Arbitrage theory in continuous time:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
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Oxford [u.a.]
Oxford Univ. Press
2009
|
| Edition: | 3. ed., 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 525 S. graph. Darst. |
| ISBN: | 9780199574742 |
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MARC
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| 100 | 1 | |a Björk, Tomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Arbitrage theory in continuous time |c Tomas Björk |
| 250 | |a 3. ed., 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XX, 525 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Arbitrage Pricing |2 stw | |
| 650 | 7 | |a Theorie |2 stw | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Arbitrage |x Mathematical models | |
| 650 | 4 | |a Derivative securities |x Prices |x Mathematics | |
| 650 | 0 | 7 | |a Arbitrage |0 (DE-588)4002820-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804140753740365824 |
|---|---|
| adam_text | 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
32
34
35
38
39
40
40
42
44
46
49
54
57
59
63
65
Differential Equations
66
5.1
Stochastic Differential Equations
66
5.2
Geometric Brownian Motion
67
5.3
The Linear SDE 70
5.4
The Infinitesimal Operator
71
2.3
Exercises
2.4
Notes
A More General One Period Model
3.1
The Model
3.2
Absence of Arbitrage
3.3
Martingale Measures
3.4
Martingale Pricing
3.5
Completeness
3.6
Stochastic Discount Factors
3.7
Exercises
Stochastic Integrals
4.1
Introduction
4.2
Information
4.3
Stochastic Integrals
4.4
Martingales
4.5
Stochastic Calculus and the
Ito
Formula
4.6
Examples
4.7
The Multidimensional
Ito
Formula
4.8
Correlated Wiener Processes
4.9
Exercises
4.10
Notes
CONTENTS
5.5
Partial
Differential
Equations
72
5.6
The Kolmogorov Equations
76
5.7
Exercises
79
5.8
Notes 83
Portfolio Dynamics 84
6.1
Introduction 84
6.2
Self-financing Portfolios
87
6.3
Dividends 89
6.4
Exercises
91
10
Arbitrage
Pricing
92
7.1
Introduction
92
7.2
Contingent Claims and Arbitrage
93
7.3
The Black-Scholes Equation
98
7.4
Risk Neutral Valuation
102
7.5
The Black-Scholes Formula
104
7.6
Options on Futures
106
7.6.1
Forward Contracts
106
7.6.2
Futures Contracts and the Black Formula
107
7.7
Volatility
108
7.7.1
Historic Volatility
109
7.7.2
Implied Volatility
110
7.8
American Options
110
7.9
Exercises
112
7.10
Notes
114
Completeness and Hedging
115
8.1
Introduction
115
8.2
Completeness in the Black-Scholes Model
116
8.3
Completeness
—
Absence of Arbitrage
121
8.4
Exercises
122
8.5
Notes
124
Parity Relations and Delta Hedging
125
9.1
Parity Relations
125
9.2
The Greeks
127
9.3
Delta and Gamma Hedging
130
9.4
Exercises
134
The Martingale Approach to Arbitrage Theory*
137
10.1
The Case with Zero Interest Rate
137
10.2
Absence of Arbitrage
140
10.2.1
A Rough Sketch of the Proof
141
10.2.2
Precise Results
144
10.3
The General Case
146
CONTENTS
10.4
Completeness
149
10.5
Martingale Pricing
151
10.6
Stochastic Discount Factors
153
10.7
Summary for the Working Economist
154
10.8
Notes
156
11
The Mathematics of the Martingale Approach*
158
11.1
Stochastic Integral Representations
158
11.2
The Girsanov Theorem: Heuristics
162
11.3
The Girsanov Theorem
164
11.4
The Converse of the Girsanov Theorem
168
11.5
Girsanov Transformations and Stochastic Differentials
168
11.6
Maximum Likelihood Estimation
169
11.7
Exercises
171
11.8
Notes
172
12
Black-Scholes from a Martingale Point of View*
173
12.1
Absence of Arbitrage
173
12.2
Pricing
175
12.3
Completeness
176
13
Multidimensional Models: Classical Approach
179
13.1
Introduction
179
13.2
Pricing
181
13.3
Risk Neutral Valuation
187
13.4
Reducing the State Space
188
13.5
Hedging
192
13.6
Exercises
195
14
Multidimensional Models: Martingale Approach*
196
14.1
Absence of Arbitrage
197
14.2
Completeness
199
14.3
Hedging
200
14.4
Pricing
202
14.5
Markovian Models and PDEs
203
14.6
Market Prices of Risk
204
14.7
Stochastic Discount Factors
205
14.8
The
Hansen-
Jagannathan Bounds
205
14.9
Exercises
208
14.10
Notes
208
15
Incomplete Markets
209
15.1
Introduction
209
15.2
A Scalar Nonpriced Underlying Asset
209
15.3
The Multidimensional Case
218
15.4
A Stochastic Short Rate
222
CONTENTS
16
17
18
19
15.5
The Martingale Approach*
