Financial engineering with finite elements:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2005
|
| Schriftenreihe: | Wiley finance series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 360 S. Ill., graph. Darst. |
Internformat
MARC
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| 300 | |a XVIII, 360 S. |b Ill., graph. Darst. | ||
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| 650 | 7 | |a Modèle économétrique |2 rasuqam | |
| 650 | 7 | |a Méthode des éléments finis |2 rasuqam | |
| 650 | 7 | |a Opties |2 gtt | |
| 650 | 7 | |a Prijzen (economie) |2 gtt | |
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Datensatz im Suchindex
| _version_ | 1804133366387179520 |
|---|---|
| adam_text | Contents Preface xv
List of symbols xvii
PARTI PRELIMINARIES 1
1 Introduction 3
2 Some Prototype Models 7
2.1 Optimal price policy of a monopolist 7
2.2 The Black Scholes Option pricing model 8
2.3 Pricing American options 10
2.4 Multi asset options with stochastic correlation 12
2.5 The steady state distribution of the Vasicek interest rate process 14
2.6 Notes 16
3 The Conventional Approach: Finite Differences 17
3.1 General considerations for numerical computations 17
3.1.1 Evaluation criteria 17
3.1.2 Turning unbounded domains into bounded domains 18
3.2 Ordinary initial value problems 22
3.2.1 Basic concepts 22
3.2.2 Euler s method 23
3.2.3 Taylor methods 28
3.2.4 Runge Kutta methods 30
3.2.5 The backward Euler method 33
3.2.6 The Crank Nicolson method 35
3.2.7 Predictor corrector methods 36
3.2.8 Adaptive techniques 38
3.2.9 Methods for Systems of equations 39
x Contents 3.3 Ordinary two point boundary value problems 46
3.3.1 Introductory remarks 46
3.3.2 Finite difference methods 46
3.3.3 Shooting methods 49
3.4 Initial boundary value problems 49
3.4.1 The explicit scheme 49
3.4.2 The implicit scheme 51
3.4.3 The Crank Nicolson method 52
3.4.4 Integrating early exercise 52
3.5 Notes 53
PART II FINITE ELEMENTS 55
4 Static 1D Problems 57
4.1 Basic features of finite element methods 57
4.2 The method of weighted residuals one element Solutions 57
4.3 The Ritz variational method 72
4.4 The method of weighted residuals a more general view 74
4.5 Multi element Solutions 75
4.5.1 The Galerkin method with linear elements 76
4.5.2 The Galerkin method with quadratic trial functions 89
4.5.3 The collocation method with cubic Hermite trial functions 93
4.6 Case studies 99
4.6.1 The Evans model of a monopolist 99
4.6.2 First exit time of a geometric Brownian motion 99
4.6.3 The steady state distribution of the Ornstein Uhlenbeck
process 101
4.6.4 Convection dominated problems 102
4.7 Convergence 106
4.8 Notes 107
5 Dynamic 1D Problems 109
5.1 Derivation of element equations 109
5.1.1 The Galerkin method 109
5.1.2 The collocation method 114
5.2 Case studies 115
5.2.1 Piain vanilla options 115
5.2.2 Hedging parameters 123
5.2.3 Various exotic options 132
5.2.4 The CEV model 142
5.2.5 Some practicalities: Dividends and settlement 150
6 Static 2D Problems 161
6.1 Introduction and overview 161
6.2 Construction of a mesh 162
6.3 The Galerkin method 165
6.3.1 The Galerkin method with linear elements (triangles) 165
6.3.2 The Galerkin method with linear elements (rectangular elements) 187
Contents xi
6.4 Case studies 187
6.4.1 Brownian motion leaving a disk 187
6.4.2 Ritz revisited 188
6.4.3 First exit time in a two asset pricing problem 191
6.5 Notes 194
7 Dynamic 2D Problems 195
7.1 Derivation of element equations 195
7.2 Case studies 197
7.2.1 Various rainbow options 197
7.2.2 Modeling volatility as a risk factor 203
8 Static 3D Problems 207
8.1 Derivation of element equations: The collocation method 207
8.2 Case studies 209
8.2.1 First exit time of purely Brownian motion 209
8.2.2 First exit time of geometric Brownian motion 211
8.3 Notes 213
9 Dynamic 3D Problems 215
9.1 Derivation of element equations: The collocation method 215
9.2 Case studies 216
9.2.1 Pricing and hedging a basket Option 216
9.2.2 Basket options with barriers 218
10 Nonlinear Problems 221
10.1 Introduction 221
10.2 Case studies 223
10.2.1 Penalty methods 223
10.2.2 American options 223
10.2.3 Passport options 227
10.2.4 Uncertain volatility: Best and worst cases 240
10.2.5 Worst case pricing of rainbow options 248
10.3 Notes 252
PART III OUTLOOK 253
11 Future Directions of Research 255
PART IV APPENDICES 257
A Some Useful Results from Analysis 259
A. 1 Important theorems from calculus 259
A. 1.1 Various concepts of continuity 259
