Financial statistics and mathematical finance: methods, models and applications
"The book will focus on elementary financial calculus, statistical models for financial data, option pricing
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chichester, West Sussex, United Kingdom
Wiley
2012
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024887651&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | "The book will focus on elementary financial calculus, statistical models for financial data, option pricing |
| Umfang: | xiv, 415 Seiten |
| ISBN: | 9780470710586 |
Internformat
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 WIR 175f 2012 A 5861 |
|---|---|
| DE-BY-TUM_katkey | 1872889 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071465848 |
| _version_ | 1821933896789393409 |
| adam_text | Titel: Financial statistics and mathematical finance
Autor: Steland, Ansgar
Jahr: 2012
Contents
Preface xi
Acknowledgements xv
1 Elementary financial calculus 1
1.1 Motivating examples 1
1.2 Cashflows, interest rates, prices and returns 2
1.2.1 Bonds and the term structure of interest rates 5
1.2.2 Asset returns 6
1.2.3 Some basic models for asset prices 8
1.3 Elementary statistical analysis of returns 11
1.3.1 Measuring location 13
1.3.2 Measuring dispersion and risk 16
1.3.3 Measuring skewness and kurtosis 20
1.3.4 Estimation of the distribution 21
1.3.5 Testing for normality 27
1.4 Financial instruments 28
1.4.1 Contingent claims 28
1.4.2 Spot contracts and forwards 29
1.4.3 Futures contracts 29
1.4.4 Options 30
1.4.5 Barrier options 31
1.4.6 Financial engineering 32
1.5 A primer on option pricing 32
1.5.1 The no-arbitrage principle 32
1.5.2 Risk-neutral evaluation 33
1.5.3 Hedging and replication 36
1.5.4 Nonexistence of a risk-neutral measure 37
1.5.5 The Black-Scholes pricing formula 37
1.5.6 The Greeks 39
1.5.7 Calibration, implied volatility and the smile 41
1.5.8 Option prices and the risk-neutral density 41
1.6 Notes and further reading 43
References 43
Arbitrage theory for the one-period model 45
2.1 Definitions and preliminaries 45
2.2 Linear pricing measures 47
2.3 More on arbitrage 50
2.4 Separation theorems in W 53
2.5 No-arbitrage and martingale measures 56
2.6 Arbitrage-free pricing of contingent claims 65
2.7 Construction of martingale measures: general case 70
2.8 Complete financial markets 73
2.9 Notes and further reading 76
References 76
Financial models in discrete time 79
3.1 Adapted stochastic processes in discrete time 81
3.2 Martingales and martingale differences 85
3.2.1 The martingale transformation 91
3.2.2 Stopping times, optional sampling and a maximal inequality 93
3.2.3 Extensions to Rd 101
3.3 Stationarity 102
3.3.1 Weak and strict stationarity 102
3.4 Linear processes and ARM A models 111
3.4.1 Linear processes and the lag operator 111
3.4.2 Inversion 116
3.4.3 AR(p) and AR(oo) processes 119
3.4.4 ARMA processes 122
3.5 The frequency domain 124
3.5.1 The spectrum 124
3.5.2 The periodogram 126
3.6 Estimation of ARMA processes 132
3.7 (G)ARCH models 133
3.8 Long-memory series 139
3.8.1 Fractional differences 139
3.8.2 Fractionally integrated processes 144
3.9 Notes and further reading 144
References 145
Arbitrage theory for the multiperiod model 147
4.1 Definitions and preliminaries 148
4.2 Self-financing trading strategies 148
4.3 No-arbitrage and martingale measures 152
4.4 European claims on arbitrage-free markets 154
4.5 The martingale representation theorem in discrete time 159
4.6 The Cox-Ross-Rubinstein binomial model 160
4.7 The Black-Scholes formula 165
4.8 American options and contingent claims 171
4.8.1 Arbitrage-free pricing and the optimal exercise strategy 171
4.8.2 Pricing american options using binomial trees 174
4.9 Notes and further reading 175
References 175
Brownian motion and related processes in continuous time 177
5.1 Preliminaries 177
5.2 Brownian motion 181
5.2.1 Definition and basic properties 181
5.2.2 Brownian motion and the central limit theorem 188
5.2.3 Path properties 190
