The concepts and practice of mathematical finance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Mathematics, finance, and risk
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | XVI, 473 S. graph. Darst. |
| ISBN: | 0521823552 |
Internformat
MARC
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| 245 | 1 | 0 | |a The concepts and practice of mathematical finance |c Mark S. Joshi |
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| 264 | 1 | |a Cambridge, U.K. [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XVI, 473 S. |b graph. Darst. | ||
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| 650 | 4 | |a Gestion du risque - Modèles mathématiques | |
| 650 | 4 | |a Instruments dérivés (Finances) - Prix - Modèles mathématiques | |
| 650 | 4 | |a Investissements - Mathématiques | |
| 650 | 7 | |a Matemática financeira |2 larpcal | |
| 650 | 7 | |a Opties |2 gtt | |
| 650 | 4 | |a Options (Finances) - Prix - Modèles mathématiques | |
| 650 | 7 | |a Portfolio-analyse |2 gtt | |
| 650 | 7 | |a Prijzen (economie) |2 gtt | |
| 650 | 7 | |a Rente |2 gtt | |
| 650 | 7 | |a Risk management |2 gtt | |
| 650 | 4 | |a Taux d'intérêt - Modèles mathématiques | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities -- Prices -- Mathematical models | |
| 650 | 4 | |a Options (Finance) -- Prices -- Mathematical models | |
| 650 | 4 | |a Interest rates -- Mathematical models | |
| 650 | 4 | |a Finance -- Mathematical models | |
| 650 | 4 | |a Investments -- Mathematics | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface page xiii
Acknowledgements xvii
1 Risk 1
1.1 What is risk? 1
1.2 Market efficiency 2
1.3 The most important assets 4
1.4 Diversifiable risk 8
1.5 The use of options 9
1.6 Classifying market participants 12
1.7 Key points 13
1.8 Further reading 13
1.9 Exercises 14
2 Pricing methodologies and arbitrage 15
2.1 Some possible methodologies 15
2.2 Delta hedging 17
2.3 What is arbitrage? 18
2.4 The assumptions of mathematical finance 19
2.5 An example of arbitrage free pricing 21
2.6 The time value of money 23
2.7 Mathematically defining arbitrage 26
2.8 Using arbitrage to bound option prices 28
2.9 Conclusion 38
2.10 Key points 38
2.11 Further reading 38
2.12 Exercises 39
3 Trees and option pricing 41
3.1 A two world universe 41
3.2 A three state model 46
vii
viii Contents
3.3 Multiple time steps 47
3.4 Many time steps 50
3.5 A normal model 52
3.6 Putting interest rates in 55
3.7 A log normal model 57
3.8 Consequences 64
3.9 Summary 66
3.10 Key points 67
3.11 Further reading 67
3.12 Exercises 68
4 Practicalities 70
4.1 Introduction 70
4.2 Trading volatility 70
4.3 Smiles 71
4.4 The Greeks 74
4.5 Alternate models 81
4.6 Transaction costs 86
4.7 Key points 87
4.8 Further reading 87
4.9 Exercises 88
5 The Ito calculus 89
5.1 Introduction 89
5.2 Brownian motion 89
5.3 Stochastic processes 92
5.4 Ito s lemma 96
5.5 Applying Ito s lemma 101
5.6 An informal derivation of the Black Scholes equation 104
5.7 Justifying the derivation 105
5.8 Solving the Black Scholes equation 109
5.9 Dividend paying assets 111
5.10 Key points 113
5.11 Further reading 114
5.12 Exercises 114
6 Risk neutrality and martingale measures 117
6.1 Plan 117
6.2 Introduction 118
6.3 The existence of risk neutral measures 119
6.4 The concept of information 130
6.5 Discrete martingale pricing 135
6.6 Continuous martingales and nitrations 144
6.7 Identifying continuous martingales 146
Contents ix
6.8 Continuous martingale pricing 147
6.9 Equivalence to the PDE method 151
6.10 Hedging 152
6.11 Time dependent parameters 154
6.12 Completeness and uniqueness 156
6.13 Changing numeraire 157
6.14 Dividend paying assets 159
6.15 Working with the forward 159
6.16 Key points 163
6.17 Further reading 163
6.18 Exercises 164
7 The practical pricing of a European option 166
7.1 Introduction 166
7.2 Analytic formulae 167
7.3 Trees 168
7.4 Numerical integration 173
7.5 Monte Carlo 176
7.6 PDE methods 181
7.7 Replication 181