223
15.6
Summing Up
224
15.7
Exercises
227
15.8
Notes
228
Dividends
229
16.1
Discrete Dividends
229
16.1.1
Price Dynamics and Dividend Structure
229
16.1.2
Pricing Contingent Claims
230
16.2
Continuous Dividends
235
16.2.1
Continuous Dividend Yield
236
16.2.2
The General Case
239
16.3
The Martingale Approach*
241
16.3.1
The Bank Account as Numeraire
242
16.3.2
An Arbitrary Numeraire
243
16.4
Exercises
246
Currency Derivatives
247
17.1
Pure Currency Contracts
247
17.2
Domestic and Foreign Equity Markets
250
17.3
Domestic and Foreign Market Prices of Risk
256
17.4
The Martingale Approach*
260
17.5
Exercises
263
17.6
Notes
264
Barrier Options
265
18.1
Mathematical Background
265
18.2
Out Contracts
267
18.2.1
Down-and-out Contracts
267
18.2.2
Up-and-out Contracts
271
18.2.3
Examples
272
18.3
In Contracts
276
18.4
Ladders
278
18.5
Lookbacks
279
18.6
Exercises
281
18.7
Notes
281
Stochastic Optimal Control
282
19.1
An Example
282
19.2
The Formal Problem
283
19.3
The Hamilton-JacobKBellman Equation
286
19.4
Handling the HJB Equation
294
19.5
The Linear Regulator
295
19.6
Optimal Consumption and Investment
297
19.6.1
A Generalization
297
19.6.2
Optimal Consumption
299
CONTENTS
19.7 The Mutual Fund Theorems 302
19.7.1
The Case with No Risk Free Asset
302
19.7.2
The Case with a Risk Free Asset
306
19.8
Exercises
308
19.9
Notes
312
20
The Martingale Approach to Optimal Investment*
313
20.1
Generalities
313
20.2
The Basic Idea
314
20.3
The Optimal Terminal Wealth
315
20.4
The Optimal Portfolio
317
20.5
Power Utility
318
20.5.1
The Optimal Terminal Wealth Profile
318
20.5.2
The Optimal Wealth Process
320
20.5.3
The Optimal Portfolio
321
20.6
The Markovian Case
322
20.7
Log Utility
324
20.8
Exponential Utility
324
20.8.1
The Optimal Terminal Wealth
325
20.8.2
The Optimal Wealth Process
325
20.8.3
The Optimal Portfolio
326
20.9
Exercises
327
20.10
Notes
328
21
Optimal Stopping Theory and American Options*
329
21.1
Introduction
329
21.2
Generalities
329
21.3
Some Simple Results
330
21.4
Discrete Time
331
21.4.1
The General Case
331
21.4.2
Markovian Models
335
21.4.3
Infinite Horizon
337
21.5
Continuous Time
339
21.5.1
General Theory
339
21.5.2
Diffusion Models
341
21.5.3
Connections to the General Theory
345
21.6
American Options
345
21.6.1
The American Call Without Dividends
345
21.6.2
The American Put Option
346
21.6.3
The Perpetual American Put
347
21.7
Exercises
348
21.8
Notes
349
22
Bonds and Interest Rates
350
22.1
Zero Coupon Bonds
350
xviii CONTENTS
22.2
Interest
Rates 351
22.2.1
Definitions
351
22.2.2
Relations between df(t,T), dp(t,T) and dr(t)
353
22.2.3
An Alternative View of the Money Account
356
22.3
Coupon Bonds, Swaps and Yields
357
22.3.1
Fixed Coupon Bonds
358
22.3.2
Floating Rate Bonds
358
22.3.3
Interest Rate Swaps
360
22.3.4
Yield and Duration
361
22.4
Exercises
362
22.5
Notes
363
23
Short Rate Models
364
23.1
Generalities
364
23.2
The Term Structure Equation
367
23.3
Exercises
372
23.4
Notes
373
24
Martingale Models for the Short Rate
374
24.1
Q-dynamics
374
24.2
Inversion of the Yield Curve
375
24.3 Affine
Term Structures
377
24.3.1
Definition and Existence
377
24.3.2
A Probabilistic Discussion
379
24.4
Some Standard Models
381
24.4.1
The
Vasiček
Model
381
24.4.2
The
Но
-Lee
Model
382
24.4.3
The
CIR
Model
383
24.4.4
The Hull-White Model
383
24.5
Exercises
386
24.6
Notes
387
25
Forward Rate Models
388
25.1
The Heath-Jarrow-Morton Framework
388
25.2
Martingale Modeling
390
25.3
The Musiela Parameterization
392
25.4
Exercises
393
25.5
Notes
395
26
Change of Numeraire*
396
26.1
Introduction
396
26.2
Generalities
397
26.3
Changing the Numeraire
401
26.4
Forward Measures
403
26.4.1
Using the
Т
-bond
as Numeraire
403
26.4.2
An Expectation Hypothesis
405
CONTENTS xix
26.5
A
General Option
Pricing Formula
406
26.6
The Hull-White
Model 409
26.7
The General Gaussian Model
411
26.8
Caps and Floors
413
26.9
The Numeraire Portfolio
414
26.10
Exercises
415
26.11
Notes
415
27
LIBOR
and Swap Market Models
417
27.1
Caps: Definition and Market Practice
418
27.2
The
LIBOR
Market Model
420
27.3
Pricing Caps in the
LIBOR
Model
421
27.4
Terminal Measure Dynamics and Existence
422
27.5
Calibration and Simulation
425
27.6
The Discrete Savings Account
427
27.7
Swaps
428
27.8