5.2.4 Brownian motion in higher dimensions 191
5.3 Continuity and differentiability 192
5.4 Self-similarity and fractional Brownian motion 193
5.5 Counting processes 195
5.5.1 The poisson process 195
5.5.2 The compound poisson process 196
5.6 Levy processes 199
5.7 Notes and further reading 201
References 201
Ito Calculus 203
6.1 Total and quadratic variation 204
6.2 Stochastic Stieltjes integration 208
6.3 The Ito integral 212
6.4 Quadratic covariation 225
6.5 Ito s formula 226
6.6 Ito processes 229
6.7 Diffusion processes and ergodicity 236
6.8 Numerical approximations and statistical estimation 238
6.9 Notes and further reading 239
References 240
The Black-Scholes model 241
7.1 The model and first properties 241
7.2 Girsanov s theorem 247
7.3 Equivalent martingale measure 251
7.4 Arbitrage-free pricing and hedging claims 252
7.5 The delta hedge 256
7.6 Time-dependent volatility 257
7.7 The generalized Black-Scholes model 259
7.8 Notes and further reading 261
References 262
Limit theory for discrete-time processes 263
8.1 Limit theorems for correlated time series 264
8.2 A regression model for financial time series 273
8.2.1 Least squares estimation 276
8.3 Limit theorems for martingale difference 278
8.4 Asymptotics 283
8.5 Density estimation and nonparametric regression 287
8.5.1 Multivariate density estimation 288
8.5.2 Nonparametric regression 295
8.6 The CLT for linear processes 302
8.7 Mixing processes 306
8.7.1 Mixing coefficients 306
8.7.2 Inequalities 308
8.8 Limit theorems for mixing processes 313
8.9 Notes and further reading 323
References 323
9 Special topics 325
9.1 Copulas - and the 2008 financial crisis 325
9.1.1 Copulas 326
9.1.2 The financial crisis 332
9.1.3 Models for credit defaults and CDOs 335
9.2 Local Linear nonparametric regression 338
9.2.1 Applications in finance: estimation of martingale measures and Ito
diffusions 339
9.2.2 Method and asymptotics 340
9.3 Change-point detection and monitoring 350
9.3.1 Offline detection 351
9.3.2 Online detection 359
9.4 Unit roots and random walk 363
9.4.1 The OLS estimator in the stationary AR(1) model 364
9.4.2 Nonparametric definitions for the degree of integration 368
9.4.3 The Dickey-Fuller test 370
9.4.4 Detecting unit roots and stationarity 373
9.5 Notes and further reading 381
References 382
Appendix A 385
A.l (Stochastic) Landau symbols 385
A.2 Bochner s lemma 387
A.3 Conditional expectation 387
A.4 Inequalities 388
A.5 Random series 389
A.6 Local martingales in discrete time 389
Appendix B Weak convergence and central limit theorems 391
B.l Convergence in distribution 391
B.2 Weak convergence 392
B.3 Prohorov s theorem 398
B.4 Sufficient criteria 399
B.5 More on Skorohod spaces 401
B.6 Central limit theorems for martingale differences 402
B.7 Functional central limit theorems 403
B.8 Strong approximations 405
References 407
Index 409
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| title | Financial statistics and mathematical finance methods, models and applications |
| title_auth | Financial statistics and mathematical finance methods, models and applications |
| title_exact_search | Financial statistics and mathematical finance methods, models and applications |
| title_full | Financial statistics and mathematical finance methods, models and applications Ansgar Steland, Institute for Statistics and Economics RWTH Aachen University, Germany |
| title_fullStr | Financial statistics and mathematical finance methods, models and applications Ansgar Steland, Institute for Statistics and Economics RWTH Aachen University, Germany |
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| title_short | Financial statistics and mathematical finance |
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| topic | BUSINESS & ECONOMICS / Econometrics bisacsh Business mathematics Calculus Wirtschaft Finanzstatistik (DE-588)4249667-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 WIR 175f 2012 A 5861
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |