Arbitrage theory in continuous time:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford <<[u.a.]>>
Oxford Univ. Pr.
2004
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 311 S. graph. Darst. |
| ISBN: | 0198775180 |
Internformat
MARC
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| 245 | 1 | 0 | |a Arbitrage theory in continuous time |c Tomas Björk |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Arbitrage theory in continuous time
Autor: Björk, Tomas
Jahr: 2004
CONTENTS
Introduction 1
1.1 Problem Formulation 1
The Binomial Model 5
2.1 The One Period Model 5
2.1.1 Model Description 5
2.1.2 Portfolios and Arbitrage 6
2.1.3 Contingent Claims 9
2.1.4 Risk Neutral Valuation 11
2.2 The Multiperiod Model 15
2.2.1 Portfolios and Arbitrage 15
2.2.2 Contingent Claims 17
25
25
26
26
27
30
31
34
35
36
36
38
40
42
45
50
53
55
59
61
Differential Equations 62
5.1 Stochastic Differential Equations 62
5.2 Geometric Brownian Motion 63
5.3 The Linear SDE 66
5.4 The Infinitesimal Operator 67
2.3 Exercises
2.4 Notes
A More General One Period Model
3.1 The Model
3.2 Absence of Arbitrage
3.3 Martingale Pricing
3.4 Completeness
3.5 Stochastic Discount Factors
3.6 Exercises
Stochastic Integrals
4.1 Introduction
4.2 Information
4.3 Stochastic Integrals
4.4 Martingales
4.5 Stochastic Calculus and the ltd Formula
4.6 Examples
4.7 The Multidimensional ltd Formula
4.8 Correlated Wiener Processes
4.9 Exercises
4.10 Notes
CONTENTS
5.5 Partial Differential Equations 68
5.6 The Kolmogorov Equations 72
5.7 Exercises 75
5.8 Notes 79
6 Portfolio Dynamics 80
6.1 Introduction 80
6.2 Self-financing Portfolios 83
6.3 Dividends 85
6.4 Exercise 87
7 Arbitrage Pricing 88
7.1 Introduction 88
7.2 Contingent Claims and Arbitrage 89
7.3 The Black-Scholes Equation 94
7.4 Risk Neutral Valuation 98
7.5 The Black-Scholes Formula 100
7.6 Options on Futures 102
7.6.1 Forward Contracts 102
7.6.2 Futures Contracts and the Black Formula 103
7.7 Volatility 104
7.7.1 Historic Volatility 105
7.7.2 Implied Volatility 106
7.8 American options 106
7.9 Exercises 108
7.10 Notes 110
8 Completeness and Hedging 111
8.1 Introduction 111
8.2 Completeness in the Black-Scholes Model 112
8.3 Completeness?Absence of Arbitrage 117
8.4 Exercises 118
8.5 Notes 120
9 Parity Relations and Delta Hedging 121
9.1 Parity Relations 121
9.2 The Greeks 123
9.3 Delta and Gamma Hedging 126
9.4 Exercises 130
10 The Martingale Approach to Arbitrage Theory* 133
10.1 The Case with Zero Interest Rate 133
10.2 Absence of Arbitrage 136
10.2.1 A Rough Sketch of the Proof 137
10.2.2 Precise Results 140
CONTENTS
10.3 The General Case 142
10.4 Completeness 145
10.5 Martingale Pricing 147
10.6 Stochastic Discount Factors 149
10.7 Summary for the Working Economist 150
10.8 Notes 153
11 The Mathematics of the Martingale Approach* 154
11.1 Stochastic Integral Representations 154
11.2 The Girsanov Theorem: Heuristics 158
11.3 The Girsanov Theorem 160
11.4 The Converse of the Girsanov Theorem 164
11.5 Girsanov Transformations and Stochastic Differentials 164
11.6 Maximum Likelihood Estimation 165
11.7 Exercises 167
11.8 Notes 168
12 Black-Scholes from a Martingale Point of View* 169
12.1 Absence of Arbitrage 169
12.2 Pricing 171
12.3 Completeness 172
13 Multidimensional Models: Classical Approach 175
13.1 Introduction 175
177
183
184
188
191
14 Multidimensional Models: Martingale Approach* 192
193
195
196
198
199
200
201
201
204
204
15 Incomplete Markets 205
15.1 Introduction 205
15.2 A Scalar Nonpriced Underlying Asset 205
15.3 The Multidimensional Case 214
13.2 Pricing
13.3 Risk Neutral Valuation
13.4 Reducing the State Space
13.5 Hedging
13.6 Exercises
Mull tidimensional Models: Martingale Approach*
14.1 Absence of Arbitrage
14.2 Completeness
14.3 Hedging
14.4 Pricing
14.5 Markovian Models and PDEs
14.6 Market Prices of Risk
14.7 Stochastic Discount Factors
14.8 The Hansen-Jagannathan Bounds
14.9 Exercises
14.10 Notes
CONTENTS
15.4 A Stochastic Short Rate
15.5 The Martingale Approach*
15.6 Summing Up
15.7 Exercises
15.8 Notes
218
219
220
223
224
16 Dividends 225
16.1 Discrete Dividends 225
16.1.1 Price Dynamics and Dividend Structure 225
16.1.2 Pricing Contingent Claims 226
16.2 Continuous Dividends 231
16.2.1 Continuous Dividend Yield 232
16.2.2 The General Case 235
16.3 Exercises 237
17 Currency Derivatives 239
17.1 Pure Currency Contracts 239
17.2 Domestic and Foreign Equity Markets 242
17.3 Domestic and Foreign Market Prices of Risk 248
17.4 Exercises 252
17.5 Notes 253
18 Barrier Options 254
18.1 Mathematical Background 254
18.2 Out Contracts 256
18.2.1 Down-and-Out Contracts 256
18.2.2 Up-and-Out Contracts 260
18.2.3 Examples 261
18.3 In Contracts 265
18.4 Ladders 267
18.5 Lookbacks 268
18.6 Exercises 270
18.7 Notes 270
19 Stochastic Optimal Control 271
19.1 An Example 271
19.2 The Formal Problem 272
19.3 The Hamilton-Jacobi-Bellman Equation 275
19.4 Handling the HJB Equation 283
19.5 The Linear Regulator 284
19.6 Optimal Consumption and Investment 286
19.6.1 A Generalization 286
19.6.2 Optimal Consumption 288
19.7 The Mutual Fund Theorems 291
19.7.1 The Case with No Risk Free Asset 291
19.7.2 The Case with a Risk Free Asset 295
CONTENTS
19.8 Exercises 297
19.9 Notes 301
20 Bonds and Interest Rates 302
20.1 Zero Coupon Bonds 302
20.2 Interest Rates 303
20.2.1 Definitions 303
20.2.2 Relations between d/(t, T), dp(t, T), and dr{t) 305
20.2.3 An Alternative View of the Money Account 308
20.3 Coupon Bonds, Swaps, and Yields 309
20.3.1 Fixed Coupon Bonds 310
20.3.2 Floating Rate Bonds 310
20.3.3 Interest Rate Swaps 312
20.3.4 Yield and Duration 313
20.4 Exercises 314
20.5 Notes 315
21 Short Rate Models 316
21.1 Generalities 316
21.2 The Term Structure Equation 319
21.3 Exercises 324
21.4 Notes 325
22 Martingale Models for the Short Rate 326
22.1 Q-dynamics 326
22.2 Inversion of the Yield Curve 327
22.3 Affine Term Structures 329
22.3.1 Definition and Existence 329
22.3.2 A Probabilistic Discussion 331
22.4 Some Standard Models 333
22.4.1 The Vasicek Model 333
22.4.2 The Ho-Lee Model 334
22.4.3 The CIR Model 335
22.4.4 The Hull-White Model 335
22.5 Exercises 338
22.6 Notes 339
23 Forward Rate Models 340
23.1 The Heath-Jarrow-Morton Framework 340
23.2 Martingale Modeling 342
23.3 The Musiela Parameterization 344
23.4 Exercises 345
23.5 Notes 347
24 Change of Numeraire* 348
24.1 Introduction 348
CONTENTS
24.2 Generalities 349
24.3 Changing the Numeraire 353
24.4 Forward Measures 355
24.4.1 Using the T-bond as Numeraire 355
24.4.2 An Expectation Hypothesis 357