7.8 Key points 183
7.9 Further reading 184
7.10 Exercises 184
8 Continuous barrier options 186
8.1 Introduction 186
8.2 The PDE pricing of continuous barrier options 189
8.3 Expectation pricing of continuous barrier options 191
8.4 The reflection principle 192
8.5 Girsanov s theorem revisited 194
8.6 Joint distribution 197
8.7 Pricing continuous barriers by expectation 200
8.8 American digital options 203
8.9 Key points 204
8.10 Further reading 204
8.11 Exercises 205
9 Multi look exotic options 206
9.1 Introduction 206
9.2 Risk neutral pricing for path dependent options 207
9.3 Weak path dependence 209
9.4 Path generation and dimensionality reduction 210
9.5 Moment matching 215
9.6 Trees, PDEs and Asian options 217
x Contents
9.7 Practical issues in pricing multi look options 218
9.8 Greeks of multi look options 220
9.9 Key points 223
9.10 Further reading 223
9.11 Exercises 224
10 Static replication 225
10.1 Introduction 225
10.2 Continuous barrier options 226
10.3 Discrete barriers 229
10.4 Path dependent exotic options 231
10.5 The up and in put with barrier at strike 233
10.6 Put call symmetry 234
10.7 Conclusion and further reading 238
10.8 Key points 240
10.9 Exercises 241
11 Multiple sources of risk 242
11.1 Introduction 242
11.2 Higher dimensional Brownian motions 243
11.3 The higher dimensional Ito calculus 245
11.4 The higher dimensional Girsanov theorem 248
11.5 Practical pricing 253
11.6 The Margrabe option 254
11.7 Quanto options 256
11.8 Higher dimensional trees 258
11.9 Key points 261
11.10 Further reading 262
11.11 Exercises 262
12 Options with early exercise features 263
12.1 Introduction 263
12.2 The tree approach 266
12.3 The PDE approach to American options 267
12.4 American options by replication 270
12.5 American options by Monte Carlo 272
12.6 Upper bounds by Monte Carlo 275
12.7 Key points 276
12.8 Further reading 277
12.9 Exercises 277
13 Interest rate derivatives 279
13.1 Introduction 279
13.2 The simplest instruments 281
Contents xi
13.3 Caplets and swaptions 288
13.4 Curves and more curves 293
13.5 Key points 295
13.6 Further reading 296
13.7 Exercises 296
14 The pricing of exotic interest rate derivatives 298
14.1 Introduction 298
14.2 Decomposing an instrument into forward rates 302
14.3 Computing the drift of a forward rate 309
14.4 The instantaneous volatility curves 312
14.5 The instantaneous correlations between forward rates 315
14.6 Doing the simulation 316
14.7 Rapid pricing of swaptions in a BGM model 320
14.8 Automatic calibration to co terminal swaptions 321
14.9 Lower bounds for Bermudan swaptions 324
14.10 Upper bounds for Bermudan swaptions 328
14.11 Factor reduction and Bermudan swaptions 331
14.12 Interest rate smiles 334
14.13 Key points 337
14.14 Further reading 337
14.15 Exercises 338
15 Incomplete markets and jump diffusion processes 340
15.1 Introduction 340
15.2 Modelling jumps with a tree 341
15.3 Modelling jumps in a continuous framework 343
15.4 Market incompleteness 346
15.5 Super and sub replication 348
15.6 Choosing the measure and hedging exotic options 354
15.7 Matching the market 357
15.8 Pricing exotic options using jump diffusion models 358
15.9 Does the model matter? 360
15.10 Log type models 362
15.11 Key points 364
15.12 Further reading 365
15.13 Exercises 366
16 Stochastic volatility 368
16.1 Introduction 368
16.2 Risk neutral pricing with stochastic volatility models 369
16.3 Monte Carlo and stochastic volatility 370
16.4 Hedging issues 372
xii Contents
16.5 PDE pricing and transform methods 373
16.6 Stochastic volatility smiles 377
16.7 Pricing exotic options 377
16.8 Key points 378
16.9 Further reading 378
16.10 Exercises 379
17 Variance Gamma models 380
17.1 The Variance Gamma process 380
17.2 Pricing options with Variance Gamma models 383
17.3 Pricing exotic options with Variance Gamma models 386
17.4 Deriving the properties 387
17.5 Key points 389
17.6 Further reading 389
17.7 Exercises 390
