adjoint problem 252
Algorithm 8.3 Formula (8.23) 253
Algorithm 9.1 Backward loop for the adjoint problem 276
|
| any_adam_object | 1 |
| author | Achdou, Yves Pironneau, Olivier 1945- |
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| callnumber-sort | HG 46024 A3 |
| callnumber-subject | HG - Finance |
| classification_rvk | SK 980 |
| classification_tum | WIR 170f |
| ctrlnum | (OCoLC)58791132 (DE-599)BVBBV019856969 |
| dewey-full | 332.64/53/01519 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64/53/01519 |
| dewey-search | 332.64/53/01519 |
| dewey-sort | 3332.64 253 41519 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV019856969 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:43Z |
| institution | BVB |
| isbn | 0898715733 9780898715736 |
| language | English |
| lccn | 2005046506 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013181547 |
| oclc_num | 58791132 |
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| physical | XVIII, 297 S. Ill., graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series2 | Frontiers in applied mathematics |
| spelling | Achdou, Yves Verfasser (DE-588)140964363 aut Computational methods for option pricing Yves Achdou, Olivier Pironneau Philadelphia Society for Industrial and Applied Mathematics 2005 XVIII, 297 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frontiers in applied mathematics Includes bibliographical references and index Options (Finances) - Prix - Modèles mathématiques Mathematisches Modell Options (Finance) Prices Mathematical models Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Optionspreis (DE-588)4115453-8 gnd rswk-swf Optionspreis (DE-588)4115453-8 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Pironneau, Olivier 1945- Verfasser (DE-588)110162900 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013181547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Achdou, Yves Pironneau, Olivier 1945- Computational methods for option pricing Options (Finances) - Prix - Modèles mathématiques Mathematisches Modell Options (Finance) Prices Mathematical models Numerische Mathematik (DE-588)4042805-9 gnd Optionspreis (DE-588)4115453-8 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4115453-8 |
| title | Computational methods for option pricing |
| title_auth | Computational methods for option pricing |
| title_exact_search | Computational methods for option pricing |
| title_full | Computational methods for option pricing Yves Achdou, Olivier Pironneau |
| title_fullStr | Computational methods for option pricing Yves Achdou, Olivier Pironneau |
| title_full_unstemmed | Computational methods for option pricing Yves Achdou, Olivier Pironneau |
| title_short | Computational methods for option pricing |
| title_sort | computational methods for option pricing |
| topic | Options (Finances) - Prix - Modèles mathématiques Mathematisches Modell Options (Finance) Prices Mathematical models Numerische Mathematik (DE-588)4042805-9 gnd Optionspreis (DE-588)4115453-8 gnd |
| topic_facet | Options (Finances) - Prix - Modèles mathématiques Mathematisches Modell Options (Finance) Prices Mathematical models Numerische Mathematik Optionspreis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013181547&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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