24.5 A General Option Pricing Formula 358
24.6 The Hull-White Model 361
24.7 The General Gaussian Model 363
24.8 Caps and Floors 365
24.9 Exercises 366
24.10 Notes 366
25 LIBOR and Swap Market Models 368
25.1 Caps: Definition and Market Practice 369
25.2 The LIBOR Market Model 371
25.3 Pricing Caps in the LIBOR Model 372
25.4 Terminal Measure Dynamics and Existence 373
25.5 Calibration and Simulation 376
25.6 The Discrete Savings Account 378
25.7 Swaps 379
25.8 Swaptions: Definition and Market Practice 381
25.9 The Swap Market Models 382
25.10 Pricing Swaptions in the Swap Market Model 383
25.11 Drift Conditions for the Regular Swap Market Model 384
25.12 Concluding Comment 387
25.13 Exercises 388
25.14 Notes 388
26 Forwards and Futures 389
26.1 Forward Contracts 389
26.2 Futures Contracts 391
26.3 Exercises 394
26.4 Notes 394
A Measure and Integration* 395
A.l Sets and Mappings 395
A.2 Measures and Sigma Algebras 397
A.3 Integration 399
A.4 Sigma-Algebras and Partitions 404
A.5 Sets of Measure Zero 405
A.6 The LP Spaces 406
A.7 Hilbert Spaces 407
A.8 Sigma-Algebras and Generators 410
A.9 Product measures 414
A. 10 The Lebesgue Integral 415
contents
A. 11 The Radon-Nikodym Theorem 416
A.12 Exercises 419
A.13 Notes 421
B Probability Theory 422
B.l Random Variables and Processes 422
B.2 Partitions and Information 425
B.3 Sigma-algebras and Information 427
B.4 Independence 430
B.5 Conditional Expectations 432
B.6 Equivalent Probability Measures 438
B.7 Exercises 441
B.8 Notes 442
C Martingales and Stopping Times* 443
C.l Martingales 443
C.2 Discrete Stochastic Integrals 446
C.3 Likelihood Processes 447
C.4 Stopping Times 448
C.5 Exercises 451
References 453
Index 461
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:01:11Z |
| institution | BVB |
| isbn | 0198775180 |
| language | English |
| lccn | 99185339 |
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| spelling | Björk, Tomas Verfasser aut Arbitrage theory in continuous time Tomas Björk 2. ed. Oxford <<[u.a.]>> Oxford Univ. Pr. 2004 XII, 311 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Arbitrage (DE-588)4002820-3 gnd rswk-swf Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Arbitrage-Pricing-Theorie (DE-588)4112584-8 s Derivat Wertpapier (DE-588)4381572-8 s DE-604 Arbitrage (DE-588)4002820-3 s Ökonometrie (DE-588)4132280-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018488155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Björk, Tomas Arbitrage theory in continuous time Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4002820-3 (DE-588)4112584-8 (DE-588)4381572-8 (DE-588)4132280-0 |
| title | Arbitrage theory in continuous time |
| title_auth | Arbitrage theory in continuous time |
| title_exact_search | Arbitrage theory in continuous time |
| title_full | Arbitrage theory in continuous time Tomas Björk |
| title_fullStr | Arbitrage theory in continuous time Tomas Björk |
| title_full_unstemmed | Arbitrage theory in continuous time Tomas Björk |
| title_short | Arbitrage theory in continuous time |
| title_sort | arbitrage theory in continuous time |
| topic | Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Arbitrage Arbitrage-Pricing-Theorie Derivat Wertpapier Ökonometrie |
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