Swaptions: Definition and Market Practice
430
27.9
The Swap Market Models
431
27.10
Pricing Swaptions in the Swap Market Model
432
27.11
Drift Conditions for the Regular Swap Market Model
433
27.12
Concluding Comment
436
27.13
Exercises
436
27.14
Notes
437
28
Potentials and Positive Interest
438
28.1
Generalities
438
28.2
The Flesaker-Hughston Framework
439
28.3
Changing Base Measure
443
28.4
Decomposition of a Potential
444
28.5
The Markov Potential Approach of Rogers
445
28.6
Exercises
449
28.7
Notes
451
29
Forwards and Futures
452
29.1
Forward Contracts
452
29.2
Futures Contracts
454
29.3
Exercises
457
29.4
Notes
457
A Measure and Integration*
458
A.I Sets and Mappings
458
A.2 Measures and Sigma Algebras
460
A.3 Integration
462
A.4 Sigma-Algebras and Partitions
467
A.5 Sets of Measure Zero
468
A.6 The
W
Spaces
469
CONTENTS
A.7 Hubert Spaces 470
A.8
Sigma-Algebras and Generators
473
A.
9
Product Measures
476
A.10 The Lebesgue Integral
477
A.ll The Radon-Nikodym Theorem
478
A.
12
Exercises
482
A.13 Notes
483
В
Probability Theory*
484
B.I Random Variables and Processes
484
B.2 Partitions and Information
487
B.3 Sigma-algebras and Information
489
B.4 Independence
492
B.5 Conditional Expectations
493
B.6 Equivalent Probability Measures
500
B.7 Exercises
502
B.8 Notes
503
С
Martingales and Stopping Times*
504
C.I Martingales
504
C.2 Discrete Stochastic Integrals
507
C.3 Likelihood Processes
508
C.4 Stopping Times
509
C.5 Exercises
512
References
514
Index
521
|
| any_adam_object | 1 |
| author | Björk, Tomas |
| author_facet | Björk, Tomas |
| author_role | aut |
| author_sort | Björk, Tomas |
| author_variant | t b tb |
| building | Verbundindex |
| bvnumber | BV035805683 |
| callnumber-first | H - Social Science |
| callnumber-label | HG6024 |
| callnumber-raw | HG6024.A3 |
| callnumber-search | HG6024.A3 |
| callnumber-sort | HG 46024 A3 |
| callnumber-subject | HG - Finance |
| classification_rvk | QK 620 QK 622 SK 980 SK 990 |
| classification_tum | MAT 624f WIR 170f |
| ctrlnum | (OCoLC)423584121 (DE-599)BVBBV035805683 |
| dewey-full | 332.64/5 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64/5 |
| dewey-search | 332.64/5 |
| dewey-sort | 3332.64 15 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed., 1. publ. |
| format | Book |
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| id | DE-604.BV035805683 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:59Z |
| institution | BVB |
| isbn | 9780199574742 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018664717 |
| oclc_num | 423584121 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-91G DE-BY-TUM DE-11 DE-N2 DE-20 DE-188 DE-634 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-M347 DE-473 DE-BY-UBG |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-91G DE-BY-TUM DE-11 DE-N2 DE-20 DE-188 DE-634 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-M347 DE-473 DE-BY-UBG |
| physical | XX, 525 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Björk, Tomas Verfasser aut Arbitrage theory in continuous time Tomas Björk 3. ed., 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XX, 525 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Arbitrage Pricing stw Theorie stw Mathematik Mathematisches Modell Arbitrage Mathematical models Derivative securities Prices Mathematics 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 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018664717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Björk, Tomas Arbitrage theory in continuous time Arbitrage Pricing stw Theorie stw Mathematik Mathematisches Modell Arbitrage Mathematical models Derivative securities Prices Mathematics 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 Pricing stw Theorie stw Mathematik Mathematisches Modell Arbitrage Mathematical models Derivative securities Prices Mathematics 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 Pricing Theorie Mathematik Mathematisches Modell Arbitrage Mathematical models Derivative securities Prices Mathematics Arbitrage Arbitrage-Pricing-Theorie Derivat Wertpapier Ökonometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018664717&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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