18 Smile dynamics and the pricing of exotic options 391
18.1 Introduction 391
18.2 Smile dynamics in the market 392
18.3 Dynamics implied by models 394
18.4 Matching the smile to the model 400
18.5 Hedging 403
18.6 Matching the model to the product 404
18.7 Key points 407
18.8 Further reading 407
Appendix A Financial and mathematical jargon 409
Appendix B Computer projects 414
Appendix C Elements of probability theory 438
Appendix D Hints and answers to exercises 449
References 462
Index 468
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Joshi, Mark S. 1969- Verfasser (DE-588)12898693X aut The concepts and practice of mathematical finance Mark S. Joshi 1. publ. Cambridge, U.K. [u.a.] Cambridge Univ. Press 2003 XVI, 473 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics, finance, and risk Finances - Modèles mathématiques Gestion du risque - Modèles mathématiques Instruments dérivés (Finances) - Prix - Modèles mathématiques Investissements - Mathématiques Matemática financeira larpcal Opties gtt Options (Finances) - Prix - Modèles mathématiques Portfolio-analyse gtt Prijzen (economie) gtt Rente gtt Risk management gtt Taux d'intérêt - Modèles mathématiques Wiskundige modellen gtt Mathematik Mathematisches Modell Derivative securities -- Prices -- Mathematical models Options (Finance) -- Prices -- Mathematical models Interest rates -- Mathematical models Finance -- Mathematical models Investments -- Mathematics Risk management -- Mathematical models Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 http://www.loc.gov/catdir/description/cam032/2003055594.html Publisher description http://www.loc.gov/catdir/toc/cam032/2003055594.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010479281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joshi, Mark S. 1969- The concepts and practice of mathematical finance Finances - Modèles mathématiques Gestion du risque - Modèles mathématiques Instruments dérivés (Finances) - Prix - Modèles mathématiques Investissements - Mathématiques Matemática financeira larpcal Opties gtt Options (Finances) - Prix - Modèles mathématiques Portfolio-analyse gtt Prijzen (economie) gtt Rente gtt Risk management gtt Taux d'intérêt - Modèles mathématiques Wiskundige modellen gtt Mathematik Mathematisches Modell Derivative securities -- Prices -- Mathematical models Options (Finance) -- Prices -- Mathematical models Interest rates -- Mathematical models Finance -- Mathematical models Investments -- Mathematics Risk management -- Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
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| title | The concepts and practice of mathematical finance |
| title_auth | The concepts and practice of mathematical finance |
| title_exact_search | The concepts and practice of mathematical finance |
| title_full | The concepts and practice of mathematical finance Mark S. Joshi |
| title_fullStr | The concepts and practice of mathematical finance Mark S. Joshi |
| title_full_unstemmed | The concepts and practice of mathematical finance Mark S. Joshi |
| title_short | The concepts and practice of mathematical finance |
| title_sort | the concepts and practice of mathematical finance |
| topic | Finances - Modèles mathématiques Gestion du risque - Modèles mathématiques Instruments dérivés (Finances) - Prix - Modèles mathématiques Investissements - Mathématiques Matemática financeira larpcal Opties gtt Options (Finances) - Prix - Modèles mathématiques Portfolio-analyse gtt Prijzen (economie) gtt Rente gtt Risk management gtt Taux d'intérêt - Modèles mathématiques Wiskundige modellen gtt Mathematik Mathematisches Modell Derivative securities -- Prices -- Mathematical models Options (Finance) -- Prices -- Mathematical models Interest rates -- Mathematical models Finance -- Mathematical models Investments -- Mathematics Risk management -- Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
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