A.1.2 Taylor s theorem 260
A.1.3 Mean value theorems 262
A.1.4 Various theorems 263
xii Contents A.2 Basic numerical tools 264
A.2.1 Quadrature 264
A.2.2 Solving nonlinear equations 268
A3 Differential equations 270
A.3.1 Definition and classification 270
A.3.2 Ordinary initial value problems 272
A.3.3 Ordinary boundary value problems 279
A.3.4 Partial differential equations of second order 285
A.3.5 Parabolic problems 287
A.3.6 EllipticPDEs 295
A.3.7 Hyperbolic PDEs 296
A.3.8 Hyperbolic conservation laws 297
A.4 Calculus of variations 299
B Some Useful Results from Stochastics 305
B.l Some important distributions 305
B.l.l The univariate normal distribution 305
B.l.2 The bivariate normal distribution 305
B.1.3 The multivariate normal distribution 307
B.l.4 The lognormal distribution 307
B.1.5 The T distribution 307
B.l.6 The central x2 distribution 309
B.1.7 The noncentral x2 distribution 310
B.2 Some important processes 310
B.2.1 Basic concepts 310
B.2.2 Wiener process 312
B.2.3 Brownian motion with drift 313
B.2.4 Geometrie Brownian motion 313
B.2.5 Itö process 314
B.2.6 Ornstein Uhlenbeck process 314
B.2.7 A process for commodities 314
B.3 Results 314
B.3.1 The transition probability density funetion 314
B.3.2 The backward Kolmogorov equation 315
B.3.3 The forward Kolmogorov equation 316
B.3.4 Steady state distributions 321
B.3.5 First exit times 322
B.3.6 Itö s lemma 325
B.4 Notes 326
C Some Useful Results from Linear Algebra 329
C.l Some basic facts 329
C.2 Errors and norms 331
C.3 Ill conditioning 333
Contents xiii
C.4 Solving linear algebraic Systems 333
C.5 Notes 339
D A Quick Introduction to PDE2D 341
References 343
Index 351
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:34Z |
| institution | BVB |
| language | English |
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| physical | XVIII, 360 S. Ill., graph. Darst. |
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| publisher | Wiley |
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| series2 | Wiley finance series |
| spelling | Topper, Jürgen 1967- Verfasser (DE-588)120683350 aut Financial engineering with finite elements Jürgen Topper Chichester [u.a.] Wiley 2005 XVIII, 360 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Eindige wiskunde gtt Ingénierie financière rasuqam Modèle économétrique rasuqam Méthode des éléments finis rasuqam Opties gtt Prijzen (economie) gtt Ökonometrisches Modell Financial engineering Econometric models Finite element method Financial Engineering (DE-588)4208404-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Financial Engineering (DE-588)4208404-0 s Finite-Elemente-Methode (DE-588)4017233-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013175828&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topper, Jürgen 1967- Financial engineering with finite elements Eindige wiskunde gtt Ingénierie financière rasuqam Modèle économétrique rasuqam Méthode des éléments finis rasuqam Opties gtt Prijzen (economie) gtt Ökonometrisches Modell Financial engineering Econometric models Finite element method Financial Engineering (DE-588)4208404-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4208404-0 (DE-588)4017233-8 |
| title | Financial engineering with finite elements |
| title_auth | Financial engineering with finite elements |
| title_exact_search | Financial engineering with finite elements |
| title_full | Financial engineering with finite elements Jürgen Topper |
| title_fullStr | Financial engineering with finite elements Jürgen Topper |
| title_full_unstemmed | Financial engineering with finite elements Jürgen Topper |
| title_short | Financial engineering with finite elements |
| title_sort | financial engineering with finite elements |
| topic | Eindige wiskunde gtt Ingénierie financière rasuqam Modèle économétrique rasuqam Méthode des éléments finis rasuqam Opties gtt Prijzen (economie) gtt Ökonometrisches Modell Financial engineering Econometric models Finite element method Financial Engineering (DE-588)4208404-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Eindige wiskunde Ingénierie financière Modèle économétrique Méthode des éléments finis Opties Prijzen (economie) Ökonometrisches Modell Financial engineering Econometric models Finite element method Financial Engineering Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013175